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THE WORLD IN THE MODEL
During the last two centuries, the way economic science is done has
changed radically: it has become a social science based on mathematical
models in place of words. is book describes and analyses that change –
both historically and philosophically – using a series of case studies to illu-
minate the nature and the implications of this change. In format, it oers
a tourist guide to economics by focussing on specic models, explaining
how economists created them and how they reason with them. is book
will be of interest to economists and science studies scholars (historians,
sociologists, and philosophers of science). But it is not a technical book;
it is written for the intelligent person who wants to understand how eco-
nomics works from the inside out and particularly the ways in which
economic models have shaped our beliefs and the world we live in.
Mary S. Morgan, Fellow of the British Academy and Overseas Fellow of
the Royal Dutch Academy of Arts and Sciences, is Professor of History
and Philosophy of Economics at the London School of Economics and
the University of Amsterdam. She has published on a range of topics
in the history and philosophy of economics: from statistics to experi-
ments to narrative, and from nineteenth-century Social Darwinism to
game theory in the Cold War. Her previous books include e History
of Econometric Ideas (Cambridge University Press, 1990) and Models as
Mediators (Cambridge University Press, 1999, coedited with Margaret
Morrison). She has also edited collections on measurement, policy
making with models, and the development of probability thinking. In
the broader sphere, the collection of essays How Well Do Facts Travel?
(Cambridge University Press, 2011, coedited with Peter Howlett) marks
the conclusion of a major interdisciplinary team project on evidence
in the sciences and humanities. Professor Morgan is currently engaged
in the project “Re-thinking Case Studies Across the Social Sciences” as a
British Academy–Wolfson Research Professor, and (during 2010–11) as
a Davis Center Fellow at Princeton University.
e World in the Model
How Economists Work and ink
Mary S. Morgan
London School of Economics
and
University of Amsterdam
Cambridge, New York, Melbourne, Madrid, Cape Town,
Singapore, São Paulo, Delhi, Mexico City
Cambridge University Press
32 Avenue of the Americas, New York, NY 10013-2473, USA
www.cambridge.org
Information on this title: www.cambridge.org/9780521176194
© Mary S. Morgan 2012
is publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without the written
permission of Cambridge University Press.
First published 2012
Printed in the United States of America
A catalog record for this publication is available from the British Library.
Library of Congress Cataloging in Publication data
Morgan, Mary S.
e world in the model : how economists work and think / Mary S. Morgan.
p. cm.
Includes bibliographical references and index.
ISBN 978-1-107-00297-5 (hardback)
1. Economics–Mathematical models. 2. Economists. I. Title.
HB135.M667 2012
330.01′95195–dc23 2011018364
ISBN 978-1-107-00297-5 Hardback
ISBN 978-0-521-17619-4 Paperback
Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or
third-party Internet Web sites referred to in this publication and does not guarantee that any content
on such Web sites is, or will remain, accurate or appropriate.
For Charles, and for Dori
vii
List of Figures, Tables, and Boxes page xii
Preface xv
1 Modelling as a Method of Enquiry 1
: 1
1. From Laws to Models, From Words to Objects 1
2. e Naturalization of Modelling in Economics 6
3. Practical Reasoning Styles 14
3.i Modelling as a Style of Reasoning 14
3.ii Modelling as a Reasoning Style in Economics 17
: , 19
4. Making Models to Reason With: Forms, Rules, and Resources 19
4.i Giving Form 20
4.ii Becoming Formal 26
4.iii Reasoning Resources 27
5. Modelling as a Method of Enquiry: e World in the Model,
Models of the World 30
6. Conclusion 37
2 Model-Making: New Recipes, Ingredients, and Integration 44
1. Ricardo, e “Modern” Economist? 44
2. Ricardo, His Economy, and the Economy of His Day 47
2.i David Ricardo, Esq. 47
2.ii Economics Matters, Experimental Farming Matters 51
3. Constructing Ricardo’s Numerical Model Farm and Questions
of Distribution 56
3.i e Numbers in Ricardo’s Principles and Experimental
Accounts 58
3.ii e Spade-Husbandry Debate 69
4. Ricardo’s Model Farm and Model Farming 73
Contents
Contents
viii
4.i ree Model Farms in One 74
4.ii A Model Farm that Worked According to Ricardo’s
Economic Ideas 75
4.iii A Model of an Individual Farm in the Period 76
4.iv A Model Farm for the Whole Agricultural Sector 78
5. Model-Making: Creating New Recipes 79
5.i Ingredients 79
5.ii Fitting ings Together: Integration and Reasoning
Possibilities 81
Appendix 1: Numerical Argument in Ricardo’s 1815 Essay 83
3 Imagining and Imaging: Creating a New Model World 91
1. Introduction 91
2. Acts of Translation or a New Way of World-Making? 93
3. Making the Mathematical Economic World in Models 96
4. e Artist’s Space versus the Economist’s Space 98
5. e History of the Edgeworth Box Diagram – as Told by Itself 106
5.i Edgeworth’s Imagination and Image 107
5.ii Pareto’s Imagination and Images 115
6. e World Newly Made in the Model: Questions of
Representation? 118
6.i Visualization 118
6.ii Newness 126
7. Seeing the World in the Model 129
8. Conclusion 131
4 Character Making: Ideal Types, Idealization, and the Art
of Caricature 136
1. Introduction 136
2. Characterizing Economic Man: Classical Economists’ Homo
Economicus 138
3. Concept Forming: Weber’s Ideal Types and Menger’s Human
Economy 141
4. Symbolic Abstraction: Jevons’ Calculating Man 145
5. Exaggerating Qualities: Knight’s Slot-Machine Man 150
6. Making a Cartoon into a Role Model: Rational Economic Man 153
7. e Art of Caricature and Processes of Idealization 157
8. Model Man’s CV: De-Idealization and the Changing Roles
of Economic Man 164
5 Metaphors and Analogies: Choosing the World of the Model 172
1. From Metaphors to Analogical Models 172
2. e Newlyn-Phillips Machine 176
3. e Machine’s Inventors: Walter Newlyn and Bill Phillips 184
Contents ix
4. Inventing the Newlyn-Phillips Machine 187
Step 1: Phillips chooses the analogy for his supply/demand model
(early 1949) 189
Step 2: Newlyn designs the blueprint for a monetary circulation
machine (Easter 1949) 194
Step 3: Phillips and Newlyn build the prototype Machine
(Summer 1949) 200
5. Analogical Models and New ings 204
6 Questions and Stories: Capturing the Heart of Matters 217
1. Introduction 217
2. Stories to Shape Model Resources: Frisch’s Macro-Dynamic
Scheme 218
3. Questions and Stories Capturing Keynes’ General eory 221
3.i Modelling Keynes’ General eory: Meade 222
3.ii Reasoning with Models: e External and Internal
Dynamics 225
3.iii Modelling Keynes’ General eory: Samuelson 228
4. Finding New Dimensions and Telling New Stories 232
4.i Modelling Keynes’ General eory: Hicks 232
4.ii Demonstrations, Variety, and Fruitfulness 236
5. Capturing the Heart of the Matter with Narratives 239
5.i Narratives and Identity in the World of the Model 239
5.ii Model Narratives and Making Sense of the Economic
World 242
5.iii Narrative as a Testing Bed for Models 246
6. Where Next? 251
7 Model Experiments? 256
1. Introduction 256
2. Experiments in the World of the Model 258
2.i Mangoldt and Jenkin 259
2.ii Marshall 267
2.iii Conceptual Work: Dening Generic Categories 270
3. Models in ‘Laboratory’ Experiments 272
4. Comparison: Model Experiments and Laboratory Experiments 277
4.i Controls and Demonstration 277
4.ii Experimental Validity and e Inference Gap 282
5. Hybrids 288
5.i Virtually Experiments 288
5.ii e Status of Hybrids 292
6. Materials Matter: Surprise versus Confoundment 293
Contents
x
8 Simulation: Bringing a Microscope into Economics 301
1. e Birth of a New Technology 301
2. Simulation: Content and Context 304
3. Shubik and Simulation 307
3.i Martin Shubik’s History 307
3.ii Models, Simulated Environments, and Simulated
Behaviour 311
4. Guy Orcutt’s History and “Microsimulation” 315
5. Bringing a Microscope into Economics 320
5.i Introducing the Analogy 322
5.ii Matters of Scale and Kind 323
5.iii Specimens = Models 325
6. How Do Simulations Work as Microscopes? 327
7. e Observation–Inference Problem 331
8. Conclusion 336
9 Model Situations, Typical Cases, and Exemplary Narratives 344
1. Introduction 344
2. War Games 345
3. e Exemplary Narrative 348
3.i e Prisoner’s Dilemma: Collaborate or Defect? 348
3.ii e Economists’ Dilemma: Individual Rationality or
Invisible Hand? 351
4. e Commentator’s Dilemma: Fitting Together Situations,
Narratives, and Cases 357
4.i Reasoning about Situations 357
4.ii Explanatory Depth: e Roles of Narratives 361
4.iii Explanatory Breadth: Taxonomies, Kinds, and Cases 368
5. Conclusion 372
10 From the World in the Model to the Model in the World 378
1. Introduction 378
2. Models: e New Working Objects of Economics 380
2.i Model Worlds and Working Objects 380
2.ii Small Worlds, Miniature Worlds, Compressed Worlds? 384
3. e Work of Working Objects 387
3.i Materials for Describing and eorizing 387
3.ii “Abstract Typical Representations” and Model
Inductions 389
4. Modelling: e New Way of Practising Economics 393
4.i Assumptions in Practices 394
4.ii Network of Models 396
4.iii Community Matters 399
xii
Figures
1.1 Quesnay’s Ta bleau Économique (1767) page 4
1.2 e Prehistory of Models 7
1.3 First-Generation Models 9
1.4 Second-Generation Models 11
1.5 Models: e Variety of Forms 22
1.6 e Reasoning Resources in Models 29
1.7 e Phillips-Newlyn Hydraulic Machine 35
2.1 Gatcomb Park, Country Home of David Ricardo 49
2.2 Ricardo’s Model Farm Showing His Laws of Distribution 67
2.3 Newspaper Report of a Farming Experiment with Spade
Husbandry 71
2.4 Ricardo’s Table from His 1815 Essay 85
3.1 Humphrey’s Modern Version of the Edgeworth Box 92
3.2 e Artist’s Edgeworth Box by Koen Engelen 99
3.3 e Artist’s vs the Modern Economist’s Version of the Box 104
3.4 Historical Sequence of Original Box Diagrams Part I 110
3.5 Historical Sequence of Original Box Diagrams Part II 119
3.6 Matching the Modern Economist’s Diagrams to the Original
Box Diagrams 124
4.1 Menger’s Consumption Schedule 143
4.2 Jevons’ Utility Curve (1871) 147
4.3 Philipon’s Art of Caricature (1834) 161
5.1 Walter Newlyn Demonstrating the Prototype
Machine 1950 177
5.2 Drawing of the Mark II Machine 179
5.3 Cartoon of the Machine from Punch, 1953, by Rowland Emett 182
5.4 Bill Phillips’ Undergraduate Essay Diagrams and the Inspiration
from Boulding, 1948/9 190
Figures, Tables, and Boxes
Figures, Tables, and Boxes xiii
5.5 Bill Phillips’ Undergraduate Monetary-Circulation Diagram,
1948/9 193
5.6 Walter Newlyn’s Blueprint Design for the Machine, May 1949 197
5.7 Bill Phillips (le) and Walter Newlyn (right) Complete the First
Tank of the Machine, Summer 1949 202
5.8 Irving Fisher’s Arithmetical, Mechanical, and Accounting
Versions of His Monetary Balance 205
6.1 Samuelson’s Arithmetic Simulation 229
6.2 Samuelson’s Model Solution Graph 231
6.3 Hicks’ IS-LL “Little Apparatus” 235
7.1 Mangoldt’s Supply and Demand Model Experiments 260
7.2 Mangoldt’s Model Experiment for Complementary Goods 263
7.3 & 7.4 Fleeming Jenkin’s Supply and Demand Curve Experiments 265
7.5 Marshall’s Diagrammatic Model Experiments 269
7.6 Chamberlin’s “Real-Model” Experimental Results 274
7.7 Smith’s First Classroom Experimental Results with
the Market Model 276
8.1 Shubik’s 1960 Bibliography: Subject Map for
“Simulation” and “Gaming” 305
8.2 Shubik’s 1960 Bibliography: Subject Map for
“Monte Carlo” and “Systems” 306
8.3 Martin Shubik’s Experiences of Simulation 311
8.4 Guy Orcutt’s New Micro-Simulation Recipe 319
8.5 Slutsky’s Random Shock Simulation 332
9.1 Game eory in Tosca 346
Tables
Table 7.1 Model Experiments and Laboratory Experiments 279
Table 7.2 Model Experiments, Laboratory Experiments, and
Inferential Scope 283
Box
Box 9.1 Koertge’s Schema 358
xv
Science is messy. Historians write seamless accounts to make it comprehensible, and
in doing so, sometimes paper over the knots and holes in scientic life. Philosophers
provide sparely argued analyses of scientic method, and in doing so may avoid the
many awkward rubs of detail. is book is not such a monograph: It oers neither
a continuous historical narrative nor a fortied philosophy of modelling. Yet, its
ambition is to oer both a history of the naturalization of modelling in economics
and a naturalized philosophy of science for economics. And it does so in the spirit
of those many others who eschew smoothness.
So – this book is not a conventional monograph. It is a series of historical case
studies through which the philosophical commentary runs. I have long described
it as a kind of travel guide: I present, as three-star tourist sites, some of the best
known, and historically signicant, models in economics, and use each as the basis
upon which to fashion a philosophical commentary about the nature of modern
economics. But readers might also nd this book something like a detective’s case-
book: my series of investigations, as I follow the clues and t them together, to
make sense of what economic modelling is all about. Case studies are the best way
that I know to gure out how science goes on. Cases not only form individual
stories that capture the practices of economic science in considerable depth, but
taken together they provide the materials for a broader account of how economics
became, and works, as a modelling science. e messy details are important – not
just because, as we know, bald narratives lack credibility, but rather because the
devil is oen in the detail, and thus larger, and important, matters cannot be under-
stood and explained without them. Aer all, what would detective novels be if the
clues were omitted as mere detail to the argument?
What else does this book not do – and what does it do? It does not try to give
a denition of models – but it does discuss the qualities that make them useful in a
science. It does not suggest that there are dierent kinds of models, but it does illu-
minate the heterogeneity of objects that count as models. It does not suggest that
models are easy to characterize, but it does argue that in order to understand them,
we should pay attention to what models are used for, and how they are used. It is not
Preface
Preface
xvi
even-handed, but does argue that models are both very useful knowledge-makers
in economics as well as being of limited use in that same domain. It is not a critique
of modelling, but it does make clear how and why they may be criticised as well as
how and why they may be valued.
Fieen years of researching, thinking, and writing about models have convinced
me that there are no easy answers to questions about what models are, and how
modelling works. Some questions are more helpful than others. Asking: What qual-
ities do models need to make them useful in a science? and What functions do
models play in a science? are more fruitful than asking What are models? Asking:
How does reasoning with models go on? and What kind of knowledge does a sci-
ence gain from its investigations with models? prompt an account of modelling (in
economics) as an autonomous epistemic genre: that is, as a way of doing science
that has its own rationale just as do other modes of science. Answering these ques-
tions is the agenda for this book.
But those een years have also persuaded me that there are lots of dierent
kinds of things that legitimately count as models in other sciences, and that they
oen look and function very dierently in those other sciences. Comparisons
between model-based sciences are extremely useful; they operate here, only
gently, as a foil. Fieen years have also taught me that looking for how a science
becomes a model-based discipline requires attention not just to the scientic
modes of reasoning, but also to questions of perception and cognition as well as
to qualities of imagination and creativity. e arts cannot be entirely taken out of
the sciences.
I am delighted to thank all those many scholars who have helped me, argued
with me, discussed issues, commented upon chapters, and generally become
involved in my attempt to understand modelling. I hope that I have captured most
of these by name in acknowledgement notes attached to each chapter – of course
none of them are responsible for my not always taking their advice. Special thanks
go to Margaret Morrison and Nancy Cartwright who were signicant research
partners at the beginning of my research; to Marcel Boumans, Harro Maas, and
Roy Weintraub who engaged with my work throughout; and to a cohort of gradu-
ate students at LSE and in e Netherlands who responded to my enthusiasm for
models in a variety of fruitful ways. Such special thanks also go to the anonymous
readers for the Press, and to others who read the manuscript as a whole, for their
many generous and positive pieces of advice (which, unfortunately, sometimes
conicted with each other); to Aashish Velkar who sorted out the permissions
and acknowledgements; to Simona Valeriani who looked aer the many gures; to
Tracy Keefe and Rajashri Ravindranathan who saw the manuscript through publi-
cation; and nally to Jon Adams for his brilliant red cover design and to Scott Parris
at Cambridge University Press, whose patience has been unfailing. I am grateful to
the Wissenschaskolleg in Berlin for hosting my rst research work on the topic
(for several months in 1995–6), to the British Academy for a Research Readership
(for a second block of time in 1999–2001), and to my Department of Economic
Preface xvii
History at the London School of Economics and my History and Philosophy of
Economics group in the Faculty of Economics and Econometrics at the University
of Amsterdam who have supported my work throughout. It has been a long een
years, but in my defence – several other things happened on the way!
Mary S. Morgan
December 2010
1
1
Modelling as a Method of Enquiry
: 1
1. From Laws to Models, From Words to Objects 1
2. e Naturalization of Modelling in Economics 6
3. Practical Reasoning Styles 14
3.i Modelling as a Style of Reasoning 14
3.ii Modelling as a Reasoning Style in Economics 17
: , 19
4. Making Models to Reason With: Forms, Rules, and Resources 19
4.i Giving Form 20
4.ii Becoming Formal 26
4.iii Reasoning Resources 27
5. Modelling as a Method of Enquiry: e World in the Model,
Models of the World 30
6. Conclusion 37
PART I: CHANGING THE PRACTICE OF ECONOMIC SCIENCE
1. From Laws to Models, From Words to Objects
Two hundred years ago, political economy was overwhelmingly a verbal science,
with questions, concepts, and a mode of reasoning all dependent on words. As a
science, classical political economy of the eighteenth and early nineteenth centu-
ries began with individuals, theorized their relations, and posited a few general
laws that operated at a community level. One of the few laws that was expressed
in mathematics was proposed by the Rev’d omas Robert Malthus, who claimed
that the growth of population, driven by passions, increased in a way that would
inevitably outstrip the more pedestrian growth of food supplies. So, he argued,
there must also be checks at work in the world: the numbers of people were kept in
e World in the Model
2
check either through the vices of disease, famine, and war, or by virtue of celibacy
or delayed marriage. While such laws might indeed have an iron grip on economic
life, it was not thought easy to perceive these laws at work amongst the complicated
changing events of everyday life. is created diculties for the art of political
economy, namely fashioning policy in line with an understanding of those scien-
tic principles of political economy.1
Economics is now a very dierent kind of activity. From the late nineteenth
century, economics gradually became a more technocratic, tool-based, science,
using mathematics and statistics embedded in various kinds of analytical tech-
niques.2 By the late twentieth century, economics had become heavily dependent
on a set of reasoning tools that economists now call ‘models’: small mathematical,
statistical, graphical, diagrammatic, and even physical objects that can be manip-
ulated in various dierent ways. Today, in the twenty-rst century, if we go to an
economics seminar, or read a learned scientic paper in that eld, we nd that
economists write down some equations or maybe draw a diagram, and use those
to develop solutions to their theoretical conundrums or to answer questions about
the economic world. ese manipulable objects are the practical starting point in
economic research work: they are used for theorizing, providing hypotheses and
designing laboratory experiments, they are an essential input into simulations,
and they form the basis for much statistical work. Economics teaching is simi-
larly bounded: students learn by working through a set of models: some portraying
decisions by individuals and companies, others representing the behaviour of the
whole economy, and for every level in between. e use of economic models has
become habitual in government policy making, in trading on nancial markets, in
company decisions, and indeed, anywhere that economic decisions are made in a
more technocratic than casual way. In economics, as in many other modern sci-
ences, models have become endemic at every level.
e signicance and radical nature of this change in economics is easily over-
looked. e introduction of this new kind of scientic object – models – involved
not just the adoption of new languages of expression into economics (such as alge-
bra or geometry), but also the introduction of a new way of reasoning to econom-
ics. And having moved from a verbal to a model-based science, economists no
longer depicted their knowledge in terms of a few general, though unseen, laws,
1 Nineteenth-century economists oen used the term “principles” in the titles of their treatises on
political economy. is term denoted both their theories and analysis of law-like elements in the
economic system as well as the appropriate means of good governance (which might have an ethi-
cal, even moral, quality). For example, Malthus’ laws of population were almost laws of nature (they
were based on individual instincts of passion and the need for food, empirical data on population
growth, and hypothesized claims about likely growth of food output), while his policy arguments
were designed around his understanding of these laws (for example, he was against social security
schemes which, in the process of supporting the poor, would interfere with the natural checks on
population growth operating within the system see Malthus, 1803).
2 For the twentieth-century development of economics into a tool-based science, see Morgan
(2003a).
Modelling as a Method of Enquiry 3
but expressed it in a multitude of more specic models. As models replaced more
general principles and laws, so economists came to interpret the behaviour and
phenomena they saw in the economic world directly in terms of those models.3
Despite the ubiquity of modelling in modern economics, it is not easy to say
how this way of doing science works. Scientic models are not self-evident things,
and it is not obvious how such research objects are made, nor how a scientist rea-
sons with them, nor to what purpose. ese diculties of denition and under-
standing are exhibited in a most concrete fashion in an example that may well be
the rst such economic model in the history of the eld.
e Tableau Économique is a wonderful numerical object: a cross between
a table and a matrix, it presents an accounting portrait of the French economy
(Figure 1.1). It shows the classes of people in the economy (farmers, manufactur-
ers, and landowners) and has a zig-zag pattern of horizontal and diagonal lines
between them with numbers on them indicating the amount of goods or money
being transferred between the groups of people. It was invented in the late 1750s
by François Quesnay, an economist, and physician in the court of Louis XV and
thus at the centre of French political life in the mid-eighteenth century.4 He treated
the Table a u as a research object, using it to conduct various numerical exercises to
explore the possibilities for the French economy to grow via agricultural invest-
ment and the subsequent circulation of the surplus created from Nature around the
classes of people in the economy. In these exercises, various numbers for the agri-
cultural surplus and the amounts circulated in the zig-zags were inserted, and then
added downwards to determine whether such an economy would grow in a stable,
balanced way, or if there was some lack of balance in the relations.
e Tab l e au Économique, as one of the earliest models in economics, makes
a ne example to introduce a book on models, for it is one of the most celebrated
in the history of economics. It can be regarded as the great-grandfather of mod-
els in many dierent economic traditions even while its own content and mean-
ing remain somewhat mysterious. Two hundred and y years later, most modern
economic models lack the decorative borders (and the dot-matrix qualities that
make it look like a needlework sampler hanging on the wall), but are otherwise not
so dierent. Models in economics are still mostly pen-and-paper objects depict-
ing some aspect of the economy in a schematic, miniaturized, simplied, way. e
most important point to note about this object, however, is that it was not simply a
passive portrait of the economy; rather, it had the internal resources for Quesnay to
3 So, by the early twenty-rst century, we nd, for example, an account in which nancial traders
acting on models make markets behave like those models (demonstrating the performativity of
economic models; see MacKenzie, 2006), and we nd economists in newspaper columns explaining
the phenomena of ordinary life by verbally reinterpreting those events as examples of these small
worlds depicted in economic models (e.g., Harford, 2008, or Levitt and Dubner, 2005 and their col-
umns in the New York Times and the London Financial Times). I return to this point in Chapter 10.
4 Examples (for there are several) of Quesnay’s Tablea u are found in Kuczynski and Meek (1972) and
in Charles (2003) who discusses the development of the diagram.
e World in the Model
4
Figure 1.1. Qu e sna y ’s Tableau Économique (1767).
Source: Private collection. (Reproduced in Loïc Charles [2003] “e Visual History of the
Tabl eau Économique”. European Journal of the History of Economic ought, 10:4, 527–50, 528.)
Reproduced here with thanks to Loïc Charles.
Modelling as a Method of Enquiry 5
investigate (by his arithmetic exercises) how such an economy as he depicted might
work. It is this possibility for manipulation that turns such pictures into models for
the economist.
It is also telling that Quesnay’s contemporaries found the Tabl e au as dicult an
object to interpret and use as do present-day economists. It is very hard for modern
economists to understand how the dierent parts of the Ta bleau relate to each other,
or to the economy he inhabited, and to reconstruct exactly how Quesnay reasoned
using the object, without the evidence uncovered by historians to explain these
things to us.5 And if we think about how Quesnay might possibly have invented this
research object, we can also appreciate that an imaginative and creative mind must
have been at work. Such diculties point to the cognitive and contingent aspects
of models: they are objects that embed theoretical and empirical knowledge that
later economists will not automatically be able to extract and articulate again, just
as non-economists cannot read or use modern economic models without consid-
erable training in the eld.
Quesnay’s Tablea u is surely a special object, unique perhaps in its day, but its
very specicity raises a number of questions that need answering. If such research
objects are so specic to time and place, and if we need to know a great deal about
their particularities to see how they work, then how can we characterize the sci-
entic practice of modelling in a general way? is raises philosophical questions:
How do economists create such research objects? What exactly is involved in sci-
entic reasoning with such objects? How does working with such objects tell us
anything about the world? at is: How should we characterize the making, using,
and learning from models as a way of doing science?
e pioneer status of Quesnay’s Tab l e au equally raises general historical ques-
tions. For while economists now nd making and reasoning with such objects the
natural way to do economics, we do not have a good account of how that happened,
nor understand how it could make such a dierence to economics as a science.
Reasoning with models is a cognitive process by which economists acquire their
knowledge and use it.6 Sometime in the past, economists had to begin to think with
such objects, and learn how to gain knowledge of economics with them, if later
generations of economists were to come to reason easily with them and take it for
granted as the method they should use.
at process of change: from economists reasoning with words to reasoning
with models, is what this book is about. e historical and philosophical aspects of
that change cannot be easily untangled. At the meta level, we can point to the consid-
erable but gradual historical shi in the way economists reason, involving elements
5 For recent scholarship that investigates the likely sources of the Table au, its various versions, and
how it was used, see particularly Charles (2003) and Van den Berg (2002).
6 Nancy Nersessian (from her 1992 paper to most recent 2008 book) has been instrumental in con-
necting the literatures of cognitive science with that of the philosophy of scientic modelling. (See
also, for examples of dierent approaches using this connection, papers by Gentner, by Vosniadou,
and by Giere in Magnani and Nersessian, 2001.)
e World in the Model
6
of both cognition and imagination that made a big dierence to the epistemology
of economics, that is, to how economists come to know things in economics. But to
understand and appreciate fully the import of these changes, we need to look at the
micro level, at the objects themselves. When we look at that level, we nd we cannot
understand how economists learn things from models without understanding how
models are used, nor understand how they are used without understanding how
they are built. But why a particular model is built, what questions it is designed to
answer, and what uses it is put to, are historically contingent. History and philoso-
phy cannot easily be pulled apart, and the cognitive and imaginative aspects of mod-
elling prove equally sticky in guring out how economists make and reason with
models. ese issues – philosophical and historical, involving elements of reasoning
and imagination – are explored in the book through the investigation of a number
of models of considerable signicance, and long life, in the history of economics. It is
by paying careful analytical attention to how these small objects are made and used
in economics that we can understand the import of the big changes in economics.
ey provide the materials for both a naturalized philosophy of modelling in eco-
nomics and a historical account of the naturalization of models in economics.7
2. e Naturalization of Modelling in Economics
ough the important historical and philosophical changes in economics are di-
cult to understand separately, a broad chronology for the historical development of
modelling over the last 200 years can be outlined. ere are three moments of time
that are important. To begin with, we can nd a few isolated examples of models
in the late eighteenth and early nineteenth centuries and so call this period the
prehistory. We then nd, in the late nineteenth century, a rst generation of mod-
ellers: a very few economists who regularly made and used such research objects.
e second generation of modellers, the real developers of the method of models,
emerged during the interwar period. Modelling then became widespread through
economics only aer the mid-twentieth century.
To make this history more concrete, and to get a real feeling for what these
research objects are, I introduce a number of signicant examples here. If we begin
with the ‘prehistory’ of models, we nd that not only does Quesnay’s Tableau
Économique exist as an object out of its time in the eighteenth century, but there
7 It is appropriate here to refer to three parallel investigations. Nersessian (2008) comes to the topic
of ‘model-based reasoning’ from cognitive science and philosophy of science, and combines mental
models, narratives, experiments, and reasoning in her account of the history of physics. Ursula Klein
(2003) uses history and philosophy of science and semiotics to explore the nexus of paper tools,
models, and experiments that created a shi of scientic reasoning and practice in chemistry (see
also Klein, 2001). eir two accounts share many of the elements of my own project for economics,
though we have put them together in somewhat dierent ways. Meli (2006), in another parallel,
discusses how the science of seventeenth-century mechanics depended on reasoning with objects.
Modelling as a Method of Enquiry 7
(a)
(b)
Figure 1.2. e Prehistory of Models.
(a) Ricardo’s Farm Accounting (1821).
Source: Piero Sraa: e Works and Correspondence of David Ricardo. Edited with the collaboration
of M.H. Dobb, 1951–73. Cambridge: Cambridge University Press for e Royal Economic
Society. Vol. I: Principles of Political Economy & Taxation, 1821, p. 84. Reproduced by permission
of Liberty Fund Inc. on behalf of e Royal Economic Society.
(b) Von ünen’s Farming Diagram (1826).
Source: Johann Heinrich von ünen, Der isolierte Staat in Beziehung auf Landwirtscha und
Nationalökonomie, Hamburg, 1826. Reprinted facsimile edition 1990. Berlin: Academie Verlag,
p. 275.
e World in the Model
8
are also very few further cases in the early nineteenth century. One is provided by a
table of farm accounts developed by the English economist David Ricardo (1821) to
explain how income gets distributed in the agricultural economy (one element of his
table is shown in Figure 1.2a). Another is the diagram (in Figure 1.2b) of far m prices
in relation to distance from towns, drawn by the German agriculturalist Johann von
ünen (1826), depicting an idealized abstract, landscape but with numbers drawn
from his experience of farming at his own estate of Tellow.8 ese three objects –
the Tableau , the accounting table, and the spatial diagram with numbers – each
designed to show how the agricultural economy worked, jut out awkwardly from
the sea of words that surround them in this early period of economic science.
In the late nineteenth century, we begin to see more regular occurrences of
these objects we are calling models, but we may also notice that the few econo-
mists involved felt they had to justify their creation and usage of these odd research
objects that they had invented to help them in their analysis. ey did not yet have
the concept or label of models and were indeed quite self-conscious about this
activity. ree important examples epitomise this rst generation of models and
modellers and their understanding of the role of models. In 1879, the British econ-
omist Alfred Marshall began to draw little diagrams to explain more clearly how
two countries trade with each other, in this case the curves depicting the oers
of German iron for English cloth and vice versa as relative prices change (Figure
1.3a).9 Marshall thought that such diagrams were useful if they could be illus-
trated with examples from economic life (and then he oen presented them in his
footnotes), but that if such pieces of mathematics were not useful, they should be
burnt! In 1881, the Irish economist Francis Edgeworth outlined a somewhat dier-
ent diagrammatic perspective on exchange relations (Figure 1.3b) to gure out the
range of possible contracts that Robinson Crusoe might strike with Man Friday to
gain his help in cultivating their island economy. Not being sure how to refer to this
way of reasoning, he labelled his analysis with the diagram as oering a “represen-
tative particular” argument (see Chapter 3). In 1892, Irving Fisher, an American
economist, designed and constructed a hydraulic mechanism to represent, explore,
and so understand the workings of a mini-economy, one with only three goods
and three consumers (Figure 1.3c).10 He accompanied this work with an outright
8 Von ünen’s original contribution appeared in 1826; an English translation of part of the study
became available in 1966, with a useful introduction. On dierent interpretations of his modelling
project, see Judy Klein (2001, pp. 114–6), who reproduces his diagram and discusses it as a mea-
suring device, and Mäki (2004), who analyses it as a theoretical model.
9 is was the rst appearance of these curves in the history of economic theorizing about trade
relations, on which Humphrey (1995, p. 41) comments: Marshall “by crystallizing, condensing
and generalizing earlier insights into a powerful yet simple visual image” was able to create an
object that made these relations “transparent”. Marshall’s 1879 diagrams and discussion were
nally published in an edition of his early works edited by Whitaker in 1975, and this diagram
provided the logo for the Charles Gide conference at which some parts of this paper were rst
presented. Marshall’s views of mathematics are discussed by Weintraub (2002).
10 Fisher’s thesis of 1891 was published in 1892 and republished in 1925, displaying a photograph of
the mechanism in the frontispiece labelled “model of a mechanism”.
(a) (c)
(b)
Figure 1.3. First-Generation Models.
(a) Marshall’s Trade Diagram (1879).
Source: Alfred Marshall, “Pure eory
of Foreign Trade”. Priv ately printed
1879, Figure 8, Marshall Library,
Cambridge. (Reprinted, London:
London School of Economics and
Political Science Reprints of Scarce
Tracts in Economics, No. 1, 1930).
Reproduced with thanks to Marshall
Library of Economics, Cambridge.
(b) Edgeworth’s Exchange Diagram
(1881).
Source: F. Y. Edgeworth, Mathemati-
cal Psychics. London: C. Kegan Paul
& Co., 1881, Figure 1, p. 28.
(c) Fisher’s Hydraulic Machine and Its
Design (constructed 1893 from 1892
design).
Source: Irving Fisher, Mathematical
Investigation in the eory of Value
and Price. esis of 1891/2. New
Haven: Yale University Press, 1925.
Frontispiece and Figure 9 on p. 39.
Reproduced with per mission from
George Fisher.
e World in the Model
10
defence of these research objects – mathematical, graphical, and real machines –
that he designed and used for his economic analysis.
It seems reasonable to locate these three economists in the rst real generation of
model-makers, and their self-consciousness about their research objects as indicative
of this moment of change. is late nineteenth century moment was noticed later on
by Arthur Pigou in 1929, who cleverly understood the diagrams and equations we
see in these examples as “tools”, labelling Edgeworth as a “tool maker” and Marshall
as a “tool maker and user”. For Pigou, these objects were “pieces of analytic machin-
ery”, “thought-tools”, or even “keystones”.11 And because economics is now depen-
dent upon such research objects, all of these examples can today be understood as
models, though, neither in the prehistory period, nor in this late nineteenth century
moment, would economists have recognised them as such or used the label.
It was in the 1930s that economists really ‘discovered’ the idea of models. It was
in that decade that these objects became conceptualized, gained the label ‘model’,
and a fuller understanding of their usefulness developed. Two economists played an
important role in this transformation, thus sparking the wider deployment of the label,
notion, and usage of models in economic analysis. In 1933, in the depths of the Great
Depression, the Norwegian economist Ragnar Frisch developed one of the rst math-
ematical models of the business cycle. Because it had certain features, particularly the
possibility to simulate a cyclical pattern, Frisch’s “macro-dynamic system” created a
new recipe for future business cycle models (see Boumans, 1999 and Chapter 6, this
volume). As a recipe, it formed the basis for the rst econometric model of a whole
economy, built by the Dutch economist Jan Tinbergen in 1936 (1937), to see how to
get e Netherlands out of the Depression. is object embedded a theory of the busi-
ness cycle into the mathematical form, along with statistical information from the
Dutch economy in the numbers (or parameters) of the equations. ese two econo-
mists won the rst Nobel Prize for Economics in 1969 for this model-based research;
one of Tinbergen’s model equations and a schema (from his slightly later US model of
1939) are shown in Figure 1.4a, while Frisch’s model is shown later in Figure 1.6.
Tinbergen was also largely responsible for transferring the term ‘model’ in the
early 1930s from physics, where it had usually referred to a material object, into
economics to refer to the statistical and mathematical objects that he and Frisch
were then developing.12 So by the middle 1930s, the label ‘model’ had come into use,
11 See Pigou’s lecture of 1929 (in his 1931), particularly pp. 2–8. Joan Robinson (1933) is more usu-
ally noted for introducing the notion of the “tool box of economics”, but she was following Pigou,
whose discussion, and prose, is more eective. Pigou’s idea of tools was quite broad – it included
not just models, but also the concurrent development of mathematical and statistical techniques.
I return to the issue of “keystones” in Chapter 10.
12 Ludwig Boltzmann had dened the term ‘model’ in the sense of a material object model, in
what has become one of the classic articles on models in the 11th edition of the Encyclopaedia
Britannica (1911). Boltzmann there provides a good view of nineteenth-century scientists’ sense
of the word. Boumans argues that it was Ehrenfest who probably broadened the scope to apply to
mathematical objects, and since Tinbergen was his assistant in the mid-1920s, this is a likely route
for the transfer of the term into economics (see Boumans, 2005, chapter 2) though there are also
scattered uses of the term by other economists in the 1920s.
(a)
(b) (c)
Figure 1.4. Second-Generation Models.
(a) Tinbergen’s US Econometric Model:
Equations and Causal-Time Process.
Source: Jan Tinbergen, Business Cycles in
the United States of America, 1991–1932.
League of Nations Publications, Series II,
Economic and Financial, 1939 II.A 16;
Equation 6.31 on p. 137 and graph 6.31 on
p. 138. Reproduced with permission from
Stichting Wetenschappelijke Nalatenschap
Jan Tinbergen.
(b) Hick’s IS-LL “Little Apparatus”.
Source: J. R. Hicks, “Mr. Keynes and the
‘Classics’; A Suggested Interpretation”
Econometrica, 5: 2 (Apr., 1937), pp. 147–
159; Figure 1, p. 153. Reproduced with
permission from e Econometric Society.
(c) Samuelson’s Keynesian Model.
Source: Paul A. Samuelson, “Interactions
between the Multiplier Analysis and the
Principle of Acceleration”. e Review of
Economics and Statistics, 21:2 (May, 1939),
pp. 75–78; text and equations on p. 76.
Reproduced with permission from MIT
Press Journals.
e World in the Model
12
though not everyone had noticed it.13 For example, in 1937 John Hicks invented a
“little apparatus” (p. 156), his IS-LL diagram (Figure 1.4b), to compare the work-
ings of J. M. Keynes’ new macroeconomics (of 1936) with that of the older classical
system. In that same year, in another attempt to turn Keynes’ theory into something
more comprehensible, James Meade provided an eight-equation algebraic treat-
ment, calling it a “A Simplied Model of Mr. Keynes’ System”, while soon aer Paul
Samuelson produced a smaller set of equations (seen in Figure 1.4c) to exemplify
and explain the Keynesian relations, describing them as “a new model sequence”
(1939, p. 75). All of these three ‘Keynesian’ models are discussed in Chapter 6.
Economists quickly broadened the scope of the label ‘model’ to refer to all kinds
of mathematical and diagrammatic and material objects. But even then, models –
as working objects and as a label – did not immediately and fully invade economics
until a bit later. Only with the next new generation of economists – for whom both
the label and the notion were unproblematic – did models cease to be special and
became commonplace. us, William Baumol (1951) used the term as naturally as
one might refer to a domestic weed when he referred to Harrod’s (1939) small set
of equations showing how an economy grows as “Mr. Harrod’s Model”, while Roy
Harrod himself (of the same older generation as Hicks and Meade) still mused
about the term as if it were some exotic imported plant:
Many years aer I had made certain formulations in the eld of growth
theory and aer Professor Domar had made similar formulations, there
began to be references to the “Harrod-Domar model”. I found myself in the
position of Le Bourgeois Gentilhomme who had been speaking prose all
his life without knowing it. I had been fabricating “models” without know-
ing it. (Harrod, 1968, p. 173)
is brief history has enabled me to indicate the historical contours of when
models were introduced and when modelling became the normal mode of reason-
ing in economists: from isolated examples in the prehistory, to a rst generation
of model-makers and users in the late nineteenth century, to a second generation
who developed these research objects explicitly as models in the 1930s. It was this
second generation who fully developed this “new practice” of modelling, as Marcel
Boumans (2005) has justly labelled it. e label, the idea, and the use of models
became the natural way to work for economists only in the period from the 1940s
onwards.
Models are not easy objects either to dene or, in general terms, describe,
but those reproduced here, some of the most important models from the history
13 Nor was its meaning stable in the 1930s (for examples of its range, see Schumpeter, 1935).
Although we see the term model taken up by those making models of Keynes’ theoretical macro-
economic system (1936), it was not one of Keynes’ terms (almost the only time he used it was in
discussing Tinbergen’s work, see Keynes, 1973, pp. 284–305). Keynes himself seemed to prefer the
term “schema” or “schematism”, which, as we will see later in Section 4.iii, has a slightly dierent
connotation: it indicates an outline, rather than an apparatus that might be manipulated.
Modelling as a Method of Enquiry 13
of economics, exemplify the sort of things that count as models in economics:
either real objects, or pen-and-paper objects that are diagrammatic, algebraic, or
arithmetic in form. Despite their variations in form, these objects share recog-
nisable characteristics: each depicts, renders, denotes, or in some way provides,
some kind of representation of ideas about some aspects of the economy. Yet,
and this is a very important point to stress, these representations are not just
pictures. Pictures of the economy go back a long way: we see shipbuilding in
the eleventh century Bayeux Tapestry and building sites in the eenth century
frescoes of the recently reopened hospital of Santa Maria della Scala in Siena.
ese depict the arrangements of labour and capital, show the technologies of the
period, and so forth – but they are not models for the economist. As I pointed out
earlier, Quesnay’s Tableau Économique was not just a depiction of the economy
but one that could be manipulated, and because it could be manipulated, it could
be reasoned with. For economists it is the possibility to reason with the dierent
kinds of representations shown in this chapter that makes them all into economic
models.14
Hick’s 1937 terminology of a ‘little apparatus’ nicely captures the manipulabil-
ity of such research objects – they are working objects that can be played around
with in various ways – even though his model is made only of paper and pen com-
pared to the real apparatus of Fisher’s earlier hydraulic model. ese two examples
have an obvious anity with the material object models used centuries earlier. For
example, models of the planetary system constructed out of papier maché and metal
rods were used by scientists to explore the workings of the universe, while articu-
lated wooden maquettes were made by architects to demonstrate the construction
of their buildings. is comparison points to another critical point about models:
they must be small enough in scale for their manipulation to be manageable in
order that they can be used to enquire – indirectly – into the workings of those
aspects of the economy depicted, just as those models of domes and the planetary
systems were. It seems natural to take over this older sense of material models from
the arts and sciences to understand the term ‘model’ that Tinbergen introduced
into economics at that time: small-scale objects depicting aspects of the economy
that can be analysed and manipulated in various ways.
But notice here how introducing this new kind of research object into eco-
nomics brought along with it a new way of reasoning to that science, a method that
economist-scientists now call simply ‘modelling’. By the latter half of the twentieth
century, mathematical modelling had become the preferred way of doing scien-
tic and policy-making economics, and had come to inhabit a number of other
domains where economists had le their mark in the scientic, public, and commer-
cial realms. And, wherever statistical data were available, econometric modelling
14 e label Tabl eau is indicative that some tables of numbers may also have this manipulable qual-
ity, and so reasoning with them is also a possibility, for example, Leontief input–output tables both
represent the economy and can be manipulated.
e World in the Model
14
became the relevant way of working – although this book is not primarily about
econometrics.15 In other words, disciplinary arguments at all levels of economics
came to hinge not just on the objects – models, but on economists’ abilities to rea-
son with them – modelling. Modelling had become the accepted mode of reasoning
in economics in the sense that it became “the right way to reason. . . . what it is to
reason rightly”.16
3. Practical Reasoning Styles
is brings us to the question of reasoning method, for though we can discern
some characteristics in common between those revered old models of the universe
resting in our science museums and the modern mathematical models of the econ-
omy, it is perhaps not so obvious that economics shares a mode of reasoning with
early astronomy.
3.i Modelling as a Style of Reasoning
Modelling is one of the six dierent “styles” of scientic thinking that Alistair
Crombie distinguishes in his Designed in the Mind: Western Visions of Science,
Nature and Humankind.17 It is worth listing them all here – in the chronological
order that they appeared in the history of the sciences.
15 e history of modelling in economics has been barely considered except in econometrics (on
which see Morgan, 1990; Boumans, 1993, 2005; Qin, 1993; and Le Gall, 2007). e parallel liter-
ature on mathematical modelling – qua modelling – is less developed, but see Boumans (2005),
who focusses on the 1920s–1930s in his discussion of it as a “new practice” in both statistical and
mathematical terms. Solow (1997/2005) oers some suggestions about its takeo in the 1950s
and as a rare exception, compares the use of mathematics to the use of modelling to argue that
economics is mainly a modelling discipline. Niehans (1990) recognises the “era of models” as a
leitmotiv for the period since the 1930s (but does not say much about its history); and Colander
(2000) portrays modelling as the “central attribute of modern economics” (p. 137). Most histo-
ries of twentieth-century economics allude to models, but the introduction of models, and their
mode of argument, are largely taken for granted. Mirowski (2002) indirectly comes closest to
dealing with this as an historical problem, but his questions are about ideas, theories, and tech-
niques of economics in the context of the Cold War, rather than about modelling itself.
16 One of the peculiar signs of this acceptance (and it may be specic to economics compared to
other scientic elds) is that economists rarely use the word theory nowadays, or if so, they use it
interchangeably with model to such an extent that many economists nd it dicult to distinguish
between the two (see Goldfarb and Ratner, 2008). I return to the point in Chapter 10. e quote
itself comes from Hacking (1992a, p. 10) and refers not to modelling in economics, but to a much
broader claim about the nature of epistemic genres in scientic reasoning, discussed in the next
section.
17 Crombie’s claim – that there are basically six styles of scientic reasoning, rst appeared in his
paper of 1988 and the volumes of Crombie’s massive three volumes: Styles of Scientic inking in
the European Traditions (1994) were in dra in 1980. us, Hacking’s review and further analysis
(1992a) come aer that rst paper but predate Crombie’s main publication of 1994.
Modelling as a Method of Enquiry 15
1. Mathematical postulation and proof
2. Experiment
3. Hypothetical modelling
4. Taxonomy (the method of classication into natural kinds)
5. Statistical
6. Historical-genetic18
ese categories label dierent ‘styles’ or ‘epistemic genres’ of scientic reason-
ing, that is, of ways of nding out about the world. ey do not provide the kind of
detailed descriptions in combination with a big picture analysis of how science goes
on that we nd in Ludwig Fleck’s ‘denkstil’, Michel Foucault’s ‘epistemes’, omas
Kuhn’s ‘paradigms’, nor Hans-Jorg Rheinberger’s ‘experimental systems’.19 Rat her,
this set of categories provides a framework for historical epistemology in the sense
that it enables the historian to track the changes in how scientists do their science.
While modern economics barely makes it into Crombie’s massive volumes, nor Ian
Hacking’s subsequent discussions, they provide the resources to understand how
modelling as an epistemic style or genre came into economics and what kind of
dierence it made.20
According to Crombie (1994), modelling grew up in the eld of early modern
sciences and arts in the making of models of natural objects – and sprang from
the desire to imitate nature, and in so doing to understand its workings. It had
joint roots in natural philosophical investigations into the relationship of the Earth
and the heavens (such as in astronomy) and in the cra skills found in the crea-
tion of objects such as imitation birds (singing, feathered, mechanical automata).
Given these roots, Crombie labelled one of its characteristic features as involving
“the construction of analogies” (1988, p. 11). Although there are good examples
of analogical models in economics, analogical aspects no longer constitute a dis-
tinguishing feature of model-making in this eld. It is therefore useful to broaden
the canvas beyond analogies to see how the desire to understand Nature (or in the
economists’ case, the economy) through some form of imitation lies at the heart
of modelling. And, just as there are many dierent genres and aims of represen-
tation in the arts, such scientic representations come in a variety of forms and
disguises.
18 e “historical derivation of genetic development” is associated with evolutionary science.
“inking in cases” is a seventh style added by Forrester (1996), as used for example in various
branches of medicine and psychiatry. Karine Chemla (2003) has argued for an eight style – the
algorithmic method. At rst sight, none of these other styles seem to be connected to modelling,
but as we shall see later in this book, the methods of taxonomy and classication, and the method
of experiment, are both found in conjunction with the method of modelling in economics, while
statistical reasoning is the basis for econometric modelling.
19 See Fleck (1935/1979), Foucault (1970), Kuhn (1962), and Rheinberger (1997).
20 As such, this account provides a parallel to Hacking’s accounts for the development of the sta-
tistical style (1992b), for the experimental (laboratory) style (1992c) and for the taxonomic style
(1993).
e World in the Model
16
e history of modelling as a reasoning style in Crombie’s account is built upon
material object models, such as those in astronomy, and so we can continue to
think of the planetary motion models of the Renaissance period as being exem-
plary for the idea of models and of how they are used for enquiry. ey were built
to represent the relationships – hypothesized by the early astronomers – between
Earth and the heavens. ey were carefully designed not just to present or illustrate
known relationships but also to demonstrate those relations that scientists supposed
to be true (their hypotheses) and thus to explain how the universe was thought to
be arranged and to work. ose models that were manipulable (rather than with
xed parts) were particularly useful in enquiries into the hidden trajectories and
contested relations of the heavenly bodies. It is this kind of physical activity of sci-
ence in general that perhaps led Ian Hacking (1992a) to suggest that Crombie’s style
of “thinking” should be replaced by “reasoning”.21 us, we might rather think of
each style as a generic kind of very practical reasoning, with dierent characteris-
tics for each style.
We learn from Crombie that the adoption of any particular style of practical
reasoning in any one eld requires its own historical account. Take, as a parallel
example to the introduction of modelling, the method of experiment. is grew
up in the early modern period as a method of analysis and synthesis “to control
[the method of mathematical] postulation and to explore by observation and
measurement” (1994, Vol. I, p. 84). Crombie dates its main development from the
thirteenth century and thereaer it took hold in various disciplines at dierent
times and places. But typically those who would adopt a new style of practical rea-
soning for their science have to argue for it, as well as demonstrate its usefulness, for
the acceptance of a new style generally institutes a change in reasoning style. is is
one reason why the histories of the dierent sciences are so replete with arguments
about how that science should be done. For example, Shapin and Schaer (1985)
analyse in detail how the method was fought over in the establishment of natural
philosophy in seventeenth century England. To follow the example into econom-
ics: classroom experiments began there in the 1940s, though the activity was suf-
ciently limited that economists experienced their own battle for the acceptance
of the experimental method within economics only in the period aer 1970. Yet it
is worth noting too, that in economics as in many modern sciences, the individ-
ual styles have begun to hybridize. us, even from the beginning of experimental
work in economics in the 1940s, modelling informed those experimentalists’ work-
ing hypotheses and models were found in their experimental designs (as we shall
see in Chapter 7).
Finally, we can also take from both Crombie and Hacking that adopting a new
reasoning style into a science does not come without signicant consequences for
its content. ere are inevitably connections between style and content, and while
21 e practical aspects of this are important: for like Hacking, I nd the term “reasoning” underrates
the importance of the “manipulative hand and the attentive eye” (Hacking, 1992a, p. 4).
Modelling as a Method of Enquiry 17
dierent sciences may rest on one or more of these styles of reasoning, that does
not imply that any scientic system can rest on any style. For example, Quetelet’s
‘average man’ of the mid-nineteenth century is a statistically dened concept and so
unthinkable without the adoption of statistical reasoning. In economics now, it is
almost impossible for economists to give an account of individual behaviour, or of
the world economic crisis, which has not been dened in terms of their economic
models and argued over using their model reasoning.
Any scientist’s ability to reason in a chosen style is thus clearly dependent on
the contingent history of that discipline, and whether that method is accepted
within it. Yet, once more or less adopted within a discipline, a style, as Hacking says,
becomes
. . . a timeless canon of objectivity, a standard or model of what it is to be
reasonable about this or that type of subject matter. We do not check to
see whether mathematical proof or laboratory investigation or statistical
‘studies’ are the right way to reason: they have become (aer erce strug-
gles) what it is to reason rightly, to be reasonable in this or that domain.
(Hacking, 1992a, p. 10)
Once accepted by a group of scientists, a style of reasoning comes to seem natural
to them, so natural that they do not question it. ey neither question its historical
origins, nor the objectivity of the knowledge gained from using the method, nor do
they appeal to any outside or higher level for its justication. at is why, Hacking
argues, once a style of reasoning is accepted in a community, reasoning rightly
means to reason in that style.22
3.ii Modelling as a Reasoning Style in Economics
Although the broad historical contours of the appearance and spread of models in
economics were outlined earlier (in Section 2), the processes by which modelling
took hold as an independent style of practical reasoning are more hazy. ere was,
of course, no blank page in economics before modelling took over. Early econo-
mists used technical and conceptual terms (the terminology of their science),
but reasoned with them in the modes of ordinary verbal argument. As modelling
developed, it rst partly overlayered and partly integrated with two other generic
practices of scientic reasoning, namely mathematical ones in the late nineteenth
century and then statistical ones in the 1920s and 1930s (in the form of economet-
rics). More recently it has become layered into the experimental and classicatory
22 Hacking even makes a stronger claim, arguing that a style becomes self-validating. For example,
statistical reasoning is validated by arguments that are coherent within statistical thinking, not by
ones from other styles of reasoning or some meta philosophical argument (see Hacking, 1992b,
and for laboratory sciences, Hacking, 1992c). is all points to the relativity of scientic method
and so the knowledge obtained by it, but it is not a radical relativity, for each of the styles is con-
sidered valid as a scientic method.
e World in the Model
18
modes of reasoning (see Chapters 7 to 9). While modelling itself became deeply
rooted in economics, so deeply rooted as to produce the overwhelmingly luxuri-
ant growth that made it – in its various forms – the dominant mode of reasoning
by the late twentieth century, it did so in forms that were either partly disguised or
manifest in hybrids.
Treating the development of modelling as an epistemic genre – that is, as a
practical mode of reasoning to gain knowledge about the economic world – does
help to part the clouds that obscure the historical gaze. It reveals to us that math-
ematics grew up in two styles of reasoning in economics at more or less the same
time in the late nineteenth century: the method of mathematical postulation and
proof and the method of hypothetical modelling using mathematical models. We
have already seen how the rst generation of model-makers in the late nineteenth
century generated a new practice of modelling, but by taking note of Crombie’s cat-
egories, we can also see why it crept in unnoticed by historians who have paid more
attention to the concurrent introduction of mathematical modes of arguing with-
out distinguishing between two styles of reasoning both involving mathematics. It
is fair to say, however, that recognising two distinct historical traditions in styles of
scientic reasoning that both involved mathematical languages, and distinguish-
ing between the method of hypothetical modelling versus that of postulation and
proof, is not always easy. is knotty historical problem is further complicated by
the fact that, as Weintraub (2002) has shown us, mathematics has its own self-
image, one that changes in its relationship with the sciences. During that late nine-
teenth century time when these two mathematical modes of reasoning came into
economics, mathematicians felt the need to have their work closely related to the
sciences, though that relationship could be mediated in dierent ways, while for
their part, economists of the time argued about the usefulness of mathematics as
both a language and as a method.23
Nevertheless, we can contrast, as exemplars of these two reasoning styles in
the late nineteenth century, Fisher’s hydraulic/mechanical model of his three-
commodity, three-person economy (pictured in Figure 1.3c) with the French econ-
omist, Leon Walras’ 1874 mathematically described general equilibrium account
for the whole economy. So, whilst Walras (amongst others) was busy introducing
what might be recognised as mathematical language and the method of math-
ematical postulation and proof, we can also distinguish objects that we can call
models, and a method of reasoning with them (including the use of mathemat-
ics), being developed by economists such as Fisher and Marshall. e fact that
Fisher built his hydraulic model to represent Walras’ ideas, and to gure out by
exploring with that physical model the process by which the latter’s mathemati-
cally postulated and proved general equilibrium might be arrived at, shows us the
23 Authorities on the history of mathematical reasoning in the history of economics are Roy
Weintraub (see his 2002 and 2008); and Giorgio Israel (see particularly Ingrao and Israel, 1987/90,
and Israel, 2002). For an insight into contemporary views, see Edgeworth (1889).
Modelling as a Method of Enquiry 19
dierence between them. e fact that both used mathematical ideas from physical
systems demonstrates not only the closeness of mathematics and the sciences (but
also shows how treacherous relying on analogies as indicators of reasoning styles
can be). Individual economists worked with dierent styles of reasoning involving
mathematics and the mathematical method, but as we should expect, their choices
were locally determined, dependent on their own histories, times, and places and
their own image of the role of mathematics in science.
Mathematics provides the languages of most modern economic model- making,
and we know that economics became mathematized at the same time as it became
a modelling science, but if we want the historical record to help us think about
modelling, then we need to turn the terms around: in order to get at modelling in
economics, we need to concentrate on the objects, on the models themselves rather
than on their mathematics. Here, as we have already found, history matters when-
ever we are discussing any specic example of a model, for models are contingent,
not timeless: we need history to understand why and how any particular model
was built, how it was used, and what understanding economists gained from it.
But to understand the development of modelling as an epistemic genre, we need
to capture and explicate the generic qualities that we can nd in the earlier models
of Quesnay, and Ricardo, just as much as the twentieth century work of Frisch and
Samuelson. To understand what is involved in this shi in economic science, a
shi in how economists reason in economics and about the economy, we need to
understand what constitutes the method of modelling in economics. Here, history
begins to take second place: it provides the materials and examples for explanation,
but we are instead concerned with philosophical questions about how models are
made, about modelling as mode of reasoning, and about the nature of modelling as
an epistemic genre.
PART II: MAKING MODELS, USING MODELS
4. Making Models to Reason With: Forms, Rules, and Resources
How do economists make models?24 e process of model-making in economics
has oen been labelled one of “formalization”, a term whose various meanings
have so twisted and turned through the history of economics that I suggest we
24 e literature on the philosophy (or methodology) of modelling in economics has seen consider-
able attention in recent years, particularly since the formation of a specialist Journal of Economic
Methodology. I have discussed the seminal contributions by various economists over the twenti-
eth century alongside some philosophical reections in Morgan, 2008/online, and surveyed the
recent work in Morgan and Knuuttila (2012). Consequently, this chapter does not provide an
additional survey: rather some elements are discussed in this chapter and others in the chapters
that follow.
e World in the Model
20
begin afresh with it.25 I focus on two meanings of the term. First, if we think about
its active form: ‘to formalize’, we imply to give form to, to shape, or to provide an
outline of something. Second, ‘formal’ contrasts with ‘informal’, meaning lacking
in exactness or in rules, whereas ‘formal’ implies something rule bound, following
prescribed forms. Making models involves both senses: models give form to, in
the sense of providing a more explicit or exact representation of our ideas about
the world, and in creating those forms we make them subject to rules of conduct
or manipulation. ese two aspects of modelling – giving form to ideas and mak-
ing them formally rule bound – are related, and if we understand how, we take a
big step towards seeing how models provide the means for reasoning within eco-
nomic science. I make use of some more examples of economic models to show
how giving form to a model and making it subject to rules of reasoning go along
together.
4.i Giving Form
All the models reproduced in this chapter – a small but representative sample from
the history of the eld – give representation to economists’ vague ideas about the
economy in various more exact forms: in diagrams, equations, pictures, and even
in physical objects. How does this happen? Commentators have found a number
of dierent ways to describe this process of ‘giving form to’ ideas, namely, as a pro-
cess of recipe making, of visualizing, of idealizing, or of choosing analogies. It is
helpful to see these four accounts as four dierent ways to understand how models
get made rather than being either labels for dierent kinds of models or as terms
used by the scientists/model-makers themselves. Nor are such accounts necessarily
mutually exclusive in accounting for any particular model-building episode.26
25 It is indicative, for example, that at the end of the nineteenth century, the taxonomy of methods
for economics given by W. E. Johnson in the Old Palgrave (the renowned dictionary of econom-
ics of 1894–6) contrasts “formal” with “narrative”, although both categories fell under the term
“descriptive economics”; meaning that they “describe the conceptions and facts with which the
science deals”. Formal methods were those which “analyse and classify” concepts and involved the
“logical processes of denition and division”. Both “Inductive” and “Deductive” methods fell on
the other side of the taxonomy tree, under the title of “constructive” methods: those that “estab-
lish laws and uniformities” (Johnson, 1896, pp. 739–48). In contrast, most modern commentators
align formal methods with mathematical methods, and thus with deduction. Some minority of
economists continue to dispute the ecacy of ‘formal methods’ in economics, arguing that for-
malism is non-neutral (see Chick and Dow, 2001), or that it narrows and leaves out too much
substantive content of importance compared to the verbal methods it supplanted (thus equating
formal with a lack of substance), an argument that seems to hold both the language of math-
ematics, and the small-scale reasoning tools of modelling, equally at fault. Two recent debates
about the meaning and content of ‘formalism’ are suggestive of the term’s extraordinary range
(see debate in Methodus, 1991, particularly contributions by McCloskey and Katzner, and in the
Economic Journal, 1998, by Backhouse and Krugman).
26 For example, as we nd in Chapter 5, both Hesse’s 1966 account of analogical modelling and
Boumans’ 1999 account of recipe-making help us understand the process of making the analogi-
cal Phillips-Newlyn hydraulic machine (see Morgan and Boumans, 2004).
Modelling as a Method of Enquiry 21
e rst of these four accounts of how models are made sees the process of
giving form to ideas about the economy as analogous to recipe-making. Boumans’
(1999) recipe notion embeds two ideas: economists choose the model’s ingredi-
ents – their ideas, intuitions, and bits of knowledge of how the economy works –
and then combine them together and fashion them to make something new. It is
critical that this model-making involves processes of integration: mixing and shap-
ing and baking the elements, ‘cooking’ them to form something whole that is not
fully recognisable from the original elements (as in chemical synthesis). It may
well be that the end product is not envisaged at the beginning, for recipe-making
is a creative process (less so for recipe-following, which produces more reliable and
known results). For example, Ricardo can be understood to have formed his model
out of a set of little accounting tables (one of which is shown in Figure 1.2a): he
integrated these elements together and reasoned with them until they emerged as
the accounts of a model farm representing the agricultural economy of his day (as
we shall see in Chapter 2). Hicks’ IS-LL model provides another good example that
can be well described as recipe-making: it was fashioned to make sense of Keynes’
ideas about the macroeconomy by tting together the simplied or basic elements
and relations of the macroeconomy (see Figure 1.4b, and discussion in Chapter 6).
Once synthesised, the new model recipe depicted certain macroeconomic relations
in a new form (the IS/LM model) that proved exible to many dierent interpret-
ations and had a remarkably long life.
A second account of model-making derives from another comparison, this
time drawing on the similarities between the practices of representation in arts
and sciences and inspired by Nelson Goodman’s work (1978). In Morgan, 2004,
I argue that the activity of model-making requires imagination to hypothesize how
the economy might work, and then the power and skill to make an image of that
idea. For example, Edgeworth’s rst drawing (1881) of the relationships between
Robinson Crusoe and Man Friday (Figure 1.3b) can be understood as his imagin-
ing and imaging the set of points on his graph where they might both be willing
to make a bargain to help each other. is little diagram gradually evolved into the
Edgeworth Box diagram in a process that was far from self-evident but depended
on the processes of imagination and image making by a sequence of dierent econ-
omists, each of whom used this particular way of envisioning economic relations
and portraying them into these little two-dimensional diagrammatic/mathemati-
cal forms (see the example by Bowley in Figure 1.5c). In this account (described in
Chapter 3), modelling, understood as a way of giving form to economic intuitions,
involves a kind of envisioning power.
A third account of model formation understands it as a process of ‘idealization’.
Philosophers of science have used this notion to explain the practices observed
in mathematical modelling in physics (e.g., McMullin, 1985). Modelling there is
portrayed as a process of picking out the relations of interest, and isolating them
from the frictions and disturbances which interfere with their workings in the real
world to give form to simpler, and ‘ideal’, world models (e.g., ‘in an ideal world,
(a)
(c)
(b)
(d)
(e)
Figure 1.5. Models: e Variety of
Forms.
(a) Jevons’ Utility Curve.
Source: William Stanley Jevons, e e-
ory of Political Economy, 1871. London:
Macmillan & Co., Figure 4, p. 49.
(b) Fisher’s Arithmetical and Mechanical
Monetary Balance.
Source: Irving Fisher, e Purchasing
Power of Money., New York: Macmillan,
1911; Arithmetic Balance, p. 18;
Mechanical Balance, p. 21. Reproduced
with permission from George Fisher.
(c) Bowley’s Version of the Edgeworth
Box.
Source: Arthur Lyon Bowley, e
Mathematical Groundwork of Economics,
An Introductory Treatise. Oxford:
Clarendon Press, 1924; Figure 1, p. 5.
Reproduced with permission from
Oxford University Press.
(d) Phillips’ Plumbing Diagram.
Source: Bill Phillips’ undergraduate essay
“Savings and Investment. Rate of Interest
and Level of Income”. Undated, 1948–
9, p. 1, Figure 3. University of Leeds,
Brotherton Library, Newlyn-Phillips
Machine Archive.
(e) Luce and Raia’s Game Matrix.
Source: Duncan R. Luce and Howard Raia
(1957) Games and Decisions. New York:
Wiley; matrix, p. 95. Reproduced with
permission from Dover Publications.
Modelling as a Method of Enquiry 23
there is no friction’). Such accounts have also been used to understand model
formation in economics. us, Nancy Cartwright has used the term to discuss how
economists made models to get at causal capacities in the economy while Uskali
Mäki has used it to describe how economists isolate particular accounts (models)
for theorizing purposes.27 As an example here, Jevons’ graphed economic man’s
experience of utility as dependent upon only two dimensions, its intensity and dur-
ation (Figure 1.5a). He did so because, by his own account, these were the two
most salient elements in motivating mans’ economic behaviour. is idealization
enabled him to leave aside six other dimensions of utility that Bentham had sug-
gested in an earlier verbal account. But this simplication also made it possible for
Jevons to represent man’s behaviour in making consumer choices into a form where
he could treat the problem mathematically.28 Such idealization processes of giving
form to economic models can be described as the formation of ideal types (using
Max Weber’s account, 1904 and 1913) or even as a process of drawing out a carica-
ture (see Chapter 4, and Morgan, 2006).
A fourth strand of literature, following Mary Hesse’s (1966) work, argues that
model-making, or giving form to a model, depends upon our cognitive abilities to
recognise similarities and our creativity in exploring those similarities.29 Scientists
choose models on the basis of similarities seen in the form, structure, content or
properties between two elds and investigate these similarities in a systematic way.
For example, Fisher (1911) chose a mechanical balance as a model for his economic
“equation of exchange” between money and goods because he recognised the simi-
larity between the elements and their relations (see Figure 1.5b and Morgan, 1999).
is ability to recognise similarities, and so to choose a form for a model, is only the
rst step, for it usually requires a lot of further work to ll out that form into a full
model. In another example, Phillips drew the little plumbing diagram (Figure 1.5d)
to help him to understand how the stocks and ows of a good interact in a market.
With the collaboration of the monetary economist Walter Newlyn, the model grew
into a large physical hydraulic machine of the economic system as a whole (see
Figure 1.7 and Chapter 5).30
27 For example, von ünen’s model has been described (by Mäki, 2004) as arrived at by the pro-
cess of “isolating” real-world aspects away for theoretical purposes, whereas it could also be
understood as a process of “causal idealization” (in Cartwright’s terms) since von ünen used
numerically based observations about his own farm in his model. On the general arguments on
idealization in economics, see Cartwright (1989) and Mäki (1992); a survey with further refer-
ences is provided in Morgan and Knuuttila (2012); Hamminga and De Marchi (1994) provide an
important collection of earlier papers on idealization reviewed in Morgan (1996).
28 Historical work suggests that Jevons’ gave form to his model not just through a process of ideal-
ization, but through an inspired transcription of ideas from several other elds and drew on his
own working experiences and on his creativity as a scientist (see Maas, 2005).
29 See also Gentner (2001).
30 Marcel Boumans (in Morgan and Boumans, 2004) has described the move from such a meta-
phor to a model as a move from a vague to a more exact form of representation: from the one-
dimensional representation of a metaphor to the two-dimensional analogical model, as in the
little diagram by Phillips of a market as a plumbing arrangement of Figure 1.5d, or to fully formed
three-dimensional model as in Fisher’s built hydraulic machine of Figure 1.3d (see Chapter 5).
e World in the Model
24
More recently, economists have themselves suggested that the point of
modelling is not to recognise analogies, but to create them, rather as Fisher
designed his analogical model of the gold standard mechanism in the late
nineteenth century (see Morgan, 1997). For example, Robert Lucas argues his
modelling of the business cycle creates “a mechanical, imitation economy”.31
Robert Sugden has argued that modellers create “credible worlds”, where the
credibility claim rests on some observed similarities in model outcomes, for
example, between those of a checkerboard puzzle with the analogous pattern of
segregated housing.32 In seeking to capture not the workings of real economies
but to mimic some aspect of it via an imagined analogous world, these practices
of design take us back to one of the historical roots of modelling in the arts
where crasmen built mechanical birds that would ‘sing’ but did not suppose
that birds were mechanical automata.
e activity of giving form to a model has been characterized in four dier-
ent ways here, and exploring and analysing these dierent ways of thinking about
model-making provide the subject matter of the next several chapters of this book.
But in this chapter, I am less concerned with the dierences in these accounts than
with the things that they have in common. When we look at the examples of mod-
els presented in this chapter, it is not obvious what these general qualities of model-
making might be. But certain points can be made, which, in part, arise from this
very variety in the nature of the objects that get made.
To begin with, these accounts all understand the scientist-economist as act-
ing in this process of model formation. It is obvious, but important to remem-
ber, that models are created by a knowing economist-scientist for a particular
purpose. Whether the scientist is best described as making a new recipe, using
his or her imagination and imaging powers, idealizing from some other account,
or choosing between dierent analogies, the point is that models don’t make
themselves.
Another shared feature is that, in making models, scientists form some kind
of a representation of something in the economy. While the activity of creating a
model can be described variously as representing, depicting, imagining, or imaging,
more generous terms such as rendering or denoting, oen seem equally pertinent
and accurate as descriptions of the activity of model-making. e very dierent
ways economist-scientists have of getting to their models, and the sheer variety
of forms they have created, support this pluralistic language. e important point
31 Lucas (1980, p. 697); he most famously said of his business cycle models that “A good model,
from this point of view, will not be exactly more ‘real’ than a poor one, but will provide better
imitations”. (1980, p. 697), leading to a discussion of the artefactual character of the results of such
modelling – see Hoover (1995) and Boumans (1997).
32 e notion of designed analogies or similarities is consistent with Sugden’s writings on how mod-
els are made and used in his discussions of the checkerboard and other examples (see his 2009
and 2002); see also Chapter 9 here. e development of ‘simulation’ in the 1960s as a way of using
models shares a mimicking aim, but without necessarily sharing any particular view of the nature
of models (see Chapter 8).
Modelling as a Method of Enquiry 25
here is that whatever term is used should not unduly limit our understanding of
what models are and how models work as a means of enquiry.33
ese accounts of model-making also suggest that forming models is not
driven by a logical process but rather involves the scientist’s intuitive, imagina-
tive, and creative qualities. When we look at the variety of objects displayed in
this chapter, it would be dicult to see what, if any, such a logical process could
possibly be that would cover all these instances. e importance of these crea-
tive qualities in the scientist’s model-making activities may reect the long-ago
roots of scientic modelling in the decorative cras. We found these evident in
the Tabl e au Économique, but they remain in the delight that economists take in
creating ‘elegant’ models.
Model-making is a skilled job. Perhaps it is not yet evident, but will become
so in the chapters that follow, that learning how to portray elements in the econ-
omy, learning what will t together, and how, in order to make the model work,
are specialised talents using a tacit, cra-based, knowledge as much as an artic-
ulated, scientic, knowledge. It is not easy to pinpoint in any general way these
skills of articulation and construction, or to see how economists acquire them
except through apprenticeship. Perhaps, like Pigou, it suces to note that some
economists have considerable talent in model-making, and that these talents of the
scientist-economist are recognised in the artefactual nature of the models that are
made. Economists recognise these talents in terms of the qualities of the models
themselves, where their term ‘fruitfulness’ indicates a model that is not just well
put together and easy to use but easy to extend, generates interesting ndings,
new questions, and so forth. Economists’ skills in articulating and craing models,
along with their imaginative and creative abilities, turn up in dierent ratios in dif-
ferent episodes of model-making, but they are all essential to the process of giving
form to models.
33 Although philosophers of science tend towards using the terminology of ‘representation’, it is the
subject of huge debate for the term raises a number of important and dicult problems. First, as
discussed here: what is the process of representation? I am sympathetic to R. I. G. Hughes’ (1997)
argument (following Nelson Goodman) that ‘denoting’ is a better term for the activity of model-
making than representing, for it makes clear that the models stands in relation to its economic sys-
tem “as a symbol for it” and that while there is “no representation without denotation”, denotation
is “independent of resemblance” (1997, S330-1). Second, how is a representation dened? (Are
models best thought of as maps, descriptions, structures, axiomatic systems, ctions, etc., or as
artefacts with exible representing relations?) e approach taken in this book, as in Morgan and
Morrison (1999), is more concerned with how scientists use models than with an analysis of them
as philosophical objects, so I use this awkward term representation as a descriptively useful one,
without apology, and leave the philosophical problems for elsewhere (see Morgan and Knuuttila,
2012), and for others (addressed in recent volumes edited by Grüne-Yano, 2009 and by Suárez,
2008; see also Knuuttila, 2005). ird, what is the nature of the representing relation? e import-
ance of this last lies in the view held by some philosophers that models have to represent the
world accurately – for example, have a structural isomorphism to the world – in order for us to
make truthful deductions about the world from them (for an early discussion in philosophy of
social sciences, see Brodbeck, 1968). I reframe this as an inference problem later in this chapter
(Section 5) and more fully later in the book.
e World in the Model
26
4.ii Becoming Formal
Each of these four processes of understanding model-making: recipe-making,
visualizing, idealizing and choosing an analogy, describes an act of giving form to
ideas about the economy. But by representing the economy in a particular form,
the economist-scientist at the same time creates an object that must obey certain
rules – which brings us to our second sense of formal: meaning subject to rule and
rigour in contrast to that sense of informal. Since in each particular case, these
rules form the rules of reasoning with that model, they eectively determine the
economist’s valid manipulation or use of that model. Where do these rules come
from? And, what kinds of rules are involved?
Rules for reasoning with a model come from two distinct aspects of the model.
First, when an economist reasons with any model, he or she must obey certain
reasoning rules according to the kind of the stu that the model is made from,
or language it is written in, or the format it has. So, these rules could be those
of geometry or algebra, of mechanics or hydraulics, etc. depending on the model.
Reasoning with Fisher’s equation, for example, was subject to the rules of arithmetic;
in contrast, reasoning with his mechanical balance model was subject to the rules
of behaviour, and so manipulation, of mechanical balances (both in Figure 1.5b).
Samuelson’s equations model (in Figure 1.4c) can be manipulated following the
formal rules for working with equations – either algebraically or arithmetically in
a simulation (and he does both, as we shall see in Chapter 6). An important point
about these kinds of rules are that they are given and xed by the substance of the
model, even where that model is a paper representation of a material model (as
in Fisher’s mechanical balance). ey are ‘formal’ rules in the sense that they are
not made them up each time the economist works with a particular model, rather,
they come ready made from the form or language the modeller has chosen for that
representation.
Second, and in contrast, allowable manipulations of the model are also deter-
mined and constrained by the economics subject matter represented in the model.
For example, Samuelson’s model of the macroeconomy must be manipulated in a
certain order, not just because the economic relations have a certain time order
(found in the equations’ subscripts) but because of the implied causal links given
by the economic content. In other cases, the characteristics and ambitions of model
economic man are used to motivate how the resources of an economic model are
used. For example, the reasoning in the Prisoner’s Dilemma model is determined
by the economists’ view of how the economic model man will act in the world of
the model. But – just as with the earlier Tab l eau Économique (in Figure 1.1) – the
matrix of numbers depicting the Prisoner’s Dilemma game in Figure 1.5e needs to
be accompanied by a text account of the economic rules for the situations that the
numbers represent before they can used in reasoning (see Chapter 9). ese kinds
of rules of manipulation don’t come with the form, they come from the economic
concepts and content that the model-maker uses in making the representation.
Modelling as a Method of Enquiry 27
ese two kinds of rules – the formal rules (those given by the form) and the
economic rules (those given by the subject matter) – taken together provide the
means of reasoning with a model.34 For example, the little hydraulic diagram from
Phillips is designed to work according to the hydraulics pictured, but is simultan-
eously subject to the rules of reasoning from the economic content enshrined in
the arrangements of the parts: where demand and supply, and price and quantity,
can be changed in particular ordered ways (Figure 1.5d). Usually the model form
is designed so that these two dierent sets of reasoning rules will be complemen-
tary in the way that the model works. But sometimes, particularly with analogical
models, they may turn out to be in conict – as indeed, happened with Fisher’s
mechanical balance, where his economic rules of adjustment at rst sight were at
odds with the mechanical ones of the balance; Fisher found a way to resolve this
dissonance by revising his economics (as we will see in Chapter 5). By the late twen-
tieth century, these dierent sources of rules in a model might no longer be sep-
arately recognisable, for modern economics had reached the point where (just as
McMullin [1985] noted in his discussion of physics) the concepts and arguments of
economics are so thoroughly intertwined with, and even drenched in, the terms of
their habitual mathematical expression that they can no longer be pulled apart. So
modern economists looking at Jevons’ graph of utility (Figure 1.5a), for example,
will nd it dicult to separate out the economic content from the mathematical
argument he made with it.
For the purposes of our investigations of modelling, we can now appreciate
how formalization here means that the economist-scientist both gives form to his
or her ideas and simultaneously makes them rule bound in the model. e model
is formed to represent their ideas about some aspects of the economic world, and
their reasoning with the model is bound by the rules appropriate to that particular
model – given by both its economic content and its language format. ese two dif-
ferent sources of rules – from a model’s format and from its subject content – deter-
mine and limit how each particular model can be used, and so, constitute the kinds
of right reasoning that are possible with that particular model. So when we look at
how an economist reasons with a model, we should expect to nd some very specic
reasoning rules being used. But what are these rules of reasoning to be used on?
4.iii Reasoning Resources
I argued earlier that representations become models only when they have the
resources for manipulation: this unlocks the puzzle of how any particular model
34 We might describe these as syntactic and semantic rules – those that come from the format (or
‘language’ structure in which the model is formed) being syntax, and those that come from the
economic meaning (the interpretation of the elements) being semantics. But this usage would not
map onto traditional philosophy of science usage, where the ‘syntactic versus semantic view of
models’ refer to dierent views of the relation of models to theories. A version of this explained
for economists is found in Hausman (1992).
e World in the Model
28
can be reasoned with.35 Here we return to Frisch, who recall was one of the rst
to produce a mathematically expressed model of the economic system as a whole
in an attempt to gure out how the elements of the economic system when put
together could create business cycles in economic activity.36
Frisch’s rst version of his model, in his now classic paper of 1933, was a
schema of economic activity (shown in Figure 1.6a here, on which capital letters
indicate stocks and lowercase letters indicate ows). It depicts his account of the
main elements in the economy: some are “visualized as receptacles” (the circles)
and “others may be visualized as machines that receive inputs and deliver outputs”
(the squares) (Frisch, 1933, p. 173). He called it a Tablea u Économique, surely a
reference back to Quesnay’s famous invention, and we can see that like that earlier
example (Figure 1.1), Frisch visualized quite a complicated set of circular ows
(indicated by arrows) around the elements in the system. Relative to Quesnay’s
Tabl e au Économique however, in which both numbers and ordering are specied
in his ‘table’, Frisch’s schema lacks the resources for the kind of model manipulation
that Quesnay was able to do. Quesnay could use his numbers, and their ordering,
to reason about the nature of the system he had depicted, and by playing around
with these numbers, explore various dierent kinds of systematic behaviour in his
model world and learn new things from so doing. Frisch’s diagram shows the ele-
ments and their links, but these can be used only for a verbal description of the rela-
tions, and verbal reasoning about them, but not for more rewarding explorations
that would tell him anything much about the behaviour of his system; indeed, with-
out those arrows, the scheme could hardly be reasoned with at all. Frisch’s schema
has limited resources for verbal reasoning and none for numerical manipulation. It
was, however, just a starting point.
From this scheme, Frisch developed a more simplied little mathematical
model connecting y, the annual production of capital goods, with x, the annual
production and consumption of consumer goods (there are no stocks held), and
zt, the amount of production going on at time t (Figure 1.6b). is little mathem-
atical model of the economic system had the resources – of both mathematical
and economic content – for Frisch to present it as a kind of machine: its form
and content could, with certain manipulations, produce a dynamic pattern. is
version of the model had sucient resources for him to carry out simulations (by
putting some parameter values in the equations) to show that the model could
generate a cyclical pattern in productive economic activity. is was an important
outcome, since one of Frisch’s main reasons for making the model was to demon-
strate that cyclical patterns could be generated by such a system of equations (see
Chapter 6).
35 Amongst the older tradition of philosophical writings on models, Black (1962), mentions manipu-
lation of models, but oers little in the way of discussion or analysis.
36 e story of Frisch’s model has been told several times in the history of economics: Morgan (1990)
concentrates on its place in the history of econometrics; Boumans (1999) on it as a new recipe in
modelling the business cycle; and Louça (2007) on its analogical aspects.
Modelling as a Method of Enquiry 29
In this example, the contrast between Frisch’s Tableau Économique and his little
mathematical model shows the importance of the presence of model resources that
can be manipulated in order to make the object useful as a model. In the schema,
there are resources that can be reasoned with, but they can not be manipulated in
such a way that you gain any understanding about the possibilities for business
cycles to occur from such reasoning. Recall that the rules for reasoning or manipu-
lation come from the model in two distinct senses – from the format (or language)
it has, and from the economic content. e schema has quite a lot of economic
content, content that can even be reasoned with to some extent, but the format is
that of a picture and pictures do not (generally) contain rules for their manipu-
lation. e equations have less content in the sense that there are fewer elements
and causal links, but the form (or language) of that content (equations) enables the
(a)
(b)
Figure 1.6. e Reasoning Resources in Models.
(a) Frisch’s Tab leau Économique.
Source: Ragner Frisch, “Propagation Problems and Impulse Problems in Dynamic
Economics”. Economic Essays in Honour of Gustav Cassel, 1933. London: George Allen &
Unwin Ltd. Figure 1, p. 174. Reproduced with permission from Ragner Frisch.
(b) Frisch’s Macro-Dynamic System.
Source: Ragner Frisch, “Propagation Problems and Impulse Problems in Dynamic
Economics”. Economic Essays in Honour of Gustav Cassel, 1933. London: George Allen &
Unwin Ltd., pp. 177 and 182. Reproduced with permission from Ragner Frisch.
e World in the Model
30
use of a deductive mode of manipulation so that Frisch can reason mathematically
about the nature of the business cycle with this version of his model.
ese examples from Frisch enable us to understand not only how the reason-
ing rules come along with the particular model that is built, but also how necessary
the resources are to provide materials to reason with. But this does not explain – in
a more general way – how those model resources are used, nor to what purpose,
though there are certainly hints in Frisch’s example. I turn now to suggest a more
general account of model reasoning.
5. Modelling as a Method of Enquiry:
e World in the Model, Models of the World
It is easy enough to say that modelling constitutes an epistemic genre, but we still
need to gure out how it functions as a way of doing economic science. Scott Gordon,
in his history and philosophy of the social sciences, argues that “the purpose of any
model is to serve as a tool or instrument of scientic investigation” (1991, p. 108).37
is forms the starting point for my claim, in the latter half of the book, that econo-
mists use models to investigate two dierent domains: to enquire into the world of
the model and to enquire into the world that the model represents.
Model-making – as we have already seen – is an activity of creating small worlds
expressed in another medium. e economist represents his/her ideas about certain
elements of the economy: the system as a whole, or people’s economic behaviour,
that they want to investigate or understand into other forms: into bits of mathemat-
ics, diagrams, machines, and even – sometimes – strictly dened verbal portraits.
e models have certain qualities – they are smaller-scale, and it is supposed, sim-
pler, than the real world, made of quite dierent materials, and their sense of repre-
sentation, imitation, or similarity might be quite opaque.38 I take up these awkward
qualities of the way economists render their accounts of the world into models in
Chapter 10, but for here, the point is rather that these representations – by design –
contain economists’ intuitions, or the things they already know, or both. at is,
sometimes these small worlds in the model primarily represent speculations and
theories about the economic world; the economist may be agnostic about how far
they represent the workings of that world, or even deny that they do so at all (as
we saw with Lucas), regarding them perhaps as parallel or imagined model worlds.
At other times, models are created primarily to incorporate (in some form) fea-
tures they already know, that is, to embody what the economist takes to be essential
37 Of course, I am not the rst to see models as instruments of enquiry in the social sciences (argu-
ably, Max Weber (1904, 1913) thought of his ideal types in this way – see Chapter 4), but few
suggestions along these lines explore how such instruments work.
38 A nice parallel is found in the studies of geologists who built small boxes and lled them with dif-
ferent materials to see what happened when big physical shocks hit them as a simulation model
for earthquakes (see Oreskes, 2007). On smallness see Chapter 10.
Modelling as a Method of Enquiry 31
features of the relevant section of the world, how the parts relate, how the elements
interact, and so forth, as with Frisch and Tinbergen. Most oen, the ‘world in the
model’ represents a combination of both economists’ ideas and their knowledge.
ese small objects, models, then have a stand-alone, autonomous, quality, that
enables them to lead a potentially double life for, I argue, models function both as
objects to enquire into and as objects to enquire with. at is, they are objects for
investigation in their own right, and they help the economist-scientist investigate
the real-world economy.39 Model investigations oer economists the possibilities to
speak both to their ideas and to their experience of the world at the same time, but
characterizing such work as a method of enquiry, exploration, even discovery, still
presents us with quite a puzzle. How do models provide such a method of enquiry
that enables this double life to go on? My answer is that model reasoning, as a
generic activity in economics, typically involves a kind of experiment.
Advancing the argument that appears later in the book, I suggest that we can
characterize model reasoning as a kind of experiment in the following way. Models
are made to address some particular purpose, and so working with a model typically
begins with the economist asking a question related to that purpose. To answer the
question, the economist makes an assumption that xes something in the model,
or changes something in the model, that is, in the diagrams or equations, or other
material, that the model is made in. He or she then investigates the eect of that
assumption, or change in the model, by manipulating the resources of the model
in a model experiment to demonstrate an answer. at demonstration is deduc-
tively made, for it uses the reasoning rules given in the language format and in the
carefully specied economic content of the model. e process of demonstration
itself prompts a narrative about the economic content. is combination of ques-
tions, experimental demonstrations, and narrative answers forms the way in which
the economist explores a particular model (see Morgan 2002 and Chapter 6). From
experimenting on the model, economists investigate and come to understand, in
the rst instance, only the world of the model. How such experimental investiga-
tions into the model might also provide some understanding about the world that
the model represents is a messier problem that I return to shortly.
Let me begin with the easy part of this double life of models: models as objects
to enquire into. Economists investigate the world in the model using this mode of
experiment to understand their economic ideas or theories. is seems odd: since
they created that little world in the model, wouldn’t they already understand it? Not
39 e ways that models function in these two domains in economics is not well accounted for by the
standard views in philosophy of science that have tended to worry about the denition of models
and to treat them either as mini-versions of theories or as ecient descriptions of data from the
world. As we will nd in the chapters that follow, the diagrammatic models of the Edgeworth
Box, Ricardo’s arithmetic chains, and Samuelson’s mathematical model of the Keynesian system
all function as independent forms: they embody ideas and knowledge about the economy, but are
themselves neither theories or data descriptions. In Morrison and Morgan (1999), we argued such
construction was responsible for the observed practical autonomy of models that enabled them to
mediate between the mathematics of theory and the empirics of observation (see Chapter 2).
e World in the Model
32
so, for if ideas about the world can be expressed very simply, economists don’t need
a model to think with. But as soon as they abstract two or three characteristics of
economic man together, or isolate two or three hypothesized relationships from the
economy at once, it becomes dicult to reason about what happens when they are
combined. at is why economists create models in the rst place, and why they
need this kind of experimental approach in order to answer questions about this
small person or world in the model.
Investigating the world in the model through such experimental means is the
way that economists explore their theories and intuitions.40 By asking questions
and making such investigations, they understand the implications of their intu-
itions, explore the limits of economic behaviour that their models imply, codify and
classify the various dierent outcomes that some more general theory might over-
look, and are prompted to develop new hypotheses about the behaviour of the ele-
ments represented in the model. For example, Samuelson wanted to know the eect
of increasing government expenditure. He found by his experiments on the little
mathematical model in his 1939 paper that the model could generate cyclical behav-
iour, explosive growth, or gradual decline in the elements of the model, according
to the numerical parameters he inserted into their relations. ese model explo-
rations provided some surprising answers about certain aspects of the Keynesian
account of the world as well as generating more understanding about the various
extant theories of business cycles.
e second part of this double life of models is the way that economists use
models as objects to enquire with, for it is clear, from the way economists work, that
the small person or world in the model also serves as an object to investigate the
aspect of the real people or real world that it is taken to represent. is aspect of
model work is much more dicult to characterize than the way economists use
models to investigate their ideas and theories.
Philosophers have problems at this point, and for good reasons. eir justly
sceptical argument goes as follows. If the model is an accurate representation –
in some way – of the relevant parts of the economic world or of economic man’s
behaviour, and if those elements can be treated in isolation, then it might be that
the results gained from model experiments can be applied directly and unambigu-
ously to the world, and give truthful statements and valid explanations about those
things in the world.41 ese ‘ifs’ are big ones – for how does the economist know
if they have an accurate model of the world? Or, that it can be treated in isola-
tion? It is this ignorance that creates philosophers’ worries about modelling, and,
40 Crombie assumed some kind of a one-for-one relationship: that “a model embodies a theory”
(1994, Vol. II, p1087), and on this basis, that the method of models oered “a characteristically
eective scientic combination of theoretical and experimental exploration.” is is certainly a
useful hint about experiments (which he does not expand), but the account of how models are
formed in this chapter, and various examples discussed in Chapters 2–6 suggest that the relation-
ships between theories and models are varied and not easy to characterise.
41 See, for a recent discussion, Cartwright (2009).
Modelling as a Method of Enquiry 33
most especially, their concern about the status of the representation involved. But
of course, it is just such problems – and this same lack of knowledge – that lead
economists, like scientists in other elds, to adopt modelling as a mode of investi-
gation in the rst place!
It may help to clarify my account of modelling as a double method of enquiry
in economics if we compare it with two of the other reasoning styles mentioned
earlier: the method of mathematical postulation and proof and the method of lab-
oratory experiment.
If we portray mathematical modelling as a version of the method of math-
ematical postulation and proof, then we could say that economists postulate the
economic world in the model and so could quite reasonably expect to make math-
ematical truths about that world in the model. is account works well for enqui-
ries into the world of the model: models can indeed be truth-makers about that
restricted and mathematical small world. But as economists recognise, these are
not truths that they can transport unconditionally to the world that the model rep-
resents. Economists (just like their astronomer forebears) understand that a model
stands in for their economic universe to enable them to explore certain properties
of that world represented in the model. But whether they can come to valid conclu-
sions about the behaviour of their actual economic universe is a much more di-
cult problem, as they know themselves.
If we make the alternative comparison with laboratory experiments, we get
an idea of how economists use a model as an object to enquire with. In this way
of understanding modelling as an epistemic genre, economists hypothesize how
the world is when they represent it in the model, and then experiment with that
world or person in the model to see how it behaves. en the important question
of whether the results of the experiment on the model can then be transferred to
the world that the model represents can be considered an inference problem. So, by
treating model enquiries as a form of experiment, the question of how this mode
of reasoning connects models to the world switches from a truth-making problem
to an inference problem, though no less dicult to answer.42 is is why I suggest
that we view modelling as a method of investigation and enquiry more akin to the
method of experiment than to the method of postulation and proof.
Of course, model experiments in economics are usually pen-and-paper, cal-
culator, or computer, experiments on a model world or an analogical world (such
as an hydraulic machine), not laboratory experiments on the real world. is has
implications for the inferences that can be made. ere are two issues here: one is
the form of the inference arguments, and the other is the power of the inferences
that can be made.
42 Others have suggested that the model-world relation might be thought of in inferential terms, but
without seriously considering the nature of the inference in practical terms, or whether the infer-
ential relation lies in the original construction of the model, or rather in its subsequent relation
back to the world (see for example Suárez, 2004 and Woody, 2004; and the essays in Grüne-Yano,
2009).
e World in the Model
34
Inference arguments from model experiments are informal: when economists
talk of ‘testing their models’ (having already assured themselves of their internal
mathematical qualities and coherence) they are interested in judging the useful-
ness of their model experiments by comparing the behaviour of the model world
to that of the real world in a kind of matching or bench-marking process. ey
may compare the model experimental behaviour of their thin model of economic
man with the behaviour of real economic people, or surmise how a particular pol-
icy change instituted in a model compares with the equivalent actual policy in the
world. A characteristic feature of these informal inference arguments from eco-
nomic models is that they oen involve narratives in making inferential or explan-
atory accounts that serve to link results from the experiment made into the world
in the model to events in the world that the model represents (discussed in various
ways in Chapters 6 to 9).43
ese informal comparisons made from model experiments to the world
clearly lack the formal decision rules based on probability measures found in statis-
tical inference, and that are used to validate and make inferences from econometric
models. But it is worth remembering that inferences made from laboratory experi-
ments also lack formal decision rules. Laboratory scientists, like modellers, depend
upon both tacit and articulated knowledge in making sense of their experimen-
tal ndings and judging their relevance within the laboratory.44 And, like model
work, laboratory scientists face the same question of whether their experimental
results can form the basis for inference beyond the laboratory, namely the problem
of external validity.45
But in another respect, clearly, the experiments made on models are dierent
from the experiments made in the laboratory, and the inferences that can be made
dier in principle. is has nothing to do with the formality or informality of the
inference argument, but rather, as I argue in Chapter 7, it is because model experi-
ments are less powerful as an epistemic genre. It does make a dierence to the power
and scope of inference that the model experiment is one carried out on a pen-and-
paper representation, that is, on the world in the model, not on the world itself.
While model experiments may surprise the economist with unexpected results, lab-
oratory experiments may confound the economist-scientist by producing results that
are not only unexpected but potentially unexplainable given existing knowledge.46
Let us look briey at a more complicated example to see how the model is
both an object to enquire into and an object to enquire with, holding these notions
of questions, deductive experiments using the resources of the model, and infor-
mal inferences, in mind. e Phillips-Newlyn Machine (shown in Figure 1.7 and
43 See Morgan (2001, 2007).
44 It is precisely this diculty that has led Deborah Mayo to advance her framework for making
inferences from experiments (see her 1996), which recognises that such inferences depend on the
knowledge of the scientist in making relevant pre- and post-experimental judgements.
45 See Chapters 7 and 8, and Guala (2005, chapter 7).
46 See discussion in Morgan (2003b, 2005).
Modelling as a Method of Enquiry 35
FOREIGN HELD
BALANCES
FOREIGN HELD
BALANCES
SURPLUS
BALANCES
SURPLUS
BALANCES
Figure 1.7. e Phillips-Newlyn Hydraulic Machine.
Source: e James Meade Archive, Box 16/3, BLPES Archives, LSE. Reproduced with permission
from the estate of James Meade.
e World in the Model
36
discussed fully in Chapter 5) is a big apparatus – a real hydraulic model – of which
we can see here only a drawing. e physical model itself operates according to
the language rules of hydraulics, with the ow of water around the machine con-
trolled by physical valves. But the overall form and parts of the of the machine are
designed to imitate the stocks and ows of money (red water) around an economy,
and the behavioural functions of the economic relations are drawn into the small
rectangular “slides” that can be seen on the drawing; these in their turn control the
opening and closing of the valves in the hydraulic system. Despite its complexity,
and even without knowing what these economic relations are, we can see how the
rules of form (hydraulics) and content (monetary macroeconomics) are instanti-
ated in the Machine.
e next point to see is how the Machine’s resources are reasoned with in an
experimental mode of investigations by using the rules of language and content.
e economist sets up the model to answer a particular question, such as: What
will happen if I increase the money in this system by increasing the liquid in the
“money tank” fed by “the central bank” (at the top right)? is is the experimental
intervention (or manipulation) into the world of the model. e pump circulates
this increased liquid through the machine, the valves control the ows according
to the economic relations ascribed in the model, and the model demonstration
churns out a set of outcomes of this experiment: the eects of this change in the
amount of money on the income in the economy is automatically charted in one of
the top right-hand corner graphs.
e Machine model has tremendous resources: it can be set up to answer any
number of questions – and thus associated model experiments. With some of these
questions the economist can enquire into abstruse points in economic theory, for
example, as to whether the interest rate is determined by the stock or ow of invest-
ment funds. Such questions and experiments about the world in the model make
demonstrations that enable those theories to be compared with each other. And
once economists have discovered how their world in the model works, they use
this knowledge to generate further questions about those theories. Another set of
questions are prompted by dierent historical or current situations that turn up
such as nancial crises or great depressions. ese deliver experimental outcomes
for the world in the model that economists will compare with the events that they
observe in the world. at is, with these questions, economists enquire with the
model into the world that the model represents. Economists may come to explain
or reinterpret or nd a new understanding about some aspects of the real-world
behaviour through these experimental means.47 at is how, by experimenting with
the model, economists can gain understanding and provide explanations of how the
47 Economists also use this model-generated knowledge to teach others their insights, for example,
economists used the Phillips-Newlyn Machine to demonstrate and explain the UK Government
policy changes (an experiment with the Machine screened by the BBC and visible now on a video
in the London Science Museum next to the Machine).
Modelling as a Method of Enquiry 37
economic world in the model works and use these in an informal way to reect on the
workings of the real economy that the model is taken to represent (see Morgan and
Boumans 2004, and Chapter 5).
So, modelling as a style of reasoning in economics works as a method of enquiry
comprising probing questions, manipulations to provide demonstrations that are
both deductive and experimental, and informal inference arguments involving ele-
ments of narrative that oer explanatory or interpretative services. ese charac-
teristics are explored in a nutshell format for Ricardo’s model farming experiments
in the next chapter. And, with a wider gaze, these characteristics of the style of prac-
tical reasoning of modelling are explored in dierent ways, and at much greater
depth, in the second half of the book.
6. Conclusion
Reasoning with models enables economists to enquire directly into their theories
or ideas about the world, and enables them to enquire indirectly into the nature of
the economic world. ey reason about the small world in the model and reason
about the big economic world with the model; they reason about the thin economic
man in the model and reason about real people with the model man. Yet, critically,
these two spaces of exploration are not always clearly demarcated: in working with
models economists oen simultaneously investigate the world in the model and the
world their model represents. In this sense, reasoning with economic models is like
reasoning with astronomical models. ose models exemplied astronomers’ the-
ories about the arrangements of the heavens, and could be used to explore the full
implications about those ideas at the very same time as being used to oer explana-
tions or accounts for particular observed events or patterns in the behaviour of the
heavenly bodies. Economic models, like those models of the planetary system, are
objects to enquire into and argue over, but at the same time ones to take to the world
and explore it to gain understanding, insight, or explanations from doing so.
e comparison between astronomical models and economic models that has
woven its way through this chapter is not just an heuristic comparison that helps us
see how economists use models, but reminds us that the modelling style of reasoning
has an illustrious history. Indeed, the scientic revolution of the sixteenth and sev-
enteenth centuries was not just one of content, but of styles of reasoning. Modelling
has been portrayed as the working method of Galileo no less, and continues to be
prevalent in modern natural sciences.48 Despite this ancestry, economists are not
quite sure that the method has a credible scientic respectability. Models are rela-
tively small and simple compared to the economic world, they are made of dier-
ent materials, and cannot well be applied directly to that world. Even so, like those
48 Hacking, for example, recognises it as the basic method of “cosmology and cognitive science –
none other than the chief modern instances of the Galilean style. . . .” (Hacking, 1992a, p. 7).
e World in the Model
38
models of the universe of earlier days, economic models may capture the heart of
the problems that economists seek to understand. Modelling is not an easy way to
nd truths about the economy, but rather a practical form of reasoning for econo-
mists, a method of exploration, of enquiry, into both their ideas and their world.
at is the thesis of this book.
Acknowledgement
Elements of this chapter were written for an address “Forms and Tools in 20th Century
Economics” to the Association Charles Gide September 1999 in Paris, at their meeting on
the theme “Modèles formels et théorie économique: histoire, analyse, épistémologiques”.
I thank Annie Cot and the Scientic Organising Committee of that society for their invita-
tion, memorable for the imposing room in the Sorbonne in which my talk took place. e
argument was subsequently presented at Duke University in February 2000. More recent
elements of the chapter have been developed for talks to development specialists at Bonn
(ZEF), at Rotterdam (econometrics seminar), at the University of Oslo’s 75th Anniversary
of their Institute of Economics, at the Summer Institute for History of Economic ought
at George Mason University, at Les Treilles, France for a workshop on style in science, at the
University of Toronto (HPS seminar), at Chung Cheng University, Taiwan (conference on
“Models and Evolution in Economics and Biology”), and at University of São Paulo, Brazil
(Symposium on the “History of Post-War Economics”). I am grateful to those who com-
mented on all these occasions. I particularly thank: Roy Weintraub for our many conversa-
tions about the history of mathematics in relation to economics; Marcel Boumans for many
discussions of modelling; Charles Baden-Fuller for commenting so carefully on various
dras of this chapter; and Sheldon Steed for research assistance.
References
Backhouse, Roger E. (1998) “If Mathematics Is Informal, en Perhaps We Should Accept
that Economics Must Be Informal Too”. Economic Journal, 108:451, 1848–58.
Baumol, William (1951) Economic Dynamics. New York: Macmillan.
Black, Max (1962) Models and Metaphors. Ithaca, NY: Cornell University Press.
Boltzmann, Ludwig (1911) “Models”. In Encyclopaedia Britannica (11th ed, pp. 638–40).
Cambridge: Cambridge University Press.
Boumans, Marcel (1993) “Paul Ehrenfest and Jan Tinbergen: A Case of Limited Physics
Transfer”. In Neil De Marchi (ed), Non-Natural Social Science: Reecting on the
Enterprise of More Heat than Light (pp. 131–56). Annual Supplement to History of
Political Economy, Vol. 25. Durham, NC: Duke University Press.
(1997) “Lucas and Articial Worlds”. In John B. Davis, D. Wade Hands, and Uskali Mäki
(eds), New Economics and Its History (pp. 63–88). Annual Supplement to History of
Political Economy, Vol. 29. Durham, NC: Duke University Press.
(1999) “Built-In Justication”. In Mary S. Morgan and Margaret Morrison (eds), Models
as Mediators (pp. 66–96). Cambridge: Cambridge University Press.
(2005) How Economists Model the World to Numbers. London: Routledge.
Brodbeck, May 1968 [1959] “Models, Meaning and eories”. In May Brodbeck (ed),
Readings in the Philosophy of the Social Sciences (pp. 579–601). New York: Macmillan.
Modelling as a Method of Enquiry 39
Cartwright, Nancy (1989) Nature’s Capacities and eir Measurement. Oxford: Clarendon
Press.
(2009) “If No Capacities, en No Credible Worlds. But Can Models Reveal Capacities?”
In Till Grüne-Yano (ed), Economic Models as Credible Worlds or Isolating Tools?
Special Issue of Erkenntnis 70:45–58.
Charles, Loïc (2003) “e Visual History of the Tableau Économique”. European Journal of
the History of Economic ought, 10:4, 527–50.
Chemla, Karine (2003) “Generality above Abstraction: e General Expressed in Terms of
the Paradigmatic in Mathematics in Ancient China”. Science in Context, 16:3, 413–58.
Chick, Victoria and Sheila Dow (2001) “Formalism, Logic and Reality: A Keynesian
Analysis”. Cambridge Journal of Economics, 25:6, 705–22.
Colander, David (2000) “e Death of Neoclassical Economics”. Journal of the History of
Economic ought, 22:2, 127–43.
Crombie, Alistair C. (1988) “Designed in the Mind: Western Visions of Science, Nature and
Humankind”. History of Science, 26, 1–12.
(1994) Styles of Scientic inking in the European Traditions, Vols. I–III. London:
Duckworth.
Edgeworth, Francis Y. (1881) Mathematical Psychics. London: Kegan Paul.
(1889) “Opening Presidential Address”, Section F: Economic Science and Statistics,
Nature, Sept. 19, 496–509.
Fisher, Irving (1892/1925) Mathematical Investigations in the eory of Value and Prices
(thesis of 1891). New Haven: Yale University Press.
(1911) e Purchasing Power of Money. New York: Macmillan.
Fleck, Ludwik (1935; 1979 translation) Genesis and Development of a Scientic Fact (trans-
lated by F. Bradley and T. J. Trenn). Chicago: University of Chicago Press.
Forrester, John (1996) “If p, en What? inking in Cases”. History of the Human Sciences,
9:3, 1–25.
Foucault, Michel (1970) e Order of ings: An Archaeology of the Human Sciences. New
York: Random House.
Frisch, Ragnar (1933) “Propagation Problems and Impulse Problems in Dynamic
Economics”. In Economic Essays in Honour of Gustav Cassel (pp. 171–205). London:
Allen & Unwin.
Gentner, Dedre (2001) Analogy in Scientic Discovery: e Case of Johannes Kepler. In
Magnani and Nersessian, 2001, pp. 21–40.
Giere, Ronald (2001) “Models as Parts of Distributed Cognitive Systems”. In Lorenzo
Magnani and Nancy J. Nersessian (eds), Model-Based Reasoning: Science, Technology,
Valu es (pp. 227–42). New York: Kluwer Academic/Plenum Press.
Goldfarb, Robert S. and Jon Ratner (2008) “‘eory’ and ‘Models’: Terminology rough
the Looking Glass”. Econ Journal Watch, 5:1, 91–108.
Goodman, Nelson (1978) Ways of Worldmaking. Indianapolis: Hackett.
Gordon, Scott (1991) e History and Philosophy of Social Science. New York: Routledge.
Grüne-Yano, Till (2009) [ed] Economic Models as Credible Worlds or Isolating Tools?
Special Issue of Erkenntnis, 70:1.
Guala, Francesco (2005) e Methodology of Experimental Economics. Cambridge:
Cambridge University Press.
Hacking, Ian (1992a) “‘Style’ for Historians and Philosophers”. Studies in the History and
Philosophy of Science, 23:1, 1–20.
(1992b) “Statistical Language, Statistical Truth and Statistical Reason: e Self-
Authentication of a Style of Scientic Reasoning”. In Ernan McMullin (ed), e Social
Dimensions of Science (pp. 130–57). Notre Dame, IN: University of Notre Dame Press.
e World in the Model
40
(1992c) “e Self-Vindication of the Laboratory Sciences”. In Andrew Pickering (ed),
Science as Practice and Culture (pp. 29–64). Chicago: University of Chicago Press.
(1993) “Working in a New World: e Taxonomic Solution”. In Paul Howich (ed), World
Changes: omas Kuhn and the Nature of Science (pp. 275–310). Cambridge, MA: MIT
Press.
Hamminga, Bert and Neil De Marchi (1994) [eds] Idealization in Economics. Amsterdam:
Rodopi.
Harford, Tim (2008) e Logic of Life. London: Little, Brown.
Harrod, Roy (1939) “An Essay in Dynamic eory”. Economic Journal, 49:193, 14–33.
(1968) “What Is a Model?” In N. Wolfe (ed), Value, Capital and Growth (pp. 173–91).
Edinburgh: Edinburgh University Press.
Hausman, Daniel M. (1992) e Inexact and Separate Science of Economics. Cambridge:
Cambridge University Press.
Hesse, Mary (1966) Models and Analogies in Science. Notre Dame, IN: University of Notre
Dame Press.
Hicks, John, R. (1937) “Mr. Keynes and the ‘Classics’: A Suggested Interpretation”.
Econometrica, 5, 147–59.
Hoover, Kevin D. (1995) “Facts and Artifacts: Calibration and the Empirical Assessment of
Real-Business-Cycle Models”. Oxford Economic Papers, 47:1, 24–44.
Hughes, R. I. G. (1997) “Models and Representation”. Philosophy of Science, 64:S325–36.
Humphrey, omas, M. (1995) “When Geometry Emerged: Some Neglected Early
Contributions to Oer-Curve Analysis”. Economic Quarterly, 81:2, 39–73.
Ingrao, Bruna and Giorgio Israel (1987) e Invisible Hand, English edition (1990).
Cambridge, MA: MIT Press.
Israel, Giorgio (2002) “e Two Faces of Mathematical Modelling: Objectivism vs
Subjectivism, Simplicity vs Complexity”. In P. Cerria, P. Fregiglio and C. Pellegrini (eds),
e Application of Mathematics to the Sciences of Nature (pp. 233–). New York: Kluwer.
Jevons, William St. (1871) e eory of Political Economy. London: Macmillan.
Johnson, W. E. (1896) “Method of Political Economy”. In R. H. Inglis Palgrave (ed),
Dictionary of Political Economy, Vol. II (pp. 739–48). London: Macmillan.
Katzner, Donald W. (1991) “In Defense of Formalization in Economics”. Methodus, 3:1, 17–24.
Keynes, John M. (1936) e General eory of Employment, Interest and Money. London:
Macmillan.
(1973) e Collected Writings of John Maynard Keynes, Vol. XIV, ed D. Moggridge.
London: Macmillan.
Klein, Judy L. (2001) “Reections from the Age of Economic Measurement”. In Judy L. Klein
and Mary S. Morgan (eds), e Age of Economic Measurement (pp. 111–36). Annual
Supplement to History of Political Economy, Vol. 33. Durham, NC: Duke University
Press.
Klein, Ursula (2001) [ed] Tools and Modes of Representation in the Laboratory Sciences.
Boston Studies in the Philosophy of Science. Dordrecht: Kluwer.
(2003) Experiments, Models, Paper Tools: Cultures of Organic Chemistry in the Nineteenth
Century. Stanford, CA: Stanford University Press.
Knuuttila, Tarja (2005) “Models, Representation, and Mediation”. Philosophy of Science, 72,
1260–71.
Krugman, Paul (1998) “Two Cheers for Formalism”. Economic Journal, 108:451, 1829–36.
Kuczynski, M. and Ronald Meek (1972) Quesnay’s Tableau Économique. London:
Macmillan.
Kuhn, omas (1962) e Structure of Scientic Revolutions. Chicago: University of Chicago
Press.
Modelling as a Method of Enquiry 41
Le Gall, Philippe (2007) A History of Econometrics in France. London: Routledge.
Leontief, Wassily W. (1946) “e Pure eory of the Guaranteed Annual Wage Contract”.
Journal of Political Economy, 54, 76–79.
Levitt, Steven D. and Stephen J. Dubner (2005) Freakonomics. New York: Harper
Perennial.
Louça, Francisco (2007) e Years of High Econometrics. London: Routledge.
Lucas, Robert E. (1980) “Methods and Problems in Business Cycle eory”. Journal of
Money, Credit and Banking, 12, 696–715.
Luce R. Duncan and Howard Raia (1957) Games and Decisions. New York: Wiley.
Maas, Harro (2005) William Stanley Jevons and the Making of Modern Economics. Cambridge:
Cambridge University Press.
MacKenzie, Donald A. (2006) An Engine, Not a Camera: How Financial Models Shape
Markets Cambridge, MA: MIT Press.
Magnani, Lorenzo and Nancy J. Nersessian (2001) [eds] Model-Based Reasoning: Science,
Technology, Values. New York: Kluwer Academic/Plenum Press.
Mäki, Uskali (1992) “On the Method of Isolation in Economics”. In Craig Dilworth (ed),
Idealization IV: Intelligibility in Science (pp. 317–51). Amsterdam: Rodopi.
(2004) “Realism and the Nature of eory: A Lesson from J. H. von ünen for Economists
and Geographers”. Environment and Planning A, 36, 1719–36.
Malthus, omas R. (1803) “An Essay on the Principle of Population”. Everyman edition,
1914, reprinted 1982. London: Dent.
Marshall, Alfred (1879) “e Pure eory of Foreign Trade”. In John K. Whitaker [ed]
(1975), e Early Economic Writings of Alfred Marshall, 1867–1890, Vol. 2, Part III.5.
London: Macmillan for the Royal Economic Society.
Mayo, Deborah (1996) Error and the Growth of Experimental Knowledge. Chicago: University
of Chicago Press.
McCloskey, D. N. (1991) “Economic Science: A Search rough the Hyperspace of
Assumptions”. Methodus, 3:1, 6–16.
McMullin, Ernan (1985) “Galilean Idealization.” Studies in History and Philosophy of Science,
16:3, 247–73.
Meade, James E. (1937) “A Simplied Model of Mr. Keynes’ System”. Review of Economic
Studies, 4:2, 98–107.
Meli, Domenico Bertoloni (2006) inking with Objects: e Transformation of Mechanics
in the Seventeenth Century. Baltimore: Johns Hopkins University Press.
Mirowski, Philip (2002) Machine Dreams: Economics Becomes a Cyborg Science. Cambridge:
Cambridge University Press.
Morgan, Mary S. (1990) e History of Econometric Ideas. Cambridge: Cambridge University
Press.
(1996) “Idealization and Modelling” (A Review Essay). Journal of Economic Methodology,
3:1, 131–8.
(1997) “e Technology of Analogical Models: Irving Fisher’s Monetary Worlds”.
Philosophy of Science, 64, S304–14.
(1999) “Learning from Models”. In Mary S. Morgan and Margaret Morrison (eds), Models
as Mediators: Perspectives on Natural and Social Sciences (pp. 347–88). Cambridge:
Cambridge University Press.
(2001) “Models, Stories and the Economic World”. Journal of Economic Methodology,
8(3), 361–84.
(2002) “Model Experiments and Models in Experiments”. In Lorenzo Magnani and Nancy
Nersessian (eds), Model-Based Reasoning: Science, Technology, Values (pp. 41–58).
Dordrecht: Kluwer Academic/Plenum Press.
e World in the Model
42
(2003a) “Economics”. In T. Porter and D. Ross (eds), e Cambridge History of Science, Vol. 7:
e Modern Social Sciences (pp. 275–305). Cambridge: Cambridge University Press.
(2003b) “Experiments Without Material Intervention: Model Experiments, Virtual
Experiments and Virtually Experiments”. In H. Radder (ed), e Philosophy of Scientic
Experimentation (pp. 216–35). Pittsburgh: University of Pittsburgh Press.
(2004) “Imagination and Imaging in Economic Model-building”. Philosophy of Science
(Proceedings of the 2002 Biennial Meeting of the Philosophy of Science Association),
71:5, 753–66.
(2005) “Experiments versus Models: New Phenomena, Inference and Surprise”. Journal
of Economic Methodology, 12:2, 317–29.
(2006) “Economic Man as Model Man: Ideal Types, Idealization and Caricatures”. Journal
of the History of Economic ought, 28:1, 1–27.
(2007) “e Curious Case of the Prisoner’s Dilemma: Model Situation? Exemplary
Narrative?” In A. Creager, M. Norton Wise, and E. Lunbeck, Science Without Laws:
Model Systems, Cases, Exemplary Narratives (pp. 157–85). Durham, NC: Duke
University Press.
(2008/online) “Models”. In S. N. Durlauf and L. E. Blume (eds), e New Palgrave
Dictionary of Economics, 2nd ed. London: Palgrave Macmillan http://www.
dictionaryofeconomics.com/dictionary
Morgan, Mary S. and Marcel Boumans (2004) “Secrets Hidden by Two-Dimensionality: e
Economy as a Hydraulic Machine”. In Soraya de Chadarevian and Nicholas Hopwood
(eds), Models: e ird Dimension of Science (pp. 369–401). Stanford, CA: Stanford
University Press.
Morgan, Mary S. and Tarja Knuuttila (2012) “Models and Modelling in Economics”; forth-
coming in Uskali Mäki (ed), Handbook of the Philosophy of Economics (one volume of
the Handbook of the Philosophy of Science. General Editors: Dov Gabbay, Paul agard,
and John Woods). Amsterdam: Elsevier/North-Holland. Available at: http://papers.
sspn.com/sol3/papers.cfm?abstract_id=1499975.
Morgan, Mary S. and Margaret Morrison (1999) [eds] Models as Mediators: Perspectives on
Natural and Social Science. Cambridge: Cambridge University Press.
Morrison, Margaret and Mary S. Morgan (1999) “Models as Mediating Instruments”. In
Mary S. Morgan and Margaret Morrison (eds), Models as Mediators: Perspectives on
Natural and Social Science (pp. 10–37). Cambridge: Cambridge University Press.
Nersessian, Nancy J. (1992) “In the eoretician’s Laboratory: ought Experimenting as
Mental Modelling”. PSA Proceedings of the Biennial Meeting of the Philosophy of Science
Association, 2, 291–301.
(2008) Creating Scientic Concepts. Cambridge, MA: MIT Press.
Niehans, Jürg (1990) A History of Economic eory. Baltimore: Johns Hopkins University
Press.
Oreskes, Naomi (2007) “From Scaling to Simulation: Changing Meanings and Ambitions
of Models in the Earth Sciences”. In Angela Creager, M. Norton Wise, and Elizabeth
Lunbeck (eds), Science Without Laws: Model Systems, Cases, Exemplary Narratives
(pp. 93–124). Durham, NC: Duke University Press.
Pigou, Arthur C. (1931) “e Function of Economic Analysis”. In Arthur C. Pigou and Dennis
H. Robertson, Economic Essays and Addresses (pp. 1–19). London: P. S. King & Son.
Qin, Duo (1993) e Formation of Econometrics. Oxford: Clarendon.
Rheinberger, Hans-Jörg (1997) Towards a History of Epistemic ings. Stanford, CA:
Stanford University Press.
Ricardo, David (1821) e Principles of Political Economy and Taxation (3 editions: 1817,
1819 and 1821; 1821 reprinted in Piero Sraa and Maurice H. Dobb (eds), Vol. 1:
Modelling as a Method of Enquiry 43
Collected Works and Correspondence of David Ricardo (1951). Cambridge: Cambridge
University Press.
Robinson, Joan (1933) e Economics of Imperfect Competition. London: Macmillan.
Samuelson, Paul A. (1939) “Interactions between the Multiplier Analysis and the Principle
of Acceleration”. Review of Economics and Statistics, 21, 75–78.
Schumpeter, Joseph A. (1935) “e Analysis of Economic Change”. Review of Economic
Statistics, 17:4, 2–10.
Shapin, Steven and Simon Schaer (1985) Leviathan and the Air-Pump. Princeton: Princeton
University Press.
Solow, Robert M. (1997) “How Did Economics Get at Way and What Way Did It Get?”
Daedalus, 126:1, 39–58 (reprinted fall 2005, Daedalus).
Suárez, Mauricio (2004) “An Inferential Conception of Scientic Representation.” Philosophy
of Science (Proceedings of the 2002 Biennial Meeting of the Philosophy of Science
Association), 71:5, 767–79.
(2008) [ed] Fictions in Science: Philosophical Essays on Modeling and Idealization. New
York and London: Routledge.
Sugden, R. (2002) “e Status of eoretical Models in Economics”. In U. Mäki (ed), Fact
and Fiction in Economics: Models, Realism and Social Construction (pp. 107–36).
Cambridge: Cambridge University Press.
(2009) “Credible Worlds, Capacities and Mechanisms”. In Till Grüne-Yano (ed),
Economic Models as Credible Worlds or Ioslating Tools? Special Issue of Erkenntnis,
70:1, 3–27.
Tinbergen, Jan (1937) An Econometric Approach to Business Cycle Problems. Paris: Hermann
& Cie.
Van den Berg, Richard (2002) “Contemporary Responses to the Tableau Économique”. In S.
Boehm, C. Gehrke, H. D. Kurz, and R. Sturn (eds), Is ere Progress in Economics? (pp.
295–316). Cheltenham: Edward Elgar.
Von ünen, Johann Heinrich ([1826]1966) Von ünen’s Isolated State (English translation
of Der isolierte Staat, 1966, translated by Carla M. Wartenberg; ed Peter Hall). Oxford:
Pergamon Press.
Vosniadou, Stella (2001) “Mental Models in Conceptual Development”. In Lorenzo Magnani
and Nancy J. Nersessian (eds), Model-Based Reasoning: Science, Technology, Valu es
(pp. 353–68). New York: Kluwer Academic/Plenum Press.
Walras, Leon (1874/1954) Elements of Pure Economics, translated by William Jaé. London:
Allen and Unwin for the American Economic Association and Royal Economic
Society.
Weber, Max (1904) “Objectivity in Social Science and Social Policy”. In e Methodology of
the Social Sciences translated and edited by Edward A. Shils and Henry A. Finch, 1949
(pp. 49–112). New York: Free Press.
(1913) e eory of Social and Economic Organisations (translated by A. M. Henderson
and Talcott Parsons, Part I of Wirtsha und Gesellscha, 1947). New York: Free Press.
Weintraub, E. Roy (2002) How Economics Became a Mathematical Science. Durham, NC:
Duke University Press.
(2008) “Mathematics and Economics”. In Steven Durlauf and Lawrence Blume (eds),
e New Palgrave Dictionary of Economics, 2nd ed. London: Macmillan; Available
online at http://www.dictionaryofeconomics.com/article?id=pde2008_M000372&
goto=M&result_number=2269.
Woody, Andrea (2004) “More Telltale Signs: What Attention to Representation Reveals
about Scientic Explanation”. Philosophy of Science (Proceedings of the 2002 Biennial
Meeting of the Philosophy of Science Association), 71:5, 780–93.
44
2
Model-Making: New Recipes, Ingredients,
and Integration
1. Ricardo, the “Modern” Economist? 44
2. Ricardo, His Economy, and the Economy of His Day 47
2.i David Ricardo, Esq. 47
2.ii Economics Matters, Experimental Farming Matters 51
3. Constructing Ricardo’s Numerical Model Farm and Questions of
Distribution 56
3.i e Numbers in Ricardo’s Principles and Experimental
Accounts 58
3.ii e Spade-Husbandry Debate 69
4. Ricardo’s Model Farm and Model Farming 73
4.i ree Model Farms in One 74
4.ii A Model Farm that Worked According to Ricardo’s
Economic Ideas 75
4.iii A Model of an Individual Farm in the Period 76
4.iv A Model Farm for the Whole Agricultural Sector 78
5. Model-Making: Creating New Recipes 79
5.i Ingredients 79
5.ii Fitting ings Together: Integration and Reasoning
Possibilities 81
Appendix 1: Numerical Argument in Ricardo’s 1815 Essay 83
1. Ricardo, the “Modern” Economist?
David Ricardo is revered by many economists as the rst ‘modern’ economist –
and equally blamed by others – for having introduced abstract reasoning into
economics. Both sides believe him to have initiated a style of economic argument
characterized by the use of small, idealized examples that seem to be hypothetical
and unconnected to the world in which he lived, but Ricardo himself found them
Model-Making: Ingredients and Integration 45
useful in arguing about practical problems and events. is description of his way
of arguing suggests that Ricardo was one of the pioneers of economic modelling.1
Consider rst an example widely known to economists: Ricardo’s argument
in favour of free trade based on his notion of comparative advantage. He made
his case using a little numerical example of the trade in wine and cloth between
Portugal and England, drawn from the experience of his day. ough Portugal
could produce both goods with less labour (i.e., she had an absolute advantage in
the production of both goods), his verbal argument with the numerical example
showed how it was advantageous for both countries to specialise and produce only
that good in which they each had a comparative advantage (England in cloth and
Portugal in wine) and then to exchange those goods with each other.2 e numeri-
cal example works so well that it has continued to feature, sometimes even with the
same countries and goods, to demonstrate the theory of comparative advantage in
modern textbooks (even though economists no longer believe in the labour theory
of value that underlies the way the numerical example worked for Ricardo). is
200-year-old example ts the way that modern economics is oen taught at an ele-
mentary level in terms of a small world, a world of two goods and two consumers:
Ricardo’s example seems already a modelled world.
But this little 2 × 2 world, and the ease with which modern economists can use it,
makes a misleading introduction to Ricardo’s work for two reasons. First, Ricardo’s
writings in political economy are generally not at all easy to follow for the modern
economist trained in modelling, for they are characterized by long chains of verbal
reasoning with numerical chains incorporated into them rather than diagrams or
mathematical equations.3 Second, these dicult numerical chains sit within a very
dierent tradition: economists of the classical school thought, and argued, in terms
of laws and principles, not models. ey did not habitually make nor reason with
models of the economy: especially created, small-world examples of how bits of
1 ere are several candidates for the title of ‘rst modern economist’, meaning one who uses the
technologies of modern economics, and a variety of national heroes to choose from. For example,
Cournot on the French side, and Jevons, on the British side, both score highly for the introduc-
tion of mathematical and statistical methods. e claims for Ricardo relate to his development of
abstract reasoning, associated here with modelling, for whom the comparable German claimant
might be von ünen, though as Chapter 1 showed, Quesnay’s Tableau Économique has prior-
ity claims as the ‘rst’ model. O’Brien (1975) claims: “Ricardo’s system was, if not entirely the
rst, certainly the rst sweepingly successful example of economic model building” (p. 37). He
describes Ricardo as “inventing these techniques” and “Ricardo’s deductive method . . . . as a pro-
cess of heroic abstraction” (p. 42) (a process labelled “the Ricardian Vice”: see Schumpeter, 1954,
pp. 472–3). As this chapter shows, my view is that Ricardo’s model-building was a mixture of
inductive and deductive work, and not a process of abstraction – on which see Chapter 4.
2 is example occurs in his Principles of Political Economy and Taxation (1817/19/21), chapter 7.
I thank Robert Went (see his 2002) for the information that there had indeed been such a switch,
with Portugal giving up making textiles and specialising in wine to trade with English cloth dur-
ing the eighteenth century (though this change was not necessarily fully to the advantage of both
countries, nor a free market decision).
3 Perhaps because Ricardo is known as the ‘rst modern economist’, a number of economists have
confessed to me that they once thought they ought to read Ricardo, but gave it up as too dicult!
e World in the Model
46
the economic system might work. For them, the economy was governed by laws,
general and strict, just as the natural world was, and the task of the economist was
to discover, or formulate, those laws taking account of the evidence of the day and
of history.
Ricardo’s work does not look as if it contains, or relies on, such things as models
and he did not consciously work in a scientic tradition that used models to rea-
son with. Yet, this chapter shows that Ricardo was indeed something of a pioneer
in modelling, though his models, like most economic models that reach us from
the past, are not self-evident things. Consider briey a less well-known numerical
example, in which he successively adds teams of ten labourers at a time to cultivate
a eld. Following its rst appearance in a footnote, this numerical example becomes
the site on which his famous laws of distribution are demonstrated. It is also the
numerical example from which Ricardo discovered just how easy it would be for
an economy to end up with no growth. In other words, this case turns out to play a
critical role in his principles of political economy, as we see in this chapter, though
the idea of adding more and more labourers to the same plot of land may seem to
us strangely unreal. Was he so remote from the agricultural realities that he did not
know about ploughs and horses!? What economic problem was Ricardo attacking?
How did questions about agriculture come up in the economic debates of his day?
Can we make sense of Ricardo’s reasoning with such numerical examples? Why did
his use of these numerical accounts look like experiments? And how did he t these
numerical chains together to play such an important role in his work?
To understand Ricardo’s numerical chains, and his reasoning with them,
requires little mathematical skill, but very considerable knowledge of the econom-
ics and of the economy of that day, as provided in the rst part of the chapter. Only
when we have that knowledge can we begin to appreciate how each of these numer-
ical chains embedded not just Ricardo’s ideas about the economy but also evidence
of the day (such as the prices of wheat, and agricultural experiments), as we nd in
the second part of this chapter.4 When pulled together – as ingredients of a recipe
are – these numerical accounts formed a model, indeed quite a sophisticated one,
for, by integrating together the separate numerical accounts, he built up a ‘model
farm’. And he used that model for ‘model farming’: processes of reasoning that
enabled him to gure out the laws of his economic system. I discuss, in the nal
part of the chapter, how these numerical chains did more than illustrate Ricardo’s
arguments and more than support his propositions: rather they functioned to dem-
onstrate Ricardo’s laws of distribution.
So Ricardo’s model farm provides a wonderful example of how the process of
model development creates understanding for an economist, and how, by providing
4 Historians of economics have not paid a great deal of attention to these numbers, with the excep-
tion of Barkai, who correctly argues that Ricardo supported his theoretical propositions “by means
of a model, the core of which is, as usual for him a numerical example” (Barkai 1986, p. 596). See
also Barkai (1959), Gootzeit (1975), and O’Brien (1975, pp. 121–9).
Model-Making: Ingredients and Integration 47
some unexpected results from the new mix of elements, economists learn from
developing the ingredients and integrating them into these small-world accounts.
I start by explaining why Ricardo was so knowledgeable about agriculture so that we
might grasp, in what follows, the originality of his way of arguing in economics.
2. Ricardo, His Economy, and the Economy of His Day
2.i David Ricardo, Esq.
David Ricardo was born in the east end of London in 1772 into a Jewish family of
successful nanciers.5 He fell in love with the Quaker girl down the street and mar-
ried in 1793; their marriage was a happy one and blessed with children, but created
family cuts on both sides. Yet he was already suciently established to make his
own way in the City of London, and enjoyed a successful career there, particu-
larly in helping to nance the British government’s engagement in the Napoleonic
Wars. His interest in economics dates from 1799, when he picked up a copy of
Adam Smith’s Wealth of Nations during a family stay in Bath, and he began to write
pamphlets and papers on matters of nance and currency. In 1814, having made a
very considerable fortune, he began to buy country estates and lent out money on
mortgages, including one on a potentially wealthy coaleld and industrial area on
the edge of Manchester.
In almost his rst letter from his country estate, Gatcomb Park in Gloucestershire,
in reply to advice from Sir John Sinclair, founder and President of the Board of
Agriculture, Ricardo wrote:
I have not quite given up the Stock Exchange; for a few months in the year,
I mean to enjoy the calm repose of a country life. ough I have a few acres
of land in hand, I am not yet become a farmer. I leave the management of
them wholly to others, and hardly take sucient interest in what is going
on, to make it probable that I shall ever be conversant with agricultural
subjects . . . (October 31, 1814)6
5 Ricardo’s published works, and a large proportion of his letters, and other items, have been edited
for publication by Piero Sraa with Maurice Dobb (1951–1973). ey are referred to here under
the title Works, followed by the volume number, and for these biographical details, see Works, X.
Historians of economics have written at impressive length and depth about Ricardo and his eco-
nomics. e classic studies remain Mark Blaug (1958) and Denis O’Brien (1975 and revised, 2004);
Samuel Hollander (1979) provides a (not uncontested) account of Ricardo’s ideas; Terry Peach
(1993) handles problems of interpretation; and Murray Milgate and Shannon Stimson (1991) dis-
cuss Ricardo’s radicalism. Donald Winch’s (1996) intellectual history of political economy in the
period provides important background. See also many papers written about Ricardo collected by
John Cunningham Wood (1985–94).
6 See letters 65–66, Works, VI, pp. 149–50. Sinclair, one of the major Scottish landowners and agri-
cultural activists of the day, was but a mere acquaintance of Ricardo.
e World in the Model
48
As good as his words, Ricardo lived partly in London, particularly during the
period when the Houses of Parliament were sitting, for he had become an MP for
a ‘rotten borough’ in 1819. Yet, he was a radical reformer, on the side of constitu-
tional reform and widening the surage until his untimely death in 1823. In addi-
tion to his political activities, he remained active in economic and nancial aairs,
as evident in a long and diverse correspondence with such as Jeremy Bentham,
Maria Edgeworth, James Mill, and of course his good friend and fellow economist
omas Malthus. But he always loved to return to his country life, and when writ-
ing from Gatcomb, Ricardo was lyrical in discussing its beauty, seen from his walks
and rides into the surrounding countryside.
e picture we have of Ricardo as an economist is one who knew, from experi-
ence, the practicalities of nance, money, and banking, and used that understand-
ing in his writings on political economy to great eect. Yet – but this is only at rst
sight – we do not get the same impression that he was knowledgeable about farming
and the land, despite the fact that such country estates, as Ricardo’s pictured here
(Figure 2.1), were not just a pretty house and park – they typically had their own
farms.7 And while Ricardo never became a gentleman-farmer, unlike some of his
friends from the City, the evidence gives us good reasons for thinking that he was
no less well informed, or less able to judge, the agricultural realities of his day than
Malthus, who was for many years the parson of a rural parish before becoming the
rst professor of political economy in England.8 For example, Ricardo’s comments
on his estate’s farming activities quickly turn into economic arguments, as we nd
in this letter, written from Gatcomb Park to James Mill:
e country here is looking very beautiful – our haymaking is now in full
vigor, and no superabundance of agricultural labour in the market. e
barley and oats I am told do not look well, but the wheat is promising. e
manufacturers have full employment for their men; Osman [Ricardo’s son]
told me yesterday that Mr. Hicks was employing his men extra hours, and
of course giving them extra pay. If the labouring class, in Agriculture, and
Manufactures, are doing well, we must console ourselves for the misfor-
tunes of landlords and tenants – they form but a small proportion of the
whole population, and it is no small comfort to reect that the losses they
sustain are more than made up by the prosperity of other capitalists. (July
9, 1821)9
7 e estate of Gatcomb Park (now known as Gatcombe Park, home of Princess Anne) included the
lordship of the manor of Minchinhampton and the land amounted to more than 5,000 acres.
8 “You are not half a country gentleman, nor a particle of a farmer”, wrote Ricardo’s good friend,
Hutches Trower – another emigre nancier from London, in November 1817 (Letter 235, Works,
VII, p. 207), who had already become fully engaged in country life, suggesting that Ricardo pay
particular attention to the planting of trees, and recommended two books that he should keep by
him (Letter 102, 23rd July, 1815, Works, VI, p. 237).
9 Ricardo’s Works, IX, p. 13. James Mill was his great debating companion and intellectual men-
tor. When both in London, they regularly walked together and argued about politics, econom-
ics, philosophy, and much else, though Ricardo’s letters to his friend rarely comment on his own
Figure 2.1. Gatcomb Park, Country Home
of David Ricardo.
Source: Piero Sraa: e Works and
Correspondence of David Ricardo. Edited with
the collaboration of M. H. Dobb, 1951–73,
Cambridge: Cambridge University Press
for e Royal Economic Society, Vol. VII:
Letters, 1816–1818, facing p. 1. Reproduced
by permission of Liberty Fund Inc. on behalf
of e Royal Economic Society.
e World in the Model
50
When Ricardo became a large landowner and lord of the manor, he duly became
an active member of that class in all the ways that would have been expected of him.
e parish of Minchinhampton, in which Gatcomb Park was situated, was both an
agricultural parish (mainly arable, with pasture for sheep) and a manufacturing
one (woollen broadcloth was the local industry), with a sizeable population.10 He
helped in the local parish, supporting the rector in rebuilding almshouses, start-
ing a school and inrmary, and so forth.11 He was elected sheri of the county
of Gloucestershire for 1818, an evident sign of establishment success and local
respect.12
At the same time, we also know that his interest in political economy had begun
to deepen and to widen from matters of currency, bullion, and trade to those of
agriculture and politics as early as 1811, three years before he became a landowner.13
By 1814 he was actively writing and lobbying against ‘the corn laws’ (where ‘corn’
refers to wheat and small grains rather than maize), which had long restricted the
import of cheap corn.14 What is less well-known, but understood from his letters,
is that in September 1814 he had been reading the House of Lords’ Report into
the Corn Laws (or more correctly into the “. . . . State of the Growth, Commerce
and Consumption of Grain. . .”) and briey discussed the “Evidence” section of that
report with Malthus. Ricardo complained that the report “discloses some impor-
tant facts, but how ignorant the persons giving evidence appear to be of the subject
[of political economy] as a matter of science”.15
is “Evidence” will prove important later: it consisted of the witness reports of
those who came to give evidence to the committee and verbatim accounts of their
cross examination by committee members. e statements range across dierent
landscape (though see Works, VII, Ricardo’s letter to James Mill, p. 170; p. 277, 12th August, 1818
and letter 274, p. 305).
10 e 1801 census recorded 3,419 people in 692 houses rising to 5,114 people in 1,116 houses in the
1831 census. is and other information about Ricardo’s country estate and the local industry has
been gleaned from Herbert’s (1976) Victoria County History of Gloucestershire. Vol. XI: e Stroud
Valleys.
11 For example, he started a local school in Minchinhampton in 1816 on the Lancastrian system, with
250 boys and girls as pupils in 1818 (see Herbert, 1976, p. 206).
12 However, he never became a magistrate for the county: possibly it was his Jewish birth, though he
became a Unitarian aer his marriage; perhaps it was because he was not a member of the land-
owning Whig elite. See biographies by Weatherall (1976) and by Henderson with Davis (1997) as
well as Works, X.
13 ese interests and their dating can be seen quite clearly from the relevant Works, III and IV and
in his letters, Vols. VI–IX.
14 He was consistent in opposing petitions for help from the landowners and farmers when prices of
grain fell – see, for example, his remarks in Works, VI, p. 47. However, it was not the case that he
let his sympathy with the plight of the labourers interfere with his views on the ‘poor law’. He was
certainly a charitable man, but decried the incentive systems inherent in the poor law.
15 Malthus found the report to be on his side: “It contains as you observe some very curious infor-
mation. e evidence is a little suspicious, though it is a good deal such as I expected from [my]
eory” (Letters 58 and 59, Ricardo to Malthus 30th August, 1814 and Malthus to Ricardo, 11th
September, 1814 Works, VI, pp. 130 and 132).
Model-Making: Ingredients and Integration 51
forms; there were personal descriptions, discussions about prices, and a wealth of
numerical farm-accounting statements presented by individual farmers and land-
lords.16 e second witness was one Edward Wakeeld, who in 1815 was to become
Ricardo’s land agent, and from then on regularly sent him letters informing him of
his duties as a good landlord, his tenant farmers’ problems, the diculty of nding
reliable new tenants, the state of the market for land, and the prices of produce.17
And from the point at which he entered Parliament in 1819, Ricardo gained a fur-
ther wealth of knowledge of the agricultural experience of Britain of his day, partic-
ularly as he sat on the Select Committee investigating agricultural distress in 1821
and 1822. He used such knowledge in his speeches in Parliament, in his writings
about agricultural issues, and in framing his policy positions.
All this suggests that far from being a wealthy absentee landowner uninterested
in farming, as he had appeared to be in 1814, Ricardo certainly became very knowl-
edgeable about the land and engaged with agricultural matters. Now, to make sense
of and appreciate Ricardo’s numerical reasonings in his political economy, we need
a better sense of the economic issues of his day and how they were perceived by
economists, such as himself, working in the classical tradition of his time.
2.ii Economics Matters, Experimental Farming Matters
e two big issues for political economists of Ricardo’s day were the growth of
population and the high price of basic food that contemporaries blamed on the
restrictive taris known as the corn laws. Agriculture lay at the heart of both
questions.
e problem of the apparently explosive growth of population was prevalent
on the tongues of the chattering intelligentsia, for it presented the most intracta-
ble question. For historians of economics, that question has been most intimately
connected with the work of Ricardo’s great friend and fellow economist, omas
Malthus.18 Recall that classical economists thought and reasoned in terms of laws
or principles that, like laws of nature, were understood to govern the economy. In
accordance with this stance, but with an unusually concise form, Malthus’ ideas
about population were proposed in two numerical ‘laws’: that food supply grew
arithmetically while population growth (if unchecked) would grow geometrically.
He argued that the eects of these two laws were shorter-run periods of misery,
alternating with comparative well-being, as economic activity uctuated around
this constraint xed by the ability of nature, and so farmers, to provide food for the
rapidly growing population.
16 e long set of tables of data that appeared separately attached to the report are not called ‘evidence’
but ‘accounts’ (almost reversing modern economists’ connotations of these terms).
17 ese unpublished letters from Edward Wakeeld can be found at the University Library in
Cambridge. Unfortunately, Ricardo’s letters in reply are not part of the collection.
18 For the ways in which the population question spread into many aspects of life and ideas in the
period, see James’ 1979 book about Malthus.
e World in the Model
52
e issue of the corn laws, the legal tari on grain that prevented imports
of cheaper foreign grains, was equally hotly debated as the most immediate and
important policy question in political economy. Ricardo rst addressed this prob-
lem in his 1815 pamphlet known as his Essay on Prots and concluded that the
tari, by keeping the price unreasonably high, was to the benet of the landlord
but to the detriment not just of the labourer but also to the capital holder.19 Corn
(wheat) prices had been extremely high from 1795 because of poor harvests and the
Napoleonic Wars. Indeed, prices had been high enough to cause food riots, changes
in the ‘poor law’ (or legal system of localised social welfare), and the extension of
arable farming into newly enclosed areas. (Ricardo commented on such riots that
occurred in London in March 1815 in one of his many letters to Malthus.20) In that
same year of 1815, Ricardo’s new country parish of Minchinhampton found the
cost of poor relief had risen to £2000 and 230 people were on permanent outdoor
relief.21 As prices fell from their peak, farmers complained and landlords’ rents were
threatened, raising demands from both groups for further tari protection under
the corn laws, while the labouring class was not in favour of such restrictions for
prices of corn and so bread prices still remained high.22 Parliament had investigated
the corn laws in 1814, but the farming interests (farmers and landlords) won the
day of course, for labourers had no vote, and the tari remained.23
For both Ricardo and Malthus, the population problem was a given – it was the
result of the iron laws of political economy. e health and growth of the farming
sector were critical for the well-being of the economy as a whole, for agriculture had
not only to feed the growing population but also, to a considerable extent, employ
them. At that time, agriculture and its associated activities still formed the larg-
est sector of the economy (despite the beginnings of industrialisation, the ongoing
success of commerce, and the fast growth in urban centres). e farming interests
themselves were well aware of their central role, and the immense importance of
19 See Works, IV: “An Essay on e Inuence of a low Price of Corn on the Prots of Stock”, 1815.
20 Works, VI, letter 77, p. 180. ese riots were not only urban aairs. Machine burning and the burn-
ing of grain barns were a feature of the period: his good friend Trower wrote to Ricardo about a
neighbour’s experience in July 1816 (Works, VII, p. 45).
21 is was against a number of households, which probably lay between 700 and 1,000 households;
see Herbert (1976, pp. 188 and 201), who also states that “from 1814, the poor in the house were
farmed” (p. 201), which I take to mean were set to work on farms within the parish.
22 At their peak in 1812, prices had been around three times the late eighteenth-century level.
Somewhat suddenly, there had been a fall in the price of corn due to a bumper harvest in 1813
and, aer peace in 1814, prices fell further. In 1815, they were still around double the prewar level,
though just below the level at which protection came in. See D. P. O’Brien (1981, p. 167) on the
discussion of high prices and their eects and Dorfman (1989) for the following fall. e full series
of corn (small grains) prices can be found in Mitchell and Deane (1971). Rents per acre, which had
been rising steadily since the 1790s, levelled o around 1815, but at double their prewar level: see
Turner et al. (1997) and Oer (1980). See Hilton (1977) on the politics of the corn laws and Snell
(1985) on the poor law of the period.
23 ere was some alteration, the 1815 act abolished the sliding scale of duties on imports and
replaced it with import prohibition when the price was below 80sh, with free imports over that
price.
Model-Making: Ingredients and Integration 53
farm productivity, in these two problems of political economy. But for the farmers,
the provision of both food and employment were practical matters to be solved,
rather than matters of scientic law.
Economic and political historians have long been aware of the importance of
the taris on corn as indicative both of the class war between the agrarian elite and
farm labourers and of the rural–urban power struggle as Britain underwent urban-
isation. Historians of economics have seen how such struggles depended on the
contemporary perception of how incomes were distributed between such groups –
or as classical economists of the day expressed it – upon ‘the laws of distribution’:
that is, of what determines the share of output between their three economic classes
of landowners, farmers (capitalists), and labourers.24 (Of course, the historical issues
stretch further than this, for Ricardo’s account of distribution laid the groundwork
for Marx’s analysis of class interests and so point to a later history of momentous
political and economic events.) Agrarian historians have long been aware of the
importance of experimental agriculture that drove the technical changes that sup-
ported the massive increase in agricultural output in that period and so prevented
the kind of food crises Malthus had envisaged. e connections between the argu-
ments over the corn laws, food security, and distribution are manifest.
Yet one link remains unexplored by historians of economics, namely the com-
mon ground and unexpected connection between the two practical domains of
political economy and experimental agriculture, and in particular the fundamental
importance of these links in Ricardo’s work. His account of distribution depended
on substantive elements from practical and experimental farming in three respects.
First, the experiments undertaken in farming at that time provided subject matter
for his political economy. Second, his numerical accounts parallelled, in numerical
form, the reports of real experiments in farming. ird, the way he used his numer-
ical accounts – his way of reasoning with them – constituted a form of experiment
that might be called a ‘numerical experiment’. His political arithmetic, or as I shall
suggest, his model and modelling, mirror the numerical expression and content of
agricultural experimental work. So to understand Ricardo’s modelling in political
economy, we must know something of this tradition of agricultural experiment.
e late eighteenth and early nineteenth centuries were an age of experimen-
tal farming in Britain, with the purpose of improving the productivity and output
of the farming sector.25 ere was a strong proselytising, even missionary, element
in these activities; successful experiments were to provide information, advice,
and even exemplary procedures for others to follow. Experimental reports such
as the supposed 500 odd found in Arthur Young’s Farmer’s Tours of the 1770s (see
Mingay, 1975) and William Marshall’s Experiments and Observations Concerning
Agriculture and the Weather (1779) went alongside agricultural handbooks
24 See particularly Overton (1996) on agrarian and economic history, Hilton (1977) on economic
and political history, and Winch (1996) on the history of economics and its political dimensions.
25 A broad survey of the movement, and its literature, is given by Wilmot (1990).
e World in the Model
54
outlining best practice, such as Alex. Beatson’s A New System of Cultivation
(1820/21). Experimental investigations in the rst two decades of the nineteenth
century, the period of Ricardo’s work in political economy, ranged over animal hus-
bandry, fertiliser testing, cultivation methods, work organisation and machine per-
formance, and so forth just as they had earlier focussed on the virtues of animal
breeding and the importance of drainage, new crops, and crop rotation. Technical
change based on such experiments was an ongoing process.26
ere was also an usually high level of political involvement in agriculture:
a number of the Whig aristocracy, owners of large land holdings, were intent on
improvement and were active in developing their own experimental farms. eir
great agricultural shows, particularly those held at Mr. Coke’s (later Earl of Leicester)
estate at Holkham Hall, Norfolk, and the Duke of Bedford’s estate at Woburn, were
sites where the latest practices were reported, new breeds shown, and visitors
escorted around the experimental plots. ese events had become high points of
the social, political, and agricultural season in the early years of the nineteenth cen-
tury. Experimental agriculture thus occupied a secure location within a politically
forceful landowning and farming elite. e personal interest shown in farming by
George III had turned it into a fashionable pursuit, and the new agricultural socie-
ties provided institutional entrepreneurship.27
e scientic experimental tradition from chemistry was also revitalised dur-
ing Ricardo’s years by the Board of Agriculture’s establishment of an annual course
of lectures by Humphry Davy in 1803, repeated until 1812.28 Such scientic work
complemented rather than replaced the work of practical eld experimenters, and
it was not necessarily regarded as a dierent kind of endeavour. Accounts of exper-
imental activities and ndings called on the work of chemists such as Dr. Joseph
Priestley alongside those of famous agricultural commentators such as Arthur
Young and practical experimentalists such as William Grisenthwaite, whose A New
eory of Agriculture of 1819 also appeared as a series of letters in the Farmers’
Journal.29 Davy’s own Elements of Agricultural Chemistry of 1814 (from his lectures)
interwove the agricultural experimental farming reports from the ‘great improvers’
26 County surveys formed the main body of agricultural information of the day from which this
variation can be understood (see Marshall’s 1817 county reports to the Board of Agriculture in
the second decade of the century – the exact period of discussion for Ricardo’s work here). For a
recent review and reassessment of the agricultural revolution see Overton (1996) and Allen (1994)
(and for specic chapters on innovating techniques of the period, see G. E. Mingay’s [1989] edited
Vol. VI in e Agrarian History of England and Wales). On Young’s reporting of experimental farm-
ing, see Mingay (1975, chapter II:4). Good examples of specic contemporary reports of technical
matters, such as crop rotation, can be found in the Farmers’ Journal of the period, for example,
September 22, 1810 (p. 176); September 14, 1812 (p. 403), and November 1, 1813 (front page).
27 See “Agricultural Literature and Societies” by Nicholas Goddard in Mingay (1989).
28 See Berman (1972) on the scientic connections of experimental farming.
29 His letters can be found, for example, in the issues of September 7 and 21 in 1818 addressed to
“Mr. Coke”. For an account of the early history of experimental work in farming and agricultural
science, see Russell (1966, p. 67, and chapters 2 and 3).
Model-Making: Ingredients and Integration 55
(the Whig landowners) with the reports from Young and ndings from eminent
scientists.
e ‘practical farmer’ was an important contributor to all this, for any interested
farmer could join in this practical science by experimenting on his own land and
write to report his ndings to the farming newspapers of the day. is was not nec-
essarily high science, nor did it require the huge investments of the wealthy land-
owners. Signicantly, experimental reports by practising farmers and landowners
(as opposed to those by ‘scientists’) described not just the agricultural experiment
and its outcomes, but also the associated costs and prots. Experimental reports
were sometimes reported in nancial terms, and if farmers reporting ‘successful’
experiments did not provide the monetary arithmetic that demonstrated increased
prot as well as productivity, they found their claims of ‘improvement’ open to
question.
Ricardo knew about all this. He was familiar with the experimental farming
activities of his day, for no intelligent and engaged political economist moving in
both the political and landed gentry circles, as he did, could have remained ignorant
of them. We already know that he knew about the practical experimental work of
farmers from his reading of the “Evidence” section of the House of Lords Report on
the corn laws in 1814 (above). We know that he also knew of the agricultural activi-
ties of the Whig landowners as well as of the new system of agriculture, for he refers
in one letter to the annual agricultural meetings (known as a “sheep- shearing”)
of 1821 at Holkham Hall as “Mr. Coke’s annual feast”.30 His letters pointed to the
importance of agricultural improvement both as a necessary requirement for
growth and as an obvious part of the experience of his day, although he does not
seem to have been directly a participant in experimental activities.31
But there is another surprising signal from which we can appreciate his famil-
iarity with the agricultural improvements of his day and the experimental element
involved. e writing in his Principles of Political Economy and Taxation (his main
contribution to economic science, which appeared in three editions in his lifetime:
1817, 1819, and 1821) is very formal, but he very occasionally moves from neutral-
ity to the rst person singular voice – and he does so precisely at the point when
he discusses the possibility of increasing agricultural output through introducing
new technology and changing farming practices!32 (is is indirect evidence, but
30 See Ricardo’s letter to Mill of August 28, 1821 (Works, IX, pp. 45–6). In fact, this was the last of
these great events, which, though they had been going for more than forty years, had become large
scale only in the early nineteenthth century. For information on the these meetings, see Goddard
(1989, pp. 377–8).
31 I have found no evidence that Ricardo’s tenants were involved in agricultural experiments, but
certainly Wakeeld was concerned about employing best practice farming. And, the erstwhile
owner of Gatcomb Park, Edward Sheppard, father of the immediate previous owner Philip
Sheppard, had experimented in sheep breeding on an estate at Avening (in the next door parish to
Minchinhampton) that had previously been held under the same ownership.
32 ere is another obvious case later where he is discussing investment along similar lines, and he
writes as the farmer-investor in his chapter “On Machinery”.
e World in the Model
56
pertinent and all too easily overlooked – so easily that I will need to point it out
when we reach that event in the next section.) And, in these places, he writes in the
rst person as both capital investor or farmer (making prots) and as landlord (col-
lecting rents) – the two roles that he has been careful to keep separate in the rest of
his chapter. ese are not just roles, but classes in the economic system, classes that
share between them the total products of the economy. As such classes they feature
in Ricardo’s model farm, as we shall see.
3. Constructing Ricardo’s Numerical Model Farm
and Questions of Distribution
My purpose in this section is to show exactly how Ricardo integrated his knowl-
edge of contemporary agricultural experience and experiments with his economic
ideas in his construction of the accounts for a numerical ‘model farm’; and that it
was through his numerical experiments using this ‘model farm’ – ‘model farming’ –
that he formulated his laws of distribution. But to show all this, I need to explain
how Ricardo’s numerical accountings are put together and to follow their sequence
through with Ricardo to the point where they demonstrate his laws of distribution.
is requires working through some rather dense material.
Let us begin where Ricardo began. As Blaug argues, “Ricardo’s theoretical
system emerged directly and spontaneously out of the great corn laws debate of
1814–16”.33 But it was Ricardo’s familiarity with the kind of evidence given in that
debate that was critical both for the development of his mode of arguing and for
the way in which his system ‘emerged’. In his rst pamphlet against the corn laws
of 1815, Ricardo used a couple of large tables to argue and demonstrate his points,
and was surprised to nd that this mode of reasoning led him to some new nd-
ings. However, his argument was constrained by the fact that a table is essentially
a two-dimensional object, and he wanted to develop a numerical argument about
the interactions of several variables (see Appendix 1).34 As his investigations into
growth and distribution in the economy proceeded further in the more thorough
33 Blaug (1958, p. 6), italics mine. Ramana (1957, p. 198) has, like Blaug, argued that this pamphlet by
Ricardo – along with contemporary ones by Malthus, Torrens, and West – were the direct outcome
of the 1814 investigations into the corn laws by Parliament. By comparison, Edward West’s 1815
pamphlet on rent, which appeared just before Ricardo’s, used numerical arguments in a somewhat
similar way to Ricardo, but in no way matched the extended table of Ricardo’s pamphlet, nor the
continuity and complexity of the numerical accounts he produced in his Principles. Malthus’ 1814
pamphlet on the corn laws and 1815 pamphlet on rent contained no use of numbers, tables, or
farm accounts while Robert Torrens’ 1815 pamphlet used numbers to a very limited extent; both
began to use Ricardo’s more sophisticated numerical examples in their later writings. On Marx’s
use of numerical examples, and artefactual elements in them, see Reuten (1999).
34 Although many tables are constructed to show lots of things varying together, such elements are
usually tabulated against one dimension, namely time. Ricardo had to juggle his three variables:
rent, capital, and prot, in order to display their interrelations within a two-dimensional table.
Model-Making: Ingredients and Integration 57
treatment in his Principles, he abandoned his attempts to argue with large tables
and used a sequence of smaller numerical chains. Each of these illustrated and
demonstrated a dierent part of his argument as relevant for the particular topic in
each chapter.
Here is where we shall see how the experimental farming of the real econ-
omy of Ricardo’s day (discussed in the previous section) – in content and numer-
ical expression – was mirrored in the numerical accounts that formed his model
farm. Ricardo’s numerical examples appear in dierent forms, sometimes running
through the lines of text, sometimes as a set of mini accounts, and sometimes in
footnotes. is is also how the farming experiments were reported in the period –
sometimes running through text, and sometimes as a set of farm accounts. I shall
show some of both the farming reports and Ricardo’s numerical examples – his
‘accountings’ (as I shall call them) – in their original forms. By comparing them,
we can see how Ricardo’s political economy used the same kinds of reports that
appeared in agricultural experimental work, and that, in content, he discussed real
problems of the agriculture of his day.
But while the numerical accounts look like illustrations of the text, in fact, they
are not quite that: they play a rather special role for they function as reasoning tools
complementary to the verbal argument.35 Each one enabled him (and his read-
ers ) to reason through what would happen in his model farm economy in rather
concrete form (the set of accountings) if dierent actions were to be taken under
various circumstances. We can think of these reasoning chains as oering numer-
ical experiments, in the sense that one thing at a time is allowed to vary so that its
immediate eects can be set out, its side eects traced out, and the nal outcomes
judged. And, as bets experiments, Ricardo usually makes it very clear which other
things are being held constant: the ceteris paribus conditions are set out and noted
each time, and each numerical experiment plays out its demonstration through a
series of related changes, or a scenario, as successively more of something is added
(e.g., more capital, more manure, etc.). ese model farm accounting experiments
eectively provide numerical ‘simulations’, showing the dierent eventualities of
dierent scenarios. It is these numerical experiments that mirror or parallel the real
agricultural experiments of his day.
Each of these accountings formed an ingredient in his model farm, and later in
this section we will see how he integrated these ingredients into his model farm. We
will also see how his numerical experiments with that model farm – that I call model
farming – led him to some unexpected, even surprising insights into the nature of
that small-world economy, insights he understood as relevant to the economy of
his day. is points us to the way in which unexpected results can emerge when a
new formal mode of reasoning is adopted, and in later chapters of this book, I shall
explore this idea, and the notion that experimentation is a more general quality of
model functioning (see Chapters 7 and 8).
35 is importance of this independent representational function is discussed further in Chapter 3.
e World in the Model
58
3.i e Numbers in Ricardo’s Principles and Experimental Accounts
For Ricardo, the fundamental problem of political economy was to understand the
distribution of gains between the economic classes. He had set for himself the chal-
lenge of understanding the laws that determined this distribution, that is, the shares
of produce that go as rent to the landlord, prots to the capital holder, and wages to
the labourer. His opening remarks of the Preface to his Principles make this clear:
e produce of the earth – all that is derived from its surface by the
united application of labour, machinery, and capital, is divided among
three classes of the community; namely, the proprietor of the land, the
owner of the stock or capital necessary for its cultivation, and the labourers
by whose industry it is cultivated . . .
To determine the laws which regulate this distribution, is the principal
problem in Political Economy . . . (Ricardo, Principles, 1821, Wor k s , I, p. 5)
Ricardo takes the correct analysis of rent to be critical to determining what these
laws are. So, though he begins his Principles with a standard account from classical
economics about labour as the source of value, he then moves immediately to the
question of rent and this drives his account through the following pages until his
laws of distribution are laid out a few chapters further on.
Rent is dened by Ricardo as:
. . . that portion of the produce of the earth which is paid to the landlord
for the use of the original and indestructible powers of the soil. It is oen,
however, confounded with the interest and prot of capital, and in popular
language, the term is applied to whatever is annually paid by the farmer to
his landlord. (Ricardo, Principles, 1821, Works, I, p. 67)36
But the denition does not motivate much on its own. Ricardo wanted to make his
account of rent absolutely clear: how rent arose; how the amounts were determined;
how it was aected by agricultural investment; and most importantly, how it fea-
tured in the distribution of income. For these purposes, a static account would not
do, for the economy was in a period of rapid change, and Ricardo needed to dem-
onstrate how his laws of distribution applied over time and how changes in each
element aected the distribution to the other classes. In this context, the problem
of population growth was an important consideration. It was not just the imme-
diate factor – the necessity of growing more food to feed the growing population
(the Malthusian problem), but also the more generally perceived agricultural/rural
problem of poverty due to lack of work, for as the population grew, not only was
more food required, but more labour was also available. Ricardo’s account of the
distribution of the product therefore needed to be supple enough to take both these
issues – food output and employment – on at once.
36 In this section, page numbers refer to the 1821 edition of the Principles, provided in Sraa’s edition
(Works, I), and reproduced by the Liberty Press for the Royal Economic Society in 2004.
Model-Making: Ingredients and Integration 59
Ricardo’s numerical accountings were motivated in his argument by the prob-
lem of increasing output of food, with solutions coming from attacking the problem
in dierent ways. In the rst substantial numerical account, Ricardo proposes that
farmers will bring in additional (more marginal) land into cultivation and he uses
this to show that, under such circumstances, rent will arise. Although the case exam-
ple of bringing new land into cultivation as a way of increasing food output for the
growing population might seem contrived, this was far from the case. Despite the
island constraint and relatively high population density for the period, there was
an ongoing process of enclosure of common pasture (or ‘wastes’) and a consequent
increase in arable acreage in England during this period. ese were the well-known
realities of the day.37
I quote Ricardo here, not just because it is the rst numerical accounting, but
because it provides a good example of his running text form of this. As readers will
see, these extracts from Ricardo require patience, not only to overcome the stylistic
devices of a 200-year-old text, in which the logic of the words and numbers com-
plement each other, but also to appreciate that Ricardo is in the process of gradually
assembling the set of ingredients for his model farm through his series of account-
ings. It is helpful also to bear in mind that he uses quarters of grain as his unit of
account.
DOCUMENT 1:
Ricardo’s Accounting 1: From his Chapter II: On Rent, Principles, 1821, Works , I,
pp. 70–1
us suppose land – No. 1, 2, 3 [of three dierent qualities] – to yield, with an equal
employment of capital and labour, a net produce of 100, 90, and 80 quarters of corn.
In a new country, where there is an abundance of fertile land compared with the
population, and where therefore it is only necessary to cultivate No. 1, the whole
net produce [aer supporting the labourers] will belong to the cultivator, and will
be the prots of the stock which he advances. As soon as population had so far
increased as to make it necessary to cultivate No. 2, from which ninety quarters
only can be obtained aer supporting the labourers, rent would commence on No.
1; for either there must be two rates of prot on agricultural capital, or ten quarters,
or the value of ten quarters must be withdrawn from the produce of No. 1 for some
other purpose. Whether the proprietor of the land, or any other person, cultivated
No. 1, these ten quarters would equally constitute rent; for the cultivator of No. 2
would get the same result with his capital whether he cultivated No. 1, paying ten
quarters for the rent, or continued to cultivate No. 2, paying no rent. In the same
manner it might be shown that when No. 3 is brought into cultivation, the rent of
No. 2 must be ten quarters, or the value of ten quarters, whilst the rent of No. 1
37 As shown, for example, in the evidence to the Lords Report in 1814; see also Mingay (1997).
e World in the Model
60
would rise to twenty quarters; for the cultivator of No. 3 would have the same prof-
its whether he paid twenty quarters for the rent of No. 1, ten quarters for the rent of
No. 2, or cultivated No. 3 free of all rent.
is numerical chain forms the rst part of Ricardo’s accounts for his model
farm. It was designed not only to outline the process of increasing output by bring-
ing new land into cultivation, but also to show how rent arose and explain its level
by connecting it with the fact that the same amount of labour and capital pro-
duced less output on the poorer quality of land than on the better. is argumen-
tation, and the numerical outcomes, depended not only on Ricardo’s denition of
rent, but also upon two classical economic assumptions, namely, the tendency of
prots to equalize and that the prot rate is determined on the least productive
land. Under these two formal conditions, as the accounting shows, rent is the dif-
ference in net produce (aer wages are paid) between the more and less produc-
tive land – so that landlords gain, as rent, the excess prots of the farmer on the
better quality land.38
Ricardo’s second alternative – and associated numerical accounting – to solve
the need for increased food by a growing population was to increase capital inputs
on the same land, again another well-observed feature of his day. He assumes that
successive capital investments will increase output (but at a declining rate), yet
prots on each unit of capital must remain equal.39 His accounting numbers show
how rent arises as the dierence between the levels of prots with dierent doses
of capital (Ricardo, Principles, 1821, Works, I, pp. 71–2). at is, on both the more
marginal land case (wherein the additional labour employed produces less out-
put) and the more enhanced capital case (wherein capital is understood to embody
labour), rent will arise because “. . . rent invariably proceeds from the employment
of an additional quantity of labour with a proportionally less return” (Principles,
1821, Works, I, p. 72).
It is not only rent that rises under these circumstances, but also the relative
price of agricultural produce. is outcome follows from the classical economics
‘labour theory of value’, which holds that it is labour alone that creates value, and
that there is a direct relationship between labour input and value. If more labour
has to be used to produce the same amount of a commodity, the value of that com-
modity will rise relative to others and vice versa. e implications for agriculture
follow:
e most fertile and most favourably situated land will be rst cultivated,
and the exchangeable value of its produce will be adjusted in the same
38 Later in the book, Ricardo develops this example by adding taxes and tithes.
39 Reich (1980) nds contemporary evidence to support Ricardo’s belief in declining returns to agri-
cultural investment, despite the period of improvement. Blaug argues that this classical assump-
tion was widely believed at the time to be correct (Blaug, 1956, pp. 159–60).
Model-Making: Ingredients and Integration 61
manner as the exchangeable value of all other commodities, by the total
quantity of labour necessary in various forms, from rst to last, to produce
it and bring it to market. When land of an inferior quality is taken into
cultivation, the exchangeable value of raw produce will rise, because more
labour is required to produce it. (Ricardo, Principles, 1821, Wor k s, I, p. 72)
He also assumes that all improvements in agriculture are labour saving and there-
fore lead to a fall in the price (or relative value) of the good:
If they did not occasion a fall in the price of raw produce they would not be
improvements; for it is the essential quality of an improvement to diminish
the quantity of labour before required to produce a commodity; and this
diminuation cannot take place without a fall of its [the commodity’s] price
or relative value. (Ricardo, Principles, 1821, Works, I, p. 80)
In his third numerical account, Ricardo discusses another feature of the
period – namely technical change in agriculture – as a way of increasing food out-
put to feed the growing population. is most interesting passage shows not only
how Ricardo tabulated some of his numerical accounts, but also his familiarity with
at least two of the main elements of the experimental farming results of the day: the
importance of manure and the role of root crops. Although the introduction of root
crops as part of a rotation system had been the work of “Turnip” (Lord) Townshend
in the eighteenth century, the best crop rotation for any particular location was still
very much a part of the experimental farming of Ricardo’s day. For example, Rudge,
in his 1813 account (for the Board of Agriculture) of Gloucestershire (wherein
Gatcomb Park lay) provided a long accounting of crop rotations in both physical
and monetary terms.
is is also the passage that shows us Ricardo thinking as a farmer – for it is at
this point that he becomes a farmer in the rst person, discussing the possibility
of himself introducing a “course of turnips” (into the eld rotation of crops), or of
himself introducing a more “invigorating manure” to his elds. (is is a rare use
of the informal rst person singular in his book, which usually remains strictly
formal.) We can see that he so far enters into the issues of agricultural improve-
ment that he speaks to us of himself as a farmer lowering rent – a benet to the
farmer, but to himself as landowner in real life, a loss in income that he will have
to bear!
DOCUMENT 2:
Ricardo’s Accounting 3: From his Chapter II: On Rent, Principles, 1821, Works , I,
pp. 80–1
e improvements which increase the productive powers of the land, are such as the
more skilful rotation of crops, or the better choice of manure. ese improvements
absolutely enable us to obtain the same produce from a smaller quantity of land. If,
e World in the Model
62
by the introduction of a course of turnips, I can feed my sheep besides raising my
corn, the land on which the sheep were before fed becomes unnecessary, and the
same quantity of raw produce is raised by the employment of a less quantity of land.
If I discover a manure which will enable me to make a piece of land produce 20
percent more corn, I may withdraw at least a portion of my capital from the most
unproductive part of my farm. . . . . . If, by the introduction of turnip husbandry, or
by the use of a more invigorating manure, I can obtain the same produce with less
capital, and without disturbing the dierence between the productive powers of the
successive portions of capital, I shall lower rent; for a dierent and more productive
portion will be that which will form the standard from which every other will be
reckoned. If, for example, the successive portions of capital [invested in the same
land] yielded 100, 90, 80, 70; whilst I employed these four portions, my rent would
be 60, or the dierence between
70 and 100 = 30 100
70 and 90 = 20 90
70 and 80 = 10 whilst the produce 80
would be 340 70
— –—
60 340
. . . . . If, instead of 100, 90, 80, 70, the produce should be increased [through
“improvement” such as manure] to 125, 115, 105, 95, the rent would still be 60, or
the dierence between
95 and 125 = 30 125
95 and 115 = 20 whilst the produce 115
95 and 105 = 10 would be increased 105
to 440 95
— –—
60 440
But with such an increase of produce, without an increase of demand*, there could
be no motive for employing so much capital on the land; one portion would be
withdrawn, and consequently the last portion of capital would yield 105 instead of
95, and rent would fall to 30, or the dierence between
105 and 125 = 20 whilst the produce will* be still 125
105 and 115 = 10 adequate to the wants of the 115
— population, for it would be 345 105
30 quarters, or –—
345
the demand being only for 340 quarters.
*omitted footnote
Model-Making: Ingredients and Integration 63
We begin to see here how his model farm is gradually being built up, for he
repeats his second accounting showing increasing investment in the top part of
the ‘table’, but then incorporates the eect of a technical change in the bottom half.
His discussion and numerical account are given in the form of a numerical exper-
iment. And it is a complicated experiment. In the rst stage there is a variation in
capital input and we see the variation in output as the ‘treatment’ is varied. In the
second stage, there is the same variations in capital inputs, but with the application
of manure (or equivalent technical improvement) and this creates a further set of
output data using the same variations in capital inputs at the same time – a kind
of double experiment. e experiments show that with technical change increas-
ing output at all levels of investment on his model farm, less capital investment is
needed to produce the same amount of food and rent falls.40
is numerical experiment can be neatly compared with an actual eld trial
experiment on the application of manure reported in a weekly, the Farmers’ Journal,
in 1817 by a farmer, or perhaps a landowner, from Tetbury, less than 10 miles from
Ricardo’s country estate:41
DOCUMENT 3:
Extract from a letter to the Farmers’ Journal, May 19, 1817, p. 154
METHOD OF EMPLOYING THE AGRICULTURAL POOR
SIR, Tetbury, April 26, 1817
. . . . . Several portions of land in a large eld, in equal divisions, were marked out,
and all planted with potatoes of the same kind, the same soil, the cultivation the
same in every respect, except that in one division no manure was put on the ground
before planting with potatoes. All the other divisions were manured with dierent
quantities of manure, progressively increasing from ten cartloads per acre up to
40 From this, Ricardo argued that aer technical change, the original output of 340 can be produced
with just three units of capital, so that if the population was already fully provided for, the nal
unit of capital could be withdrawn bringing net produce back to 345, but also reducing rent by
30. us, in this account, technical change can aect both the amount of capital (that needs to be
invested in agriculture) and rent. (See O’Brien [1975, pp. 126–9] for discussion of the assump-
tions and possible artefacts of the numbers chosen in this numerical experiment.) is tendency
of the prot rate to fall with technical change has been called “Ricardo’s Paradox” – see Oer
(1980).
41 Evans and Ruy’s Farmers’ Journal and Agricultural Advertizer, more generally known as the
Farmers’ Journal, was a weekly paper, the rst agricultural newspaper, and lasted from 1807 until
taken over in 1832 (see Goddard, 1989). I don’t know if Ricardo read the journal, but its readers
were certainly familiar with his views reported in the paper and felt entitled to take issue with
them. On one occasion at least: January 17, 1820, a correspondent from Bedfordshire outlined
a set of hypothetical farm accounts assessing the impact of the corn laws in a letter explicitly
addressed as “Questions to Mr. Ricardo”.
e World in the Model
64
forty, which was the highest quantity put on any division; the consequence was,
that the crop without any manure, cost £6. per acre, including rent, &c. and pro-
duced 24 sacks per acre, which sold, at 5s per sack, for exactly £6.; and, therefore,
le no prot whatever for the grower, or interest for his capital employed. e other
divisions produced from two and a half to four sacks additional for every addi-
tional cart-load of manure (which was chiey sweepings of the streets of a town,
and cost 5s the load when on the ground); and the highest, manured at 40 load of
manure to the acre, yielded 160 sacks of Potatoes per acre, which at 5s per sack is
£40. or £150.per cent prot. . . . .
A. L.
is neat example shows how Ricardo’s numerical farming experiments in polit-
ical economy grew up alongside and mirrored the agricultural experiments of his
day. e reporting of this exemplary experiment also looks like some of Ricardo’s
numerical experiment accounts that run through the text, while the kind of tabular
appearance that we see above in some of Ricardo’s work can also be found in some
of the many other farming experiments reported in various accounting formats in
that same journal in the period, as we will see later.
Let me move now directly to the h numerical account in Ricardo’s series.42
is is the one I mentioned at the beginning of the chapter, where he adds labour
to the eld in units of ten men at a time, and that sent me on this quest to under-
stand the content and style of Ricardo’s strange reasoning style. For the rst time,
prices of corn and rent in monetary form have appeared in the example. (Note that
the prices quoted here are within the normal range of corn prices for 1815-23: £4
or 80 shillings being reasonable; £5 or 100 shilling being high; 1817 was an excep-
tionally high year, being around 120 shillings or £6.) e addition of the monetary
unit of account, which runs alongside the output account, makes this h account-
ing more dicult to follow, even when the reader has worked carefully through the
previous accountings (numbers 1–3), which contain the ingredients to help make
sense of this one.
e rationale or motivation for this next accounting (Document 4) is not so
clearly given as for the earlier examples. As a nal footnote to Ricardo’s chapter “On
Rent”, it oers itself as an explanation of an otherwise cryptic statement about the
nature of rent under circumstances of increasing labour input: “First, he [the land-
lord] obtains a greater share, and, secondly, the commodity in which he is paid is of
greater value” (Ricardo, Principles, 1821, Works, I, p. 83). e accounting experiment
42 e fourth numerical account (1821, p. 82) is hardly developed in Ricardo’s chapter but gives
gures to consider alternative improvements to agriculture – those resulting from “such as the
plough and the thrashing machine, economy in the use of horses employed in husbandry, and a
better knowledge of the veterinary art, are of this nature.” (1821, p. 82). ese involve capital inputs
that save labour directly rather by altering the fertility of the land.
Model-Making: Ingredients and Integration 65
is designed to make sense of this, and, as we can see (below), Ricardo assumes that
with successive doses of extra labour, as with extra doses of capital investment, out-
put will increase but at a declining rate, and so rent increases in terms of quarters of
grain as labourers are added. But in each round of adding labourers, the price of a
quarter of grain also rises (recall from above: the labour theory of value of the clas-
sical economists argues that as more labour is required to produce an equivalent
amount of corn, the value of the corn must rise). So landlords get a double benet:
they get more grain (as rent) and the value of each quarter rises, which explains the
cryptic comment above. is accounting also unravels one of Ricardo’s apparently
paradoxical statements earlier: “Corn is not high because a rent is paid, but a rent
is paid because corn is high” (1821, p. 74). is statement may seem opaque, but its
causal structure is clear to anyone who has worked carefully through the numerical
accountings. Once again, because of its importance, I provide the full text for this
accounting:
DOCUMENT 4:
Ricardo’s Accounting 5*: From his Chapter II: On Rent, Principles, 1821, Wo rks, I,
pp. 83–4 footnote
To make this obvious, and to show the degrees in which corn and money rent
will vary, let us suppose that the labour of ten men will, on land of a certain quality,
obtain 180 quarters of wheat, and its value to be £4 per quarter, or £720; and that
the labour of ten additional men will, on the same or any other land, produce only
170 quarters in addition; wheat would rise from £4 to £4 4s. 8d. for 170: 180: : £4:
£4 4s. 8d; or, as in the production of 170 quarters, the labour of 10 men is necessary
in one case, and only of 9.44 in the other, the rise would be as 9.44 to 10, or as £4 to
£4 4s. 8d. If 10 men be further employed, and the return be
160, the price will rise to £4 10 0
150, . . . . . . . 4 16 0
140, . . . . . . . 5 2 10
Now, if no rent was paid for the land which yielded 180 quarters, when corn
was at £4 per quarter, the value of 10 quarters would be paid as rent when only 170
could be procured, which at £4 4s. 8d. would be £42 7s. 6d.
20 quarters when 160 were produced, which at £4 10 0 would be £ 90 0 0
30 quarters . . . . . 150 . . . . . . . . . . . . . . . . . . . . . . . . 4 16 0 . . . . . . . . . 144 0 0
40 quarters . . . . . 140 . . . . . . . . . . . . . . . . . . . . . . . . 5 2 10 . . . . . . . . . 205 13 4
100 100
Corn rent would increase in 200 and money rent in the 212
the proportion of 300 proportion of 340
400 485
e World in the Model
66
*is accounting 5 might be somewhat easier to follow as reformatted here. Holding
L (land) quality and K (capital) constant and increasing Lb (labour) inputs (assum-
ing declining output with successive units of labour), the accounting is:
L Lb O’put Price Rent Money
Qlty Qtrs per Qtr Qtrs Money Index
1 10 180 £4 0 0 0
1 +10 +170 £4.4.8 10 £42.7.6 100
1 +10 +160 £4.10.0 20 £90.0.0 212
1 +10 +150 £4.16.0 30 £144.0.0 340
1 +10 +140 £5.2.10 40 £205.13.4 485
is accounting in Document 4 starts o relegated to a footnote, and so looks as
if it is a minor point. And in the context of the other accounts earlier in the chapter,
the addition of more labourers to the eld can be understood as another solution to
the population/food problem. But the example soon comes to form the basis for two
further extensions to the accounts that move Ricardo to his laws of distribution.
e rst part of this move towards the laws of distribution is in the chapter “On
Wages”, where Ricardo extends the numerical account of adding men to the eld as
in Accounting 5, to explore the eect on wages of the increase in the price of corn
as more labour is used on the same land in his Accounting 6. In the second devel-
opment, in the chapter “On Prots”, Ricardo explores the eect on farmers’ prof-
its of increasing labour input. In this numerical Accounting 7 (Figure 2.2, below),
Ricardo rst repeats his numbers of the eect of increasing labour input on wages
and price of corn (as in his Accounting 6), and then explores the consequent eect
of all these things working together on the farmer’s prots and on the landlord’s
rent.43 In other words, Ricardo adds in two more ingredients of the model farm
accounts: the eects of increasing labour usage on wages and prots. is enables
him to use this numerical accounting in a demonstration of how the whole product
is shared between the three classes: farmer, landlord, and labourers. Because of its
importance once again, I provide here Ricardo’s full accounting statement, repro-
duced from the denitive Sraa edition (as Figure 2.2).
is nal numerical account is extremely important. It is the place where we
can see the model farm fully built, and we can see how it constitutes the medium
in which his arguments about distribution – and his laws of distribution – emerge
and are demonstrated in full.44 e accounting experiments with the model farm
show that as more labour is employed and food output grows, prots decline and
43 Reich (1980) attempts to analyse how far the share of rent rose during Ricardo’s life and to look at
the empirical basis for Ricardo’s arguments about rent in corn and rent in money. I merely note
here that Ricardo assumes that wages consist of a corn amount and a money wage amount and
uses numbers that are close to the prices of corn and money wages paid in his time.
44 See O’Brien (1975) on interpretations, and Barkai (1959) on consistency in the example.
Model-Making: Ingredients and Integration 67
Figure 2.2. Ricardo’s Model Farm Showing His Laws of Distribution.
Source: Piero Sraa: e Works and Correspondence of David Ricardo. Edited with the collaboration
of M. H. Dobb, 1951–73, Cambridge: Cambridge University Press for e Royal Economic
Society, Vol. I: e Principles of Political Economy and Taxation, 1821, from p. 116. Reproduced
by permission of Liberty Fund Inc. on behalf of e Royal Economic Society.
e World in the Model
68
rents take up their share while real wages remain constant. ese distributional
outcomes are each consistent with Ricardo’s previous ndings with his separate
accountings, but the eect of combining these ingredients is not easily predict-
able. And it is the combination that ‘determines’ the laws of distribution, the task
he had set himself out to solve in his Preface. Using these numerical accountings
integrated into a model farm, he had succeeded far more eectively than with his
earlier 1815 table in deriving results about a complex system of relations.
Finally comes the unexpected ‘punchline’ to these laws of distribution: Ricardo
continues his numerical experiment to discover that if more and more men keep
being added to the eld, there comes a point where the whole of the distribution,
beyond the amount that goes to labourers as a subsistence wage, goes only to the
landlord (£2880 in rent or 144 quarters of grain) while the farmers’ prots fall to
zero. And since prots must equalize at the lowest rate set in agriculture, this sets a
base level of zero prots for the economy as a whole. is would mean no further
capital investment in the economy and so no growth. While this state of stagnation
had been envisaged and feared by classical economists, it was Ricardo’s model farm
that succeeded in demonstrating how it might happen.
Whereas Malthus worried about population growth because of the vice and
misery that accompanied it, for Ricardo the more serious danger was that, in
the absence of any technical change, as more and more of the population were
employed in farming, prots would fall so far that there would be no investment,
and so stagnation in the economy. For both Malthus and Ricardo, these outcomes
were tied up with their numerical reasonings. For Malthus, those outcomes came
from his proposed numerical laws of population (that population grew geometri-
cally, and food supply arithmetically). For Ricardo, it was the other way around: the
laws of distribution and their surprising eects were discovered from his reasoning
with his numerical accountings, that is, his laws emerged from reasoning with his
model farm.
Not all Ricardo’s contemporaries appreciated the innovative way in which he
argued with his model farm. Ricardo reported that the premier French economist
of the day, Jean-Baptiste Say, had complained that he (Ricardo that is) “had made
demands too great on the continued exercise of thought on the part of my reader,
and had not suciently relieved him or assisted him by a few occasional examples,
and illustrations, in support of my theory.”45 Perhaps the problem was that some
readers of that day did not realise that they were being given helpful examples in
these numerical chains, while to some current readers, it is the particular examples,
such as adding many more labourers to elds, that seem a little odd.
In the broad context of the overall argument in Ricardo’s Principles, this
example of adding labourers to the same elds initially looks as if he was just cov-
ering the case for completeness of his argument – an articial, hypothetical case.
But when he continues with this accounting, and uses it as the basis for his account
45 Letter from Ricardo to Trower describing Say’s response; Works, Vol. VII, p. 178.
Model-Making: Ingredients and Integration 69
of distribution among the three economic classes dened in classical economics –
landlords, farmers/capitalists, and labourers – we become aware that it is a very
important case indeed. Although the example does not seem to t into the trad-
itional range of agricultural experiment and agricultural improvements (of adding
manure or of introducing new adding machinery), it turns out that this example,
of adding more and more men to a eld, is not at all a hypothetical case but rather
an actual proposal of Ricardo’s day. Adding labourers to elds was tried by a num-
ber of experimenting farmers during this period because of a contemporary pol-
icy debate on ‘spade husbandry’, a debate that spoke directly to the fundamental
problems that Ricardo was dealing with in political economy. is combination
of policy and scientic interest meant that this example would not only make sense
to his contemporaries but also made it the relevant case for exploring those issues
of distribution that interested him.
3.ii e Spade-Husbandry Debate
e ‘spade husbandry’ debate took place between about 1816 and the mid-1820s,
just the time that Ricardo was writing his Principles.46 is debate, over the pro-
ductivity eects of employing large numbers of labourers in agriculture engaged
both with the issues raised in the experimental farming of the day about the pro-
ductivity of dierent forms of agriculture, and with contemporary worries about
the condition of the labouring classes. On the former point about productivity:
spade husbandry was a labour-intensive kind of cultivation, a generic technol-
ogy rather than any one particular technique. Proponents argued that employing
labour in spade husbandry would increase yields per acre so much that product
prices could fall and labour could be paid more. It might be understood as some-
thing like the agricultural sector equivalent of Adam Smith’s well accepted, but
still somehow magical recipe for manufacturing epitomised in the pin factory,
in which the productivity gains from the division of labour were so great that
employing more labourers would lead to a more than proportional increase in
output, spreading wealth through the nations.47 Opponents argued that increased
labour usage must increase labour costs and therefore prices, despite a possible
rise in yield per acre. So, in an immediate sense, the ecacy of spade husbandry
was an open question of the day – open to argument and to experimental test.
But for Ricardo’s Principles, the spade-husbandry solution – of adding more men
46 Discussions about spade husbandry pre-, and postdate this particular period of intense debate,
and are associated with both radical reformers’ or utopianists’ and paternalists’ solutions to pov-
erty in the middle nineteenth century (see Chase, 1988). Archer (1997) argues that the provision
of allotments (spade-husbandry small plots) was associated with periods of rural unrest from
Ricardo’s period through until the 1840s; Moselle (1995) discusses the protability of such small-
scale farming; while others consider settlements such as the Chartist land colonies as a solution to
urban poverty (see Armytage, 1958).
47 West (1815, pp. 24–5), writing about rent just before the debate really got going in the weekly
papers, suggested indeed something like this analogy.
e World in the Model
70
to the elds – was precisely the solution that, according to Ricardo’s account (in
Accounting 7), had the power to reduce prots and so capital investment to zero.
Stagnation – the most dreaded worry of classical political economists and the
most notable prediction – would necessarily follow.
Yet the real problems had also to be taken seriously. ere was a particularly
high level of ‘distress’ caused by a lack of employment in the late 1810s, due to the
sudden fall in prices of arable crops that induced farmers to lay o labourers, and
this in turn added to the burdens on the parish-based poor law supporting unem-
ployed labourers. And remember that it was the parish, via its landowners, that
held the nancial and moral responsibility for looking aer the poor and destitute,
a matter that could certainly not be ignored by a landowner such as Ricardo whose
several country estates employed many farm labourers and in a period in which the
new industrial opportunities for employment in factories were still in their infancy.
Ricardo’s own country parish saw a considerable increase in the number of poor
supported by the parish in these years. ese were the short-run and immediate
problems for each farmer, for each labourer and for every parish, that is, for the
local political economy. e spade-husbandry debate addressed both productivity
and poverty issues. Proponents of spade husbandry claimed that their techniques
increased yields and increased labour employment, and so reduced expenditures
on the poor, thus potentially killing not two, but three, birds with one stone.
Spade husbandry appeared to oer landowners the possibility of providing
protable (to the landowner) employment to local unemployed labourers as an
alternative to supporting those same people via the local poor law. For a visionary
utopian scheme, there was Robert Owen’s 1819 proposal, discussed in Parliament,
for a model community using spade husbandry as part of a gardening utopia.48 A
capitalistic agriculture alternative was found in Sir John Sinclair’s proposal in 1819
to set up a joint stock company for a big investment in spade husbandry on mar-
ginal land.49 is widely publicized scheme was designed to put large amounts of
the unemployed labouring poor to work, but also to be prot making, and so be
attractive to potential investors.
Judging by the Farmers’ Journal, spade husbandry was subject to many actual
experiments as well as to these two projected schemes of Owen and Sinclair. In
this connection, recall that Mr. A. L.’s manure experiment of 1817 (reported in
Document 3) appeared under the title “Method of Employing the Agricultural
Poor”: it employed considerably more labour, as well as increasing output, and the
writer added a note linking his letter to the spade husbandry debate. On April 5,
1819 (front page, and p. 106), Mr. William Falla of Gateshead reported a number of
experiments, including one in which he extrapolates from his real experiments to
provide calculations for an extremely labour-intensive version of spade husbandry
48 See for example, Ricardo’s speech on the plan, Works V, pp. 30–5.
49 is scheme was to cultivate 10,000 acres of land close to London by spade husbandry. See e
London and Provincial Sunday Gazette and Political Inquisitor, February 7, 1819.
Model-Making: Ingredients and Integration 71
involving “transplanting 232,320 plants [wheat seedlings] at 4½p per 1000” by
hand!50 “A. Rasp,” a farmer from Gloucestershire, reported (see Figure 2.3) on the
Figure 2.3. Newspaper Report of a Farming Experiment with Spade Husbandry.
Source: Farmers’ Journal, November 6, 1820, p. 354, extract from letter entitled: “On Cultivation,
Chiey by Manual Labour”.
50 Farmers’ Journal, January 10, 1820 (front page), “C. W. P. in Gainsborough” provides calculations
from hypothetical spade husbandry of the “garden” type. On June 26, 1820 in the same journal
(again on the front page), an anonymous “Cultivator” of Hampshire reports his actual experiment
on the use of spade labour in potato cultivation.
e World in the Model
72
advantages of manual over horse ploughing in working the soil, providing exact
details of his cultivation methods for beans and the reasons he uses them; he also
details the cost to himself and the good return in wages to the labourer from his
cultivation experiment, neatly reported in parallel columns.51
By contrast, Mr. J. L. James, writing on a eld version of spade husbandry,
reported his observations in a way that substitutes lyric qualities for the prosaic
details and serious accounting usually provided in these reports:
DOCUMENT 5:
Extract from a letter to the Farmers’ Journal, May 10, 1819 (front page)
ON SPADE HUSBANDRY
SIR, London, April 30, 1819
. . . . . . having read in your Journal Mr Crowther’s letter on Spade Husbandry, with
his invitation to all persons to witness its method and produce, I turned my horse
with the intention of merely riding through his farm . . . . I was so struck with the
number of hands I saw bespangled over its elds, as it were like stars in the sky, that
I resolved on a more minute examination. . . . . . .
I then saw a eld, which this spring had been breast ploughed (what we call
drenchering,) and burnt, and a number of men were then employed in breast-
ploughing in the barley, at 12s per acre, and it certainly le the land lighter and
more likely to produce a great crop than if it had been ploughed with horses: the
men I found could earn, some 10s., some 12s., and some 15s. weekly according
as they were more or less expert hands. We then inspected several elds, about
y or sixty acres of wheat, which it appeared had not been ploughed but twice
in eight years, and it certainly had a most promising appearance. . . . e whole
parish seemed like a large machine, impelled by the prime mover, and all its sub-
ordinate parts performing their necessary oces with the regularity of wheels and
pinions. . . . . .
J. L. James
e spade husbandry debate petered out in the early 1820s, and judging from
the discussion in the Farmers’ Journal, it remained an open question whether, or
perhaps under what local conditions, and for what crops, spade husbandry would
show increasing yields (at least over some range) as labour input rose, or, as in
Ricardo’s numerical example, decreasing yields. Ricardo remained committed to
the classical economic view that technical change was always labour saving (as we
51 ere appear to be some errors in the accounting, but the general point is made.
Model-Making: Ingredients and Integration 73
learnt earlier), but he remained interested in the productivity claims of spade hus-
bandry. He expressed himself open to the evidence in his speech on “Mr. Owen’s
Plan” in Parliament in 1819, and he discussed the merits of the method in his notes
on Malthus text in 1820, and in reporting Mill’s views in 182152:
Mill does not shew the eect that would be produced by spade hus-
bandry, but the eect that would follow from an increasing people, which
should constantly require an additional proportion of the population to
be employed in husbandry. He would recommend spade husbandry, if it
could be shewn that the capital and labour employed in it, yielded more
than an equal capital and the same quantity of labour in plough or machin-
ery husbandry. (Ricardo, Works, IX, p. 56)
e point here is not the validity of the productivity claims, but rather that we
have found, in these spade husbandry experimental reports, an obvious contem-
porary reference point – and one known to Ricardo – for his case of adding labour
to elds, as well as many examples of the accounting format. And it is also par-
ticularly notable that we nd in this farming literature not only the reports of
real agricultural experiments on this question, but also accounting for the kind
of hypothetical farming or scenario calculations that Ricardo himself used in his
model farming. e most obvious dierence in these agricultural accountings
compared to Ricardo’s numerical accounting experiments are that the categories
of rent and prot are not always separated out. In the contributions to the Farmers’
Journal there tend to be only two factors: labourers and the farmer, suggesting per-
haps that the contributors were yeoman farmers. In contrast, in the earlier 1814
Lords Report Evidence about the corn laws, witnesses were usually either tenant
farmers or landlords’ agents and generally separated out capital returns from rents
in their accounts quite carefully. e second dierence is that contributors to the
debate, farmers or landowners, provided a commercial analysis showing their own
protability, not a general analysis of political economy in order to discern the law
of distribution of the classical system as Ricardo was striving to do with his model
farm.
4. Ricardo’s Model Farm and Model Farming
According to Alan Bennett’s play e Madness of King George (1995), both farm-
ing and the adjective ‘model’ were in fashionable use in Ricardo’s time. e term
‘model farm’ actually came into circulation only somewhat later; nevertheless,
I feel no qualms in using it for the numerical accountings that Ricardo created
52 Ricardo confessed he did not agree on the general principles of Owen’s plan but did think it
would be a good idea to ascertain the facts of the method (Works, V, p. 31 Speech in Parliament,
December 16, 1819 on “Mr. Owen’s Plan”). On Malthus, see Works, II, pp. 38–9.
e World in the Model
74
and ‘model farming’ for the way he used them to understand the economic
system.53
4.i ree Model Farms in One
Ricardo developed his model farm accounts to investigate particular questions
about the nature of rent and the problems caused by population growth, and to
determine the laws of distribution. To answer these questions, he created a set
of accounts for an imaginary farm, but not in one move. Rather, as this history
has shown, these accountings were built up step by step through his successive
chapters, so that the model farm and its behaviour emerged only gradually as dif-
ferent possibilities were posed and answered. e model farm was not a simplied
version of a real farm, for the numbers and their relations did not come, number
by number, from a particular set of farm accounts. Nor can we describe his set
of numbers as an abstract version of such a farm – they seem all too concrete.
Nor were his numerical accounts deduced directly from the laws of the classical
system, though they obeyed them. Rather, the model farm he developed was an
independently conceived object, using typical numbers from the agriculture of
his day and with the elements constructed to behave according to his ideas about
the dierent elements involved. To use the language of Chapter 1, he formalized
his ideas and knowledge – in the sense of giving form to them and making them
rule bound, in the model farm accounts. His model farm accounts were the places
where both specic agricultural facts and his concepts and ideas about rents, prof-
its, and so forth were brought together and integrated with the laws of political
economy of his school.
But there is something very unusual about Ricardo’s model farm. Of course it
was only a pen-and-paper object, but it represents and functions as a model in three
dierent senses at the same time, as:
A model farm that worked according to the various denitions, concepts, •
and laws of political economy in his Principles,
A model of real individual farms in terms of contemporary numbers and •
particular experiences, and
A model for the whole farming sector since the eects he worked through •
were those that would be evidenced at the aggregate economy level, not the
individual farm level.
53 e lm version of Alan Bennett’s play (1995) nishes with “model” almost as a refrain. ough
this was indeed the period when model farm buildings were being built (see Martins, 1980) and
the term “experimental farm” was occasionally used, the term “model farm” as a vehicle for the dif-
fusion of best practice farming (not just buildings) became widespread only in the mid-nineteenth
century (as a search of the journals reveals).
Model-Making: Ingredients and Integration 75
Let me justify these claims and explore the elements that enter into Ricardo’s model
farm so that we can understand more clearly how there is only one model farm, but
it can represent and function in all three of these domains.
4.ii A Model Farm that Worked According to Ricardo’s Economic Ideas
e rst thing to stress is that the model farm Ricardo created through his numer-
ical accounts is not quite what historians of economics have called “Ricardo’s corn
model” to refer to the general economic relationships of the system that Ricardo
posited. Rather the model being discussed here is Ricardo’s numerical model
farm, a pen-and-paper object, whose construction and behaviour depend on the
incorporation of a number of Ricardo’s denitions, concepts, and assumptions
of classical political economy and his views of how these were related together.
Ricardo’s model farm represents the elements of that system of political econ-
omy, and therefore should behave according to that system, but it is not itself
the system of those relations. It has a separate existence that allows it to function
autonomously.54
e main denitions, concepts, and assumptions that go into Ricardo’s numer-
ical farm model – as far as they are reported in this chapter and in the order they
came into the accounts – can be listed as follows:55
DOCUMENT 6:
Elements of the Classical System Used in Ricardo’s Model Farm
(a) Categories of the classical system: three economic classes: landowners, cap-
ital holders (farmers) and labourers.
(b) Problem addressed: population growth and the various suggested solutions
for increasing food output.
(c) Denition of rent as the return to landowner of the productive powers of
the soil.
(d) Law of prot rates to equalize.
(e) Assumption that the prot rate is determined on the least productive land.
(f) Determination of rent as the dierence in net produce (aer costs) between
the most compared to the lesser, and to the least, productive land.
54 See Morgan and Morrison (1999, chapter 2).
55 is list includes all the ones needed for the model farm accountings, but they were not always
fully listed each time in the discussion of the accounts in Section 3 above. Nor have I covered all of
Ricardo’s accounts, so the list above is not necessarily exhaustive, but is sucient for the accounts
discussed in this chapter.
e World in the Model
76
(g) Law of declining returns to increases in capital and labour inputs in
agriculture.
(h) Assumption that all technical improvements are labour saving, so produc-
tivity is dened in terms of labour required.
(i) Core assumption of classical economics: the “labour theory of value”.
Labour determines the value of a good; if less labour is needed to produce
the good, the value of the good is lower and if more is needed, there is a
higher value of the good. (With (h) above, the ceteris paribus consequence
of technical improvements is a fall in the value of the product because less
labour is needed.)
(j) Convention that wages consist of a monetary amount and a corn amount.
(k) Distribution of the product is shared three ways according to the ‘classes’ of
the classical system, but the distribution itself is determined by the various
denitions, assumptions and laws above.
(l) Tendency law of the prot rate to fall.
If we were to go back into Ricardo’s numerical accountings, we would nd
that all these elements of the classical system (denitions, concepts, assumptions,
and laws) were gradually embedded into the workings of the model farm as the
sequence of accountings built up. For example, at critical points, as we have seen,
the labour theory of value dictated the way prices changed in response to changes
in output due to technical change or to additions of labour. And we have also seen
how rent was not treated symmetrically with prot and wages: land was not a fac-
tor of production whose costs must be covered; rather, rent arose only due to a
shortage of land of the best quality. is last point (item f in the list) was the most
distinctive element of Ricardo’s particular version of classical economics. Ricardo’s
nal account for his model farm, Accounting 7, reproduced in Figure 2.2, is consis-
tent with the full list of elements, and the numerical experiments worked according
to the behavioural and accounting assumptions of this list. But there was no one
element in that list that determined how those model farm accounts were struc-
tured, nor could the numerical farm model be deduced from them for there is no
one-for-one equivalence between the elements of the model farm accounts and the
set of conceptual elements in that list. e model farm is a separate object in which
each of those conceptual elements has found representation. Of course, as we have
seen, these were not the only things that might be found embedded in the model
farm accountings.
4.iii A Model of an Individual Farm in the Period
At this point we might remember where we started the chapter – namely with the
criticism by some that Ricardo is thought to be responsible for making arguments
using abstract examples that seem remote from the actual economy of his time.
Model-Making: Ingredients and Integration 77
is is clearly not tenable in respect of his work in this area, for there are three ways
in which we have seen that Ricardo’s model farm accountings held strong empirical
content and so can be taken as a model of actual or typical farms of his day.
First, the numbers used for the numerical cases. Ricardo liked to pretend that
the numbers he dealt with in his text bore little relation to the numbers of his econ-
omy in order to claim generality for his resulting ‘principles’:
In all these calculations I have been desirous only to elucidate the princi-
ple, and it is scarcely necessary to observe that my whole basis is assumed
at random, and merely for the purpose of exemplication. e results,
though dierent in degree, would have been the same in principle, how-
ever accurately I might have set out in stating the dierence in the number
of labourers necessary to obtain the successive quantities of corn required
by an increasing population, the quantity consumed by the labourer’s fam-
ily etc., etc. (Ricardo, Principles, 1821, Works, I, p. 121)
However, as I have already suggested, many of his numbers were not randomly
chosen – the price of corn, the level of wages, and so forth were all ones within the
range of gures in typical farm experience of the period.
A second aspect of the model farm’s attachment to his world came in the con-
tent and form of Ricardo’s numerical accountings compared to the experimental
farming reports of the time. We have already discussed the characteristics of the
experimental farming of this period, when big landowners ran experimental farms
and practical farmers undertook experiments on their own elds to determine the
best crop rotations, the best forms of manure, and the best methods of cultiva-
tion. We can see how these were parallelled in Ricardo’s sequence of accountings,
which suggested taking more land into cultivation (via enclosure and extending
arable cultivation); by increased capital investment; and by innovations in agricul-
ture such as crop rotation, manuring – even by spade husbandry. His model farm-
ing experiments were all closely related to the actual farming experiments of his
period. We have also seen how Ricardo’s numerical accountings looked very much
like the reports of these farm experiments. Sometimes, as in the manure experiment
reported by Mr. A. L. from Tetbury, these reports were in running text; other times,
as in Mr. Rasp’s accounts for his spade husbandry experiment, they were tabulated
into a set of accounts detailing physical outcomes and the prot to be expected, or
that had been made, from their experimental interventions. Similar accounts were
typically oered as evidence in ocial reports or in agricultural surveys where the
experiments were not controlled eld trials but reports of the normal variations
from crop rotations – a kind of continuing natural experimental activity of many
farmers of the day.56 ese ways of reporting agricultural activities – by laying out
56 As we know, Ricardo was certainly familiar with these reports that gure in the “Evidence” attached
to the House of Lords’ 1814 report into the corn laws. Such kinds of reports are littered through the
county studies for the Board of Agriculture of Ricardo’s day.
e World in the Model
78
numerical accounts – suggest another way in which Ricardo’s numerical examples
can be seen as being well attached to his world. In this parallel, Ricardo’s farming
accounts can be understood as experimental farming reports for a ‘model’ farm
with some very special economic features and using hypothetical economic science
experiments, not physical agricultural experiments.
ird, Ricardo’s numerical examples chosen for his model farming, and the
motivation for each, could all be related to lively discussions in political econ-
omy of the day. As we have seen, population growth not only formed one of the
primary problems for political economists, but was also one of the main items of
contention in broader intellectual circles. e newly established census of popula-
tion, begun in 1801 (and continuing at 10-year intervals) had seemed to conrm
Malthus’ worries, and the various aspects of increased population were widely
understood to provide serious policy problems in the provision of adequate food
supply, and employment and poverty relief for the growing numbers of labour-
ers. For Ricardo in his arguments with Malthus, the important contemporary
economic issues had been the eects of population growth on wages and eco-
nomic growth, and the dynamic relationship between wages and the well-being
of labourers. In this context, Ricardo’s model farm experiments showed him that
whereas technical change in agriculture might, in the short run, increase food out-
put in line with population growth, the increased workforce eect of population
growth remained the longer-run problem. is was the fundamental reason why
Ricardo used the example of adding more men to elds throughout his discussion
of distribution issues, for it was this numerical experiment that most eectively
captured the whole set of economic concerns of the day. at it was also the case in
his model farming which crystallized the dismal predictions of classical political
economists – because it demonstrated a process that drove prots to zero – was an
unexpected and surprising outcome.
4.iv A Model Farm for the Whole Agricultural Sector
e third way in which the model farm functioned for Ricardo was as a version
of the agricultural economy as a whole. How do we know this? An individual
farmer who sets about experimenting with manure will gain a return in additional
output, but an individual farmer adding labourers to a eld will hardly alter the
price of corn, for that is determined by all the farms together in the aggregate. But
in Ricardo’s example, the price of corn does alter, so that clearly Ricardo’s farm
accounts functioned not only as a model of the individual farm, but as a model
of the agricultural sector as a whole. is has not gone unnoticed. Blaug argues
that in Ricardo political economy, “the whole economy is a giant farm, distribut-
ing its product among landlord, tenant farmer, and hired laborer” (Blaug, 1968,
p. 508). O’Brien refers to this as “Ricardo’s ‘collectivization’ – the treatment of
the agricultural sector as one giant farm” (O’Brien, 1975, p. 130). An alternative
view, suggested by Patten (1893), is to think of Ricardo taking an individual farm,
Model-Making: Ingredients and Integration 79
farmer, labourer, and landlord to represent the agricultural experience of typical
landlords, labourers, and so forth, and thus representative of the general whole.
Either as the typical farm that stands in for the whole, or as the giant aggregate
farm, Ricardo’s model farm accounts thus do double duty as representing both the
individual case and the aggregate.
However, this double duty does create certain problems of interpretation, and
O’Brien even refers to this aggregation as a kind of ‘trick’ (O’Brien, 1975, p. 123).
For example, in the reproduced Accounting 7 (Figure 2.2), the numbers in the top
part of the table relate back to the variation in Accounting 5 (Document 4), in
which we are thinking about individual farms with outputs varying along with
increasing doses of labour inputs, while the bottom half of the table is for just one
of those lines: a farm using one set of labourers harvesting 180 quarters of grain.
Yet, as Barkai noted, Ricardo moved from this latter “pattern of the distributional
shares of the product for a single dose only” to attribute it “to the economic sys-
tem as a whole” (Barkai, 1966, pp. 287–88).57 is raises a question as to whether
the revealed laws of distribution for that specied individual farm carry over to
those farms with other doses of labourer, and so raises doubts about the system as
a whole. While the pattern may transfer across, the levels or proportions may be
dierent. ese are the kinds of interpretation diculties that have worried the few
scholars who have wrestled with these numerical pieces in order to produce a con-
sistent version of Ricardo’s system.
5. Model-Making: Creating New Recipes
5.i Ingredients
Ricardo’s model farm was created out of conceptual elements and out of empir-
ical elements. ese ranged from conventional items (such as denitions and
laws, along with numbers from farming), but also less obvious empirical ele-
ments (such as the experimental farming tradition). Marcel Boumans (1999)
gives an account of this mode of model-making as a process akin to developing a
new recipe. He suggested that we think of all these conceptual and empirical ele-
ments as ingredients that have to be integrated together to form a model, much
like the ingredients of a new kind of cake have to be chosen and then mixed
together. But though the form of Ricardo’s numerical accounts mimicked those
of experimental farming reports, the model farm that Ricardo created did not
follow the existing recipe of real farming accounts; instead, his farm was con-
ceived as a new recipe – a new model in economic science, where the ingredients
of his accountings operated according to the laws, concepts, and denitions of
that science.
57 See also Barkai (1959).
e World in the Model
80
By virtue of its clever construction involving elements of both, Ricardo’s model
farm mediated between his ideas about how the economy worked and the practi-
cal economic realities.58 Morgan and Morrison (1999, chapter 2) suggest that the
possibilities for models to function autonomously in science in this way, and so
enable scientists to investigate both their theories and the world, depend on a cer-
tain independence of the elements used in their construction. Boumans’ recipe
analogy shows us in what sense these elements are independent – namely as a list
of separate ingredients: the small world in Ricardo’s model was made up from some
ingredients that relied on empirical information and others that came from the
fundamental laws of classical political economy.
Boumans’ recipe analogy also nicely indicates how model-making involves a
degree of exibility. A model, like a recipe, needs to be open in the sense that it can
incorporate some variations in the set of ingredients. We see how this ts Ricardo’s
work – not only did the numerical accountings dene a model farm in which a
combination of conceptual elements were tted together, but they were also tted
together in such a way that would be exible to the dierent ideas about how an
increased population might be supported according to contemporary experience
of agricultural change. at exibility to dierent elements, to suggested questions
and so solutions, was a feature of his accounting that allowed them to be extended
to answer a number of questions about the world depicted in the model – both as
individual farm and as aggregate farm.
But there are limits here. A recipe in which all the ingredients change, or are
put together in a very dierent way, is no longer recognisable as the same recipe
and there is no reason why such a new recipe should give us anything edible or a
new model be useful or fruitful. A model that is completely exible and open to
all questions and uses might prove doubtful in providing denitive outcomes, as
might one in which the elements are not suciently integrated together. A degree
of constraint in model design would seem to be a necessity. Ricardo’s model farm
was supple enough to be used to discuss a range of eventualities – both theoretical
and empirical – as we have seen in the series of accountings. But it was also con-
strained by its elements in ways that meant that the spade-husbandry case – in its
strongest claims – was problematic for his model farm.
e strong case for spade husbandry envisaged that the introduction of more
labourers would increase yields per acre and per labourer, for example, through dif-
ferent kinds of ploughing (substituting labour and light ploughs for heavier horse-
plough teams), more hoeing, and hand transplanting of seedlings, to such a degree
that more labourers could be protably employed, and that their wages could be kept
high. Such a claim for labour working in agriculture was incompatible with other
ingredients of Ricardo’s model farm, for he assumed declining yields per labourer
as labour input was increased and that all technical changes were labour saving.
58 See Wise (1993) for a discussion of mediating technologies in other contemporary sciences.
Model-Making: Ingredients and Integration 81
Such assumptions were compatible only with the weaker claims of spade husbandry,
namely of increasing yields per acre, but not per labourer (as in his accountings 5–7),
and so prices of corn rose as this happened because of the labour theory of value.
us the strong productivity claims of spade husbandry could not be incorporated
into the behaviour of Ricardo’s model farm – unless of course the model farm were
to be reconstructed in some of its fundamental ingredients. He did not do so. Even
though spade husbandry might have provided the real economy solution to the eco-
nomic problem that worried him, such a solution could not be easily incorporated
into his model for some of the less exible elements of the recipe forbade it.
5.ii Fitting ings Together: Integration and
Reasoning Possibilities
An important insight that comes from Boumans’ analysis is that integration of the
elements in the model does not just happen; it has to be eected by some kind
of moulding process or device that creates something whole out of the bits. In
Boumans’ cases, this moulding is done by the choice of mathematical formalism.
In Ricardo’s case, the integrating device for his model farm is an accounting con-
vention: it is neither the accounting conventions of double entry books, nor even
the simple conventional expenses and prot/loss accounts preferred by his contem-
porary farmers. Rather, Ricardo uses a set of more general accounting conventions
to provide the integrating element in his numerical accountings, namely, that the
total output must all be allocated to the economic factors, that all the items must
add to the total, and that inputs and outputs must balance in both real and mon-
etary terms. It was these principles that both moulded and held Ricardo’s model
farm accounts together. Such an integration is critical to the use of a model and to
how productively it functions.
Words are certainly adequate to state the labour theory of value, or the deni-
tion of rent, or the role of adding manure, or even the tendency of the prot rate
to fall. But what happens when you put these elements and events – and more –
together? Many times, Malthus and Ricardo argued their way over the same ground
as we have just covered in model farming: the ground being the likely progress in
the economy towards growth or stagnation; the impact of population growth, of
extending cultivation, of technical change in agriculture and their eects on wages,
on rent, on prots, on investment; on the progress of the agricultural sector versus
manufacturing; and on the dierences between nominal and real wages. We can see,
in the many written interchanges of correspondence between Ricardo and Malthus,
that they found it very dicult to argue these complex cases with just words. ey
used the verbal methods of classical economics to reason about the problem, to sort
out the ceteris paribus conditions, and to get their arguments to work according to
their instincts. But they found themselves falling into convoluted reasoning chains,
and oen failed to convince each other.
e World in the Model
82
Both Mathus and Ricardo sometimes used small numerical examples in their
arguments with each other.59 But such examples were developed more persuasively
by Ricardo into his model farming accounts, and these then provided him a way
around this problem of making convincing cases about any system involving so many
elements and so many variable aspects – as any political economy that had preten-
sions to be about the world must do. We can recall, from earlier in this chapter. e
diculties Ricardo had in using the two-dimensional table of his Essay in order to
see what happened when he put several variables together, where each was behav-
ing according to its own specied economic laws. Creating the model farm in his
Principles enabled him to overcome the dimensionality constraints of reasoning with
a table for it enabled him to integrate the dierent conceptual elements, denitions,
laws, and so forth (listed in the last section) together along with the empirical ele-
ments of agriculture that he believed important. is was not something that could
be done verbally, and as he already knew, was dicult to do in a table with only two
dimensions.
Ricardo used the series of pen-and-paper experiments with his model farm –
model farming – not just to answer particular questions with particular outcomes
and stories, nor just to show how the various individual elements of his economics
tted together but also – most importantly – to show how they worked together in
all their possible variations. In the process, Ricardo’s model farming moved from
simple experiments with only one element of variation (ones that almost consti-
tuted thought experiments) to a multidimensional experiment in which the vari-
ation in many inputs and outputs could be shown together. Turning the elements
(his ingredients) into a model farm, a farm that also acted as representative of the
agricultural economy as a whole, enabled him to solve – in an interesting and inno-
vative way, two major problems. One was the problem of how to show lots of things
happening at once and the other was to show how his various ideas and assump-
tions work together at the same time to create a particular set of outcomes. ese
are things he could not have achieved just with the written text. ey depended on
his forming a model and reasoning with it, that is, on his model farm and in his
model farming.
is reasoning relied on his model farm not just because that model formal-
ized these ideas – gave form to his ideas, nor because it also made them behave
formally – it made them rule bound (see Chapter 1). e reasoning also depended
on the way the elements of that object were held together by the integrating device
of accounting, so that the bits were forced into behaving consistently with each
other. is meant that when one bit of the puzzle was changed, it had immediate
59 eir numerical arguments are particularly a feature of the period 1815–16, when Ricardo was
working from his Essay to his Principles. ese numerical examples occur again in 1820 when
Ricardo is writing notes on Malthus’ new Principles (1820). At this later stage, they both used such
numerical calculations not as illustrations, but as ways of thinking and to demonstrate the results
of their theorizing to each other. Malthus tended to drop these thinking tools in his published
work, whereas Ricardo incorporated them.
Model-Making: Ingredients and Integration 83
implications that other bits must also change – the set of ingredients that went
into the model were independent, but they were not all independently available for
manipulation at the same time; it was only as an integrated whole that the model
could be properly experimented with.
We see all this most obviously in Ricardo’s nal accounting (reported in Figure
2.2 in Section 3), where all the elements worked out in previous accountings are
brought together to determine, and to demonstrate, how the general distribu-
tion works. Each bit of the puzzle – development of rent, increased labour input,
increased prices, eect on money rent, and so forth – had been discussed in previ-
ous accountings. e nal farm accounts integrated all the parts so that they worked
together and enabled him to show the overall outcome in a scenario of changes in
inputs, outputs, prices, rent, prots, and wages.
It is this nal accounting that reveals Ricardo’s laws of distribution – these
laws of distribution dictate what happens to the share of wages, prots, and rent as
changes occur in the economy. ese laws of distribution are not the set of assump-
tions (listed in Document 6 earlier) that were built into the model farm accounts,
nor are they self-evident from studying individual elements, their behaviour, or
the structure of the model farm. Rather, they fall out of his model farming, out of
his way of melding the evidence, relationships, and conceptual elements, together
using the accounting conventions, and using the model in an experimental way.
Ricardo used his model farm, and model farming as the means to discover how the
distributional outcomes are determined. So, the laws of distribution and their deter-
mination are not illustrated by the numerical accounts, nor are they merely shown
by working alongside Ricardo through his experiments with the model farm, rather
they are demonstrated in the sense that they deductively emerge from the creation
and use of the model farm as an integrated set of farm accounts.
Appendix 1: Numerical Argument in Ricardo’s 1815 Essay
Ricardo’s 1815 pamphlet known as his Essay on Prots, was fully titled “An Essay
on e Inuence of a low Price of Corn on the Prots of Stock”.60 is essay
contained the rst statement of Ricardo’s system of political economy and his
laws of distribution, but was only an important half-way stage in the way that he
argued for these laws – a way that marked something of a departure in economic
argumentation. In this 1815 essay against the corn laws, Ricardo was primarily
concerned with the relation between the price of corn and prots. He discussed
60 See Ricardo, 1821, Works, IV, pp. 1–41. As with all works by Ricardo, there is a debate about this
1815 table and what it does and does not show about Ricardo’s ‘corn model’. See O’Brien (1975,
pp. 132–5) for an analysis of the table and the extent to which other arithmetical examples could
be constructed consistent with Ricardo’s assumptions. Hollander (1979) discusses the table as a
numerical showcase for what is known as the ‘Ricardian model’, referring to the more generaliz-
able theoretical claims of the Ricardian system.
e World in the Model
84
the relative distribution of returns to the landlord and the farmer ( capital holder)
from capital investment in agriculture and from extending agriculture onto
unused or more marginal lands as a way of increasing produce to feed the ris-
ing population. His analysis, shown through numerical argument, suggested that
it would be better to import cheap corn than use capital in agriculture with a
declining prot rate.
e rst part of his argument in the 1815 Essay used a running arithmetic
example that was then reported using a table (reproduced here), actually an elab-
orate double table of hypothetical farm accounts, in which he needs to show how
both rent and prots change as investment takes place. In the top half, he shows
the eect of increased inputs of capital (measured in quarters of wheat) on less
fertile land, or equivalently land that was further from market, so that there is a
declining net product in wheat (aer paying costs) on each capital input. Because
of the principle that “the general prots of stock being regulated by the prots
made on the least protable employment of capital on agriculture” (1815, p. 13),
the prot rate must be the same on each capital input. e excess prot over costs
on the more fertile land compared to the less fertile land goes as rent. e top
part of the table shows, with great elaboration, what happens to prots and rent
for each section of capital input, as successive units of capital are applied and
the prot rate is equalized. It needs this degree of elaboration because each time
another portion of land with attendant capital input is drawn into cultivation, the
numbers for prot on capital and rent change on all previous portions of land, so
they all have to be shown again for each change in capital investment. is is done
by showing the changing inputs of capital on the le hand side, the changing rate
of prot and net output in the next two columns and then in successive columns
the eect on prots and rents for all the sections of land for that capital input. is
device of reporting each column separately allows him to show the process going
on (in Figure 2.4).
ere are three points of economic content in the table that we should note here
that are relevant for the chapter. First, as yet, the table did not show the position
of the labouring class in the distribution analysis, although his essay and letters
of the period show that he was fast working out the full explanatory account of
distribution that appeared intact from the rst edition of his Principles in 1817.
Second, although he argued about, and used his table to demonstrate, the eects of
increased capital investment and increased cultivation of marginal land, his argu-
ment with the table purposely assumed that there was no technical change in agri-
culture (though again, such changes were discussed in the essay). is assumption
was precisely made to point out the dangers of falling prot levels in the absence of
technical changes, such changes being the main means by which capital would oth-
erwise continue to nd protable investments. ird, his table demonstrated why
he argued against the taris on corn: if cheaper foreign corn could be imported,
there would be no need to expend cultivation and capital onto more marginal land
where the prot rate would fall.
Figure 2.4. Ricardo’s Table from His 1815 Essay.
Source: David Ricardo: “e Inuence of a low Price of Corn on the Prots of Stock” [1815] from Piero Sraa: e Works and Correspondence of Da-
vid Ricardo. Edited with the collaboration of M. H. Dobb, 1951–73, Cambridge: Cambridge University Press for e Royal Economic Society, Vol. IV:
Pamphlets and Papers, 1815–1823, p. 17. Reproduced by permission of Liberty Fund Inc. on behalf of e Royal Economic Society.
e World in the Model
86
ere are three points about Ricardo’s mode of arguing that are worth making.
First, although in principle the top table events could be happening simultaneously,
the bottom schedule assumes that these are sequential events, and cumulates the
totals as if for successive periods. In the England–Portugal trade example men-
tioned at the beginning of the chapter, we can view the two situations with or with-
out trade can either as alternative scenarios or as a change between times. In the
1815 table, it is essential that this is a time process, for Ricardo’s thesis is based on
the assumptions
that no improvements take place in agriculture, and that capital and pop-
ulation advance in the proper proportion, so that the real wages of labour,
continue uniformly the same; – so that we may know what peculiar eects
are to be ascribed to the growth of capital, the increase of population,
and the extension of cultivation, to the more remote, and less fertile land.
(Ricardo, 1815, p. 12)
So, Ricardo is interested in the growth process and the use of increased capital
inputs in solving the problem of feeding the increased population. Time would
not be necessary, if each addition could be thought of as an alternative scenario,
but it is necessary here in that the table reects the classical economists’ concern
with feeding a growing population while at the same time worrying about the
“tendency of the prot rate to fall” over time. In an economy as whole, Ricardo
proposed that this prot rate is determined by agricultural prots and if prof-
its fall to zero there, they fall everywhere, so investment ceases and stagnation
follows.
Second, Ricardo shows his delight in the way the table demonstrated some-
thing strange and new in showing that increased capital input would rst raise
prots in quarters of wheat and then reduce it while rent and net produce both
continued to rise: “is is a view of accumulation which is exceedingly curious,
and has, I believe, never before been noticed” (Ricardo, 1815, p. 16). Ricardo took
this nding to be an essential element of his set up, rather than an artefact of
the numbers chosen in the table (on which, compare Reuten’s [1999] account of
Marx’s numerical arguments). e point for us is that it gives a rst inkling of how
economists can learn things by using a set of accounts or a numerical ‘model’. It
is the results that seem counterintuitive or surprising that alert the economist to
the fact that something new has come out of the model-making and model-using
process.
ird, in the context of this chapter’s discussions, we might want to note his
disclaimer, footnoted before the table, that “It is scarcely necessary to observe, that
the data on which this table is constructed are assumed, and are probably very far
from the truth. ey were xed on as tending to illustrate the principle. . . . .” (1815,
p. 15). Given his familiarity with the political economy of his day (even before he
Model-Making: Ingredients and Integration 87
became a landowner), and the evidence of his letters, there is reason to be quite
suspicious of such statements.
Acknowledgement
is chapter grew out of a paper rst given to my departmental colleagues in May 2003; at
the History of Economics Meeting at Duke in July 2003; at the Economic History Seminar,
Oxford (November 2003); Seminar: “Knowledge and Society”, Institute of Historical
Research, London (December 2003); the “Histoire et Philosophie de la Mesure” Université
Paris 7 (December 2003); the University of California, San Diego, Science Studies Group
(January, 2004); and nally a LSE workshop on the “Facts” project (see working paper
Morgan 2005) in May 2005. I am grateful for comments on all these occasions. My thanks
also to Lesley Stringer, Márcia Balisciano, and especially Xavier López del Rincón Troussel
for splendid research assistance; and to librarians at the University Library in Cambridge
and Goldsmiths Library (Senate House) in London for help with Ricardo papers and pam-
phlets. Parts of this chapter were drawn from Experimental Farming and Ricardo’s Political
Economy of Distribution (LSE Working Papers on “e Nature of Evidence: How well Do
‘Facts’ Travel?”, No. 03/05, Department of Economic History, 2005).
References
Allen, Robert (1994) “Agriculture during the Industrial Revolution”. In R. Floud and
D. McCloskey (eds), e Economic History of Britain since 1700, Vol. I: 1700–1860
(pp. 96–122). Cambridge: Cambridge University Press.
Archer, John E. (1997) “e Nineteenth-Century Allotment: Half an Acre and a Row”.
Economic History Review, 50:1, 21–36.
Armytage, W. H. G. (1958) “e Chartist Land Colonies 1846–1848”. Agricultural History,
32:2, 87–96.
Barkai, H. (1959) “Ricardo on Factor Prices and Income Distribution in a Growing
Economy”. Economica, 26, 240–50.
(1986) “Ricardo’s Volte-Face on Machinery”. Journal of Political Economy, 94:3, 595–613.
Beatson, Alexander (1820/1) A New System of Cultivation. London: Bulmer and Nicol.
Bennett, Alan (1995) e Madness of King George. London: Faber and Faber.
Berman, Morris (1972) “e Early Years of the Royal Institution 1799–1810: A Re-Evaluation”.
Science Studies, 2:3, 205–40.
Blaug, Mark (1956) “e Empirical Content of Ricardian Economics”. Journal of Political
Economy, 64, 41–58.
(1958) Ricardian Economics. New Haven, CT: Yale University Press.
(1968) “David Ricardo”. In David L. Sills (ed), International Encyclopaedia of the Social
Sciences, Vol. 13 (pp. 507–12). New York: Macmillan.
Boumans, Marcel (1999) “Built-In Justication”. In Mary S. Morgan and Margaret Morrison
(eds), Models as Mediators: Perspectives on Natural and Social Science (pp. 66–96).
Cambridge: Cambridge University Press.
Chase, Malcolm (1988) ‘e People’s Farm’. Oxford: Clarendon Press.
e World in the Model
88
Cunningham Wood, John (1985–1994) David Ricardo: Critical Assessments, 7 volumes.
London: Croom Helm/Routledge.
Davy, Humphry (1814) Elements of Agricultural Chemistry. London: Longman, Orme,
Brown, Green, and Longmans.
Dorfman, Robert (1989) “omas Robert Malthus and David Ricardo”. Journal of Economic
Perspectives, 3:3, 153–64.
Farmers’ Journal (1807–1832) Originally Evans and Ruy’s Farmers’ Journal and Agricultural
Advertizer. Various issues.
Goddard, Nicholas (1989) “Agricultural Literature and Societies”. In Gordon E. Mingay
(ed), e Agrarian History of England and Wales, Vol. VI: 1750–1850 (pp. 361–83).
Cambridge: Cambridge University Press.
Gootzeit, Michael J. (1975) David Ricardo. New York: Columbia University Press.
Grisenthwaite, William (1819) A New eory of Agriculture. London: Neville.
Henderson, John P. with John B. Davis (1997) e Life and Economics of David Ricardo.
Boston: Kluwer.
Herbert, N. M. (1976) [ed] Victoria County History of Gloucestershire. Vol. XI: e Stroud
Valleys. Oxford: Oxford University Press/University of London.
Hilton, Boyd (1977) Corn, Cash, and Commerce: e Economic Policies of the Tory
Governments, 1815–1830. Oxford: Oxford University Press.
Hollander, Samuel (1979) e Economics of David Ricardo. University of Toronto Press;
London: Heinemann.
House of Lords (1814) “First and Second Reports from the Lords Committee appointed to
enquire into the state of the Growth, Commerce and Consumption of Grain, and all
laws relating thereto”. July 25, 1814, Parliamentary Papers, 1814–5, Vol. V.
James, Patricia (1979) Population Malthus: His Life and Times. London: Routledge and
Kegan Paul.
Malthus, omas R. (1814) “Observations on the Eects of the Corn Laws”. Reprinted in
e Pamphlets of omas Robert Malthus (1970) (pp. 95–131). New York: Augustus
Kelley.
(1815) “An Inquiry into the Nature and Progress of Rent”. Reprinted in e Pamphlets of
omas Robert Malthus (1970) (pp. 171–225). New York: Augustus Kelley.
(1820) Principles of Political Economy Considered with a View to eir Practical
Applications. London: John Murray.
Marshall, William (1779) Experiments and Observations Concerning Agriculture and the
Weather. London: J. Dodsley.
(1817/1968) e Review and Abstract of the Country Reports to the Board of Agriculture,
Vol. 5. New York: Augustus Kelley.
Martins, S. W. (1980) A Great Estate at Work. Cambridge: Cambridge University Press.
Milgate Murray and Shannon C. Stimson (1991) Ricardian Politics. Princeton, NJ: Princeton
University Press.
Mingay, Gordon E. (1975) Arthur Young and His Times. London: Macmillan.
(1989) [ed] e Agrarian History of England and Wales, Vol. VI: 1750–1850 Cambridge:
Cambridge University Press.
(1997) Parliamentary Enclosure in England. London: Longman.
Mitchell, B. R. and Phyllis Deane (1971) Abstract of British Historical Statistics. Cambridge:
Cambridge University Press.
Morgan, Mary S. (2005) “Experimental Farming and Ricardo’s Political Economy of
Distribution”. LSE Working Papers on “e Nature of Evidence: How Well Do ‘Facts’
Travel?”, No. 03/05, Department of Economic History.
Model-Making: Ingredients and Integration 89
Morgan, Mary S. and Margaret Morrison (1999) Models as Mediators: Perspectives on
Natural and Social Science. Cambridge: Cambridge University Press.
Moselle, Boaz (1995) “Allotments, Enclosure, and Proletarianization in Early Nineteenth-
Century Southern England”. Economic History Review, 48:3, 482–500.
O’Brien, Dennis P. (1975) e Classical Economists. Revised 2004. Oxford: Clarendon Press.
(1981) “Ricardian Economics and the Economics of David Ricardo”. Oxford Economic
Papers, 33, 352–86.
Oer, Avner (1980) “Ricardo’s Paradox and the Movement of Rents in England, c. 1870–
1910”. Economic History Review, 33:2, 236–52.
Overton, Mark (1996) Agricultural Revolution in England: e Transformation of the
Agrarian Economy, 1500–1850. Cambridge: Cambridge University Press.
Patten, Simon N. (1893) “e Interpretation of Ricardo”. Quarterly Journal of Economics,
7, 22–52.
Peach, Terry (1993) Interpreting Ricardo. Cambridge: Cambridge University Press.
Ramana, D.V. (1957) “Ricardo’s Environment”. Indian Journal of Economics, 38, 151–64.
Reich, M (1980) “Empirical and Ideological Elements in the Decline of Ricardian Economics”.
Review of Radical Political Economics, 12:3, 1–14.
Reuten, Geert (1999) “Knife-edge Caricature Modelling: e Case of Marx’s Reproduction
Schema”. In Mary S. Morgan and Margaret Morrism (eds), Models as Mediators:
Perspectives on Natural and Social Science (pp. 196–240). Cambridge: Cambridge
University Press.
Ricardo, David (1815) “e Inuence of a Low Price of Corn on the Prots of Stock”. In
Sraa, Vol. IV.
(1821) e Principles of Political Economy and Taxation (3 editions:1817, 1819 and 1821;
1821 edition reprinted as Sraa, 1951, Vol. 1).
Collected Works. See Sraa (1951–1973).
Rudge, omas (1813) General View of the Agriculture of the County of Gloucester, Drawn
up for the Consideration of the Board of Agriculture and Internal Improvement. London:
Sherwood, Neely and Jones.
Russell, John E. (1966) A History of Agricultural Science in Great Britain, 1620–1954.
London: Allen and Unwin.
Schumpeter, Joseph A. (1954) History of Economic Analysis (ed: Elizabeth B. Schumpeter).
New York: Oxford University Press.
Snell, K. D. M. (1985) Annals of the Labouring Poor. Cambridge: Cambridge University
Press.
Sraa, Piero (1951–1973) e Works and Correspondence of David Ricardo. Edited with the
collaboration of M. H. Dobb. Cambridge: Cambridge University Press for e Royal
Economic Society; reproduced by e Liberty Press, 2004.
Torrens, Robert (1815) Essay on the External Corn Trade. London: Longman, Rees, Orme,
Brown and Green.
Turner, Michael E., J. V. Beckett and A. Aon (1997) Agricultural Rents in England, 1690–
1914. Cambridge: Cambridge University Press.
Weatherall, David (1976) David Ricardo: A Biography. e Hague: Martinus Nijho.
Went, Robert (2002) e Enigma of Globalization: A Journey to a New Stage of Capitalism.
London: Routledge.
West, Edward (1815/1903) Essay on the Application of Capital to Land (Reprint of Economic
Tracts, Series 1, No. 3. Baltimore: Johns Hopkins University Press.
Wilmot, Sarah (1990) ‘e Business of Improvement’: Agriculture and Scientic Culture in
Britain, c.1700–c.1870. Historical Geography Research Series, No. 24.
e World in the Model
90
Winch, Donald (1996) Riches and Poverty: An Intellectual History of Political Economy in
Britain, 1750–1834. Ideas in Context, 39. Cambridge: Cambridge University Press.
Wise, M. Norton (1993) “Mediations: Enlightening Balancing Acts, or the Technologies of
Rationalism”. In Paul Horwich (ed), World Changes: omas Kuhn and the Nature of
Science (pp. 207–57). Cambridge, MA: MIT Press.
91
3
Imagining and Imaging: Creating
a New Model World
1. Introduction 91
2. Acts of Translation or a New Way of World-Making? 93
3. Making the Mathematical Economic World in Models 96
4. e Artist’s Space versus the Economist’s Space 98
5. e History of the Edgeworth Box Diagram – as Told by Itself 106
5.i Edgeworth’s Imagination and Image 107
5.ii Pareto’s Imagination and Images 115
6. e World Newly Made in the Model: Questions of Representation? 118
6.i Visualization 118
6.ii Newness 126
7. Seeing the World in the Model 129
8. Conclusion 131
1. Introduction
e Edgeworth Box is an economic model with which all economists are familiar.
It began life in 1881, underwent substantial development over the next decades,
and continues in use today: a modern version is shown in Figure 3.1. It is a small-
scale, manipulable, diagrammatic object – undoubtedly a model – made to repre-
sent the exchange relations between two individuals. It introduced important new
conceptual materials into economics and has functioned primarily as a device for
theorizing with. e form, the content, and the history of this model can all be
taken as exemplary both for the development of modelling in economics and for
the movement to make economics a mathematical science. ese late-nineteenth-
century developments of modelling and mathematization are intimately linked in
the discipline, though it is not clear exactly how, nor why it matters.
e pioneers who introduced mathematics into economics in the late nineteenth
century argued that it would make economics more scientic, because
economic
ideas expressed in mathematics are expressed more exactly, and reasoned about
e World in the Model
92
more rigorously, than when expressed in words. ese claims are also constitutive
of what is involved in the activity of modelling, for, as I argued in Chapter 1, model-
making gives form to ideas about the world and in the process gives formal rules to
reason with. Yet, mathematization and model-making are not the same move: all
models require a language of representation, but these need not be mathematical
ones.1 e model of economic man was developed (as we shall see in Chapter 4)
primarily in verbal terms, and each new version formed a specic portrait of a
model man to argue with. Analogical models are sometimes found produced in
the original language of the analogy rather than in mathematical descriptions
of them, such as Fisher’s mechanical balance or the Newlyn-Phillips hydraulic
machine (both found in Chapter 5), and these necessarily obey the language rules
of those analogical objects and elds.2 And while it is fair to say that, historically
Figure 3.1. Humphrey’s Modern Version of the Edgeworth Box.
Source: Tom Humphrey “e Early History of the Box Diagram” (1996). Economic Quarterly,
82:1, 37–75, gure 1. Reproduced with permission from the author, Tom Humphrey, and
e Federal Reserve Bank of Richmond.
1 As argued in Chapter 1, mathematics came into economics in the late nineteenth century, both in
modelling and as the method of postulation and proof. is ‘mathematization’ was controversial
within the economics discipline, though historians of economics have largely taken for granted the
terms of those historical contests, from the pioneers and detractors, as ones of methodology and
modernism. A notable exception is Weintraub (2002), whose wonderfully idiosyncratic study suc-
cessfully challenges the received view in many dierent respects. His chapter 5 (with Ted Gayer)
addresses the issue of mathematics as a neutral language, and is particularly relevant here.
2 Historians of economics have also paid considerable attention to the importance of analogies and
metaphors in the content expressed in mathematical economics (Mirowski, 1989) and to the evo-
lution of such ideas (e.g., Ingrao and Israel, 1990). ese are valuable metaphor-lead histories.
Yet not all analogical thinking provides for a ready-made mathematical economics (see Boumans,
1993, and more broadly, my Chapter 5), and if mathematics came into economics not from subject-
analogies but via formal analogies, that is between the form of economic ideas and mathematical
forms, this takes us back to mathematizing as a change of language (see my Chapter 4 discussion of
mathematical idealization).
Imagining and Creating Images 93
considered, the mathematical languages became preeminent in model-making, to
treat this development merely as a matter of language choice not only misses how
and why modelling relates to mathematization in economics. It also risks seriously
underestimating what was involved in modelling as a signicant development in
the practical reasoning modes of economics. So there are cognitive issues about
these historical changes in the way economics is expressed that need to be seriously
considered and claried.
But there are deeper issues that stem from the synchronous development of
mathematics and modelling. New forms of expression within a discipline involve
not just a change of method and the ways that scientists do their work, but also
changes in the things that they express. As scientists imagine their world, and make
images of that world in new forms, they also form new concepts to work and argue
with. Modelling as a new way of visualizing the economy, and mathematics as a new
language of expression, both prompt conceptual change. New ways of expressing
economic ideas – models and mathematics – lead to new things being expressed.
So the cognitive struggles these new processes of visualization entail are rewarded
by the new conceptual developments that come from them.
In this chapter, the focus is on the joint processes of visualization – imagining
the economic world and making an image of it – in creating small model worlds.
I start with the cognitive aspects of these changes in ways of expressing economics
and move into the conceptual aspects of these new modes of visualization before
turning to the historical development of the Edgeworth Box to show how – in prac-
tice – cognition and visualization are interconnected.
2. Acts of Translation or a New Way of World-Making?
If we start out by thinking of mathematics primarily as a language, then we might
portray mathematical model-making as a process of translating economics from
words to mathematics. But in general there is no reason why translating between
two such dierent kinds of language, from the older verbally expressed economics
into mathematical forms, should be easy. e problem of translating words into
mathematics might be compared with translating from words to drawings. e dif-
culty of this latter action is succinctly expressed by Ivins (1953) in discussing how
an artist could depict a botanical specimen, that he had not himself seen, from a
verbal description by someone who had:
It is doubtful if any much more intricate intellectual process can be imag-
ined than the translation of a linear series of verbal symbols, arranged
in an analytical, syntactical time order, into an organization of concrete
materials, and shapes, and colours, all existing simultaneously in a three-
dimensional space. (Ivins, 1953, p. 160)
Any account of the transition to modelling using mathematical modes of expression
in economics needs to recognise a similar kind of cognitive depth in the problem.
e World in the Model
94
Understanding model-making in economics as a process of translating verbal
economics into mathematics not only understates the cognitive tasks involved, but
also mistakes the nature of the problem in two ways. First, there is the question of
deciding on the appropriate mathematical language, for there is not one mathemat-
ical language but many. Second, there is the problem of knowing what it is that is
to be transcribed.
First then, even where there is a simple translation from words into mathe-
matics, the choice of mathematical language – and so form – is not necessarily
obvious. Economists can translate a straightforward verbal discussion of supply-
and-demand behaviour into mathematics, but they still have a choice of ways to
represent the behaviour. ey might translate these hypothetical schedules of how
people behave into two intersecting lines on a diagram (as Alfred Marshall did, as
we see in Chapter 7) or translate it into two equations – but the semantics and syn-
tax of these representations dier. Many economists assume that they are exactly
equivalent (and even say that they are ‘formally’ equivalent) but they are no more
equivalent than, for example, a couple of sentences written in Dutch and translated
into English. In that case, the words themselves will have dierent connotations of
meaning (the semantics), the sentence structure may well be dierent (the syntac-
tics), the symbols will be dierent (the words representing things will be dierent),
and some languages will require more symbols to express the ideas than others.
And, as I pointed out in Chapter 1 – these dierent formal languages have implica-
tions for the rules of manipulation of those models. So, rather than characterizing
model-making as a process of mathematical translation, we might better say that
it means choosing a kind of mathematics that enables economists to represent the
aspects of the economy that interest them into an appropriate form.
e second problem might be labelled as one of transcription. Even if the laws
of economics are written in mathematics, as some nineteenth-century economists
certainly believed, they are not there waiting to be transcribed.3 Economists don’t
know for sure what those laws are; as Irving Fisher suggests, they perceive them
only dimly:
e eort of the economist is to see, to picture the interplay of economic
elements. e more clearly cut these elements appear in his vision, the
more elements he can grasp and hold in mind at once, the better. e eco-
nomic world is a misty region. e rst explorers used unaided vision.
Mathematics is the lantern by which what before was dimly visible now
looms up in rm, bold outlines. e old phantasmagoria disappear. We see
better. We also see further. (Fisher, 1892, p. 119)
e intuitions that economists have about the economic world, and wish to express
in mathematics, may be very opaque and they use their imaginations to create model
3 See Le Gall (2007), who refers to such economists as ‘natural econometricians’, ones who believed
that careful use of statistics will reveal these mathematical laws.
Imagining and Creating Images 95
versions of the world as a way to explore those ideas. Here mathematics can be
helpful for, as Fisher (1892) argued, the mathematical method is the manipulation
of symbols as “aids to the human memory and imagination”, where “a symbol may
be a letter, a diagram or a model” (pp. 107, 106). So this activity of modelling helps
economists to express their intuitions, and indeed, they may come to understand
their ideas about how the world works only by making such small-world images.
us, both terms, ‘translating’ and ‘transcribing’, underestimate the task of
making an economic world in a model through mathematization. Translating is
not a rote activity but one in which material choices with consequences have to be
made. Transcribing makes a strong ontological commitment: it suggests that the
laws of economics are written in mathematics and economists merely had to gure
out how to decipher their own Book of Nature. Recognition of the presence and
importance of model-making in the mathematization of economics suggests not
acts of translation, or of perception and transcription, but rather ones of cognition
and of portrayal as economists sought to understand their world.
ese terms – of nding appropriate formulations, or of turning intuitions into
representations – suggest that we might gain from thinking about mathematical
model-making as acts of creation. Nelson Goodman’s Ways of Worldmaking (1978)
stresses how scientists and artists are involved in making sense of the world in
similar kinds of ways. Both groups make versions of the world as a way of under-
standing it and giving us insight into how it works.4 Understanding mathematical
modelling as a process of world-making focusses on economists’ ability to create
new accounts of the economic world, ones that would enable them to see further
or see more clearly. Portraying scientic modelling as acts of representation akin
to those of artists enables us to appreciate the role of both imagining and imaging
in world-making, and so the relevance of a term that has connotations of both
these, namely, visualization. is term is more naturally tted to artists’ work, and
certainly needs to be broadly interpreted if, as I intend, it is to apply to the ways
scientists make their accounts of the world. For economists, as for any scientists,
the process of making accounts of the world involves conceptual as much as per-
ceptual work. It takes both intuition and imagination to develop the abstract con-
cepts required to portray the economic world into a model. If we view modelling in
economics as the struggle to envision how the economic world works and express
that conceptual understanding in new forms, including mathematical ones, we get
to the broad and deep sense of visualization that I mean. In model-making, visual-
ization and understanding are inseparable.5
4 I interpret Goodman’s idea that both scientists and artists make versions of the world as that both
groups make representations of the world. Goodman is careful not to use the term representation
so broadly; R. I. G. Hughes (1997) interprets Goodman’s ideas in the context of model-making as
‘denotation’.
5 De Marchi (2003) is one of the few to have discussed this cognitive aspect of visualization in the
history of economics (see also the other papers in the ‘mini-symposium’ on visualization edited by
Leonard, 2003). Two books of essays that interpret visualization broadly within the history, sociology,
e World in the Model
96
3. Making the Mathematical Economic World in Models
How does this analysis of what it takes to create new forms of expression in
economics relate to the historical process of such a change? e arguments above
suggest that to make economics in the more exact forms provided by mathemat-
ics, economists needed not only those more exact languages, but they also had
to imagine mathematical representations of the world – that is, models – within
which their economic ideas could be expressed, just as to verbalise a particular
idea about economics requires a verbal description of the economic world in which
those ideas make sense. We all take our verbally described economic world as a
matter of habit. at verbally expressed economy – the nouns, verbs, descriptive
phrases and relations between them that economists still use – grew up over the
past centuries in such a way that their theories and descriptions of the economic
world could be expressed within that domain, within that version of the world.
e habits and the conventions of any symbolic system necessarily constrain what
can be expressed for, as Goodman wrote: “ough we make worlds by making
versions, we no more make a world by putting symbols together at random than a
carpenter makes a chair by putting pieces of wood together at random” (1978, p.
94). But those habits and conventions do not prevent innovation, for economists
continue to revise and remake versions of the economic world in whatever their
adopted language.
Creating a mathematically expressed economics was, historically, a process
similar to that of creating a verbal economics. Economists made their mathemat-
ical versions of the economic world, just as their forebears had made their verbal
ones, from many dierent sources of inspiration. It was no simple linear process.
Weintraub (2002) argues persuasively for us to see it as an ongoing interaction
between economists and mathematicians over a period in which both the image
and content of both elds are changing. From this complex and contingent histor-
ical process, economists came to think about the economic world in mathemati-
cal ways and so to represent it to themselves in new languages and new forms of
representation. Both were needed, so that over time, the elements of these new
mathematical economic worlds, their meanings, how they are symbolised, and
what relations are assumed, all came to be taken for granted. Economists argu-
ing for mathematization were proposing, in eect, a new way of world-making,
and philosophy of science, but that do not fully extend the notion to mathematical representations
are Lynch and Woolgar (1990) and Baigrie (1996). e classic work on visualization that includes
mathematics within its prole is Arnheim (1969). My focus here both contrasts with, and goes along
with, that of Bruno Latour in his clever 1986 article on visualization (reprinted in Lynch and Woolgar,
1990, under a dierent title). One can see the mathematical models of economics as having many of
the properties of immutable mobiles that he discusses in that paper. But contra Latour, my aim here is
not to think about mobility, but to problematize both visualization and cognition, on which see, from
dierent standpoints and generations, Toulmin (1953) and Nersessian (2008).
Imagining and Creating Images 97
one that required not only new languages but also new representations. It is from
this requirement for new representations that modelling became naturalized in
economics.
Two contrasting examples of model-making, one taken from the early
nineteenth century by Ricardo, and the other – the Edgeworth Box – from the
rst real generation of modellers later that century, may help to illuminate the
role of models in this process of mathematical world-making. For Ricardo (in
the previous chapter), it was natural to turn to the arithmetic of accounting for
expressing the relations in the agricultural economy and for his reasoning about
it. It was also natural for him as a landlord and nancier to use technical or con-
ceptual terms that were close in meaning to those of everyday use and that could
match the observable equivalents given in numbers, such as wages, prices, prots,
and so forth. Even when, as for rent, his economic concept was not quite the same
as that of the people in his economy, it was close enough in denition to be repre-
sented in the same accounting terms. It is not just the language of the terms in his
model farm that tted well enough to the common sense of economic arithmetic,
but that, as I showed, the format for Ricardo’s representations matched the kind of
experimental farming reports we found in his early-nineteenth-century economy.
So Ricardo took his terms and numbers largely ready made and chose accounting
rules for his arithmetic reasoning chains. But his model farm is dicult to pin
down as a separate manipulable image, for it emerged only when he worked the
bits and pieces of elementary relations – his ingredients – together in his reason-
ing with them.
In later nineteenth-century modelling, the process of imagining and image-
making involved more conceptual work along with the analytical work. In this
chapter, we see how Edgeworth fashioned a model to portray abstract concepts:
ones that had not previously been displayed in representations, rather than, as
Ricardo did, observable things with everyday labels. e visual elements of the
Box that carries Edgeworth’s name are not illustrations of something seen, but
conceptual elements that have to be imagined before they can be imaged. Some of
the elements are mathematical, and so have to be expressed in mathematical forms.
But mathematics by itself does not dictate the model, for how these conceptual
bits t together is done by making an image of their economic relations, that is,
by making a model. e economists who successively contributed to creating the
Edgeworth Box had to gure out both the language of representation and the nature
of that new representation, both mathematical and economic, in its format. Making
a mathematical economic world with models was a tall order. And, despite the best
eorts of Edgeworth and others of his generation, it could not, and was not, done
all at once.
What then can say of the historical relation between modelling and mathemat-
ization? Model-making, I suggest, owered during the late nineteenth century and
throughout the twentieth-century process of mathematization for two reasons. One
e World in the Model
98
is that exactly the kinds of qualities needed in making a new mathematical version
of the world are those found in model-making, namely, the abilities to be imagina-
tive about the world and to make images of it in new, nonverbal forms. e other
is that model-making provided a way of generating the vocabulary and forms of
the new way of thinking, and so of providing the new “working objects” on which
mathematical economic descriptions could be rened and tested.6 Model-making
became a critical element of this process of mathematical world-making in eco-
nomics precisely because, by its nature, it involved making the new representations
that were a necessary part of that process of world-making. is is my visualization
thesis in its most broadly construed form, but it encompasses the second thesis
developed in this chapter, namely that concerned with newness. ese two the-
ses – visualization and newness – cannot be argued for separately nor supported
independently. e arguments go along together. ese new representations that
came with modelling and mathematics involved conceptual elements that could
not be expressed in the old forms. So, both the nature and content of the new rep-
resentations, and the grammar they entailed, changed the way economists picture
the economy. In learning to create and use these new representations, economists
came to understand and see a dierent version, a newly made version, of the eco-
nomic world.
4. e Artist’s Space versus the Economist’s Space
e Edgeworth Box is a small world in a model, fathered by the economists in
the late nineteenth century who wanted economics to become a mathematical
discipline. It has since had a long and active life that continues into the present
time. But I am concerned here not with its life but with its creation story. I present
versions of that model’s origin and development from three disparate sources:
pictures of the Box’s development made by an artist of today, the original dia-
grams from economists’ historical development of the Box, and some modern
representations of that history. e comparative analysis of these three sets of
diagrams provides the materials for me to explore the roles of imagination and
image-making in creating economic models and the new conceptual elements
that they entail.7
I begin this account of model-making with an artist’s visualization of the
Edgeworth Box made to illustrate a retirement lecture by Prof. Arnold Merkies
from the Free University in Amsterdam in 1997. Here is a section of his printed
text; the charming illustrations are by Koen Engelen (Figures 3.2a–d).
6 e tag “working objects” comes from Daston and Galison (1992) and its import will be discussed
in Chapter 10.
7 It might be argued that I am weighting the scales in favour of my argument about visualization
because the model case I use is a diagram, and so its visual components are innate, yet C. S. Peirce
treats all mathematical reasoning as ‘diagrammatic’ (on which see Homan, 2004).
Imagining and Creating Images 99
Extract from Zo by Arnold H. Q. M. Merkies (1997, pp. 8–9), pictures by Koen
Engelen (Figure 3.2 reproduced with thanks to, and by permission of, ©A. H. Q.
M. Merkies), text translated by Ada Kromhout.
e market economy
What then about the Western method: the much-praised neoclassical system, or,
in today’s slogan, the market economy. In order to be able to analyse this, mathe-
matical economists tend to simplify the world. We will put the magnifying glass on
Koen Engelen’s pictures once more:
A closer look at the world
First, we isolate two people from the ve billion people inhabiting the world:
Two selected individuals with their possessions
(Figure 3.2a)
(Figure 3.2b)
e World in the Model
100
Next, we concentrate on the possessions of only two of their goods, for example,
cheese and wine:
e two individuals with cheese and wine only
In the bottom le corner we have Albert, and Beatrice is in the top right corner. His
colour is yellow, and her colour is green. e actual division of their possessions
of cheese and wine is indicated in the box. Such a reduction of the rich world into
merely some cheese and a bottle of wine is typical of the behaviour of the mathe-
matical economists: reduce the problem to a size on which we can pronounce.
And, nally, we substitute shadowy gures, who behave according to our wishes, for
the real individuals. We now are le with a rectangle, the so-called Box of Edgeworth:
Only cheese and wine
(Figure 3.2c)
(Figure 3.2d)
Imagining and Creating Images 101
As we can see from the text extract and the pictures involved, Merkies’ explanation
of how we reach the Edgeworth Box model is to start with a picture of the whole
world, then “simplify” by taking a magnifying glass to look closely at some detail of
the world, then “isolate” two “selected” individuals with all their possessions, then
“concentrate” on only two of their possessions, and then, nally, the people are made
abstract and their behaviour becomes ideal when we “substitute for the real individu-
als shadowy gures who behave according to our wishes” (Merkies, 1997, pp. 8–9).
I have picked out certain terms from Merkies’ account and repeated them here
precisely because they resonate so eectively with the way that philosophers of
science sometimes describe the process of creating mathematical models as one
entailing simplication, isolation, abstraction, and idealization (a process to be dis-
cussed in Chapter 4).8 According to this account, economists take the world and
convert it into something else: something simpler than the complexity that is there;
something that isolates a few relevant important parts from the whole; something
that is abstract rather than concrete; and something that is ideal and perfect rather
than real and messy. What is this something that has these characteristics? Is it
even necessarily a model? And does not such a description implicitly assume that
economists know the real world that they simplify and idealize, from which they
abstract and isolate?
Merkies’ description of dening the Edgeworth Box echoes exactly these ideas:
take the world, simplify, isolate, abstract, and idealize. ose philosophers seem
to have it right aer all! But we should not give in to their simplication account
so easily here because it omits something crucial, namely that the process also
involves making a representation of the economy, making a model of the economy.
As the real world is shorn away, rst the goods become shadows, the people lose
their detailed character and then disappear altogether, but at the same time we see
an image gradually emerging, depicting rounds of cheese and bottles of wine lined
up along two sides of a box, and a colour coding in the goods that indicates own-
ership by the absent people (see the colour plate of Figure 3.2). e illustrations by
the artist, Engelen, make us realise the important role of developing the image as he
makes a new representation at each stage of the model-making.
Modern economists too would create this Box by simplifying the complex
world. But they would start with the simplest case of one individual and one good,
and then add a second person with another good, gradually building up the ele-
ments of the diagram. And, since most economists are familiar with this Box, they
will habitually ll in all sorts of other details – details not shown in these pictures,
but to be seen in the later gures – without any further thought.
For economists reading this book, I ask please suspend your familiarity with
the usual elements, properties, and powers of this well-known little box model and
ponder a little these particular pictures. Bring back the imagination to ask: Why do
8 Good examples of this kind of account of how models are made, from philosophers of economics
from several dierent traditions, can be found amongst the papers in Hamminga and De Marchi
(1994) and are discussed in Morgan (1996).
e World in the Model
102
the two individuals line up in this antagonistic stance opposite each other? Why did
two colours (yellow and green) initially used for cheese and wine suddenly switch
to be colour coding for the two individuals so that in the nal picture the cheeses
and wines become dual coloured? How did the box ever get into the picture in the
rst place? Indeed, until the last picture, there is nothing in the narrative descrip-
tion about any box, and yet it appears as an element from the rst simplication
move. And why is it that, with this narrative of Albert and Beatrice and the won-
derful pictures, we do not yet have enough elements to make an Edgeworth Box?
Indeed, why did the artist stop there and not draw the other elements that econo-
mists habitually place in the Box?
Let me begin with the last question and provide some of the following parts of
Merkies’ narrative, which move beyond that supported by Engelen’s pictures:9
e neo-classicists assume that Albert and Beatrice will start negotiating
together until they decide upon a division they both consider to be bet-
ter than their initial situation: barter is taking place. e characteristics
ascribed to the two individuals guarantee they jointly nd a solution. ese
characteristics are, among other things, that they both prefer having a bit
of both goods to having much of only one good. ey have what is called
‘convex preferences’. So there is no teetotaller present. . . .
If we expand our small world, we meet with considerably more dicul-
ties. is expansion goes as follows. Suppose we had Albert’s possession of
money taken as a starting point, instead of his possession of cheese. And
suppose that, aer some bargaining, Beatrice is willing to give up two of her
bottles of wine in exchange for one hundred of Albert’s guilders. If Albert
agrees, the barter has resulted in a price of 50 guilders per bottle. at is
the so-called equilibrium price. Other individuals, with the same convex
characteristics as those of Albert and Beatrice, can now enter our small
world and also bid for Beatrice’s wine. We can also continue this process
by exchanging money against all other goods. us, ultimately, it appears
that it can be mathematically proven that, where there is free barter, equi-
librium prices can be established for all goods. is is the so-called Nash
equilibrium, named aer Nash, who, in 1994, received the Nobel Price for
his work published in the early Fiies.
Now, if there are only people of the convex kind living in our world, and
if there is freedom of trade under fair rules of play, then the Nash equi-
librium is a very attractive situation. Economists then speak of a Pareto-
optimal division. It is this division which the neoclassicists envisage as
the ideal picture: in a Pareto-optimal division, no one will feel the need
9 Merkies’ lecture compared various aspects of neoclassical versus socialist economics. e section of
his text omitted between my two quotations here, and between the paragraphs in the second quo-
tation, uses the case of Albert and Beatrice and the Box to point out that such a form of analysis in
neoclassical economics ignores questions of the initial distribution of goods and is concerned only
with the benets of trading what is already owned; see Section 6.i here for further discussion.
Imagining and Creating Images 103
to change the situation within the rules of play. Adherents of this theory
have an even stronger result: it can be proven that this same Pareto-optimal
division can be achieved also through freely varying prices, so through the
market mechanism, the invisible10 hand of Adam Smith. For economists,
this is familiar territory. It is the basis of the belief in the working of the
market mechanism. (Merkies, 1997, translated Kromhout, pp. 9–10)
It is extraordinary that the use of this little box model takes us so far so quickly.
In three paragraphs, Merkies moves the argument from Albert and Beatrice in one
act of bartering cheese for wine to equilibrium prices, Nash equilibrium, Pareto
optimality, and Smith’s invisible hand account of the market mechanism. Of course,
these results depend not only on many more assumptions than are evident in the
simplifying and isolating ones mentioned in the painter’s series of Figure 3.2, but
they also require the full Edgeworth Box as developed in historical series of Figures
3.4 and 3.5 rather than the pictorial versions here. e full Box supports such results
because it entails additional elements, of which only one is made explicit in this
commentary, namely that these are “people of the convex kind”. at is, the econo-
mist’s Box incorporates not only the elements of the perceptual world but also adds
in conceptual elements from economic theory that are required for reasoning to
such conceptual results as Pareto optimality, Nash equilibrium, and so forth.
e artist has taken the Box picture as far as possible in the realm of percep-
tion and illustration, the realm of what can be simplied and isolated from the
world. e artist can go no further in representing the world via such a process
of isolating and simplifying without becoming an economist. e economist adds
in the apparatus of the invisible individuals’ indierence curves to represent the
preference map of each individual. On these can be built the apparatus of oer
curves, contract curves, bargaining ranges, and so forth, all representations of the
economic world but expressed in the conceptual terms of Merkies’ second piece of
text (and whose historical development is discussed below). e contrast is made
vivid in Figure 3.3, which sets a modern version of the Box (our Figure 3.1, from
Tom Humphrey, 1996) alongside one of the artist’s diagrams (our Figure 3.2c, from
Merkies, 1997). e conceptual machinery is expressed in this modern Box dia-
gram, and it enables economists to argue in conceptual spaces, spaces beyond or
behind the perceptual space. e world of people and goods may be illustrated in
miniature in the Box by the artist, but the economic concepts have to be visualized:
imagined and imaged into that same space by the economist.
e dierence between the perceptual space of illustration and conceptual
space of visualization is discussed by Michael Mahoney (1985) in relation to per-
spective drawing and the new mechanics of the Scientic Revolution. He sets out to
10 In the Dutch text here it says ‘inwissel hand’, which would translate into something like ‘exchange
hand’. However, the translator suggests that in the Dutch text a typing error was made and assumed
that Merkies meant the ‘invisible hand’ (which would be expected for the text). is typographi-
cal error has been conrmed by Merkies in correspondence; however, the notion of an ‘exchange
hand’ is equally inviting in the context here!
e World in the Model
104
(a)
(b)
Figure 3.3. e Artist’s vs the Modern Economist’s Version of the Box.
Figure 3.3a. Source: Tom Humphrey “e Early History of the Box Diagram” (1996)
Economic Quarterly, 82:1, 37–75, gure 1. Reproduced with permission from the author,
Tom Humphrey, and e Federal Reserve Bank of Richmond.
Figure 3.3b. Source: Zo by Arnold H.Q.M. Merkies, 1997, pp. 8–9. Reproduced with thanks
to, and by permission of, ©A.H.Q.M. Merkies.
Imagining and Creating Images 105
destroy the Edgerton esis, namely that there was a direct causal link between the
Renaissance improvements in the drawing of machines and the development of the
science of mechanics. Mahoney argues that although the engineer-artists of those
days drew in new ways (they learned to provide accurate representations of physi-
cal objects in three-dimensional space), they did not draw new things; that is, these
new ways of drawing did not reveal the inner scientic principles of the machines.11
Rather, the science of mechanics at that time already treated the machine as
. . . an abstract, general system of quantitative parameters linked by math-
ematical relations [so]. . .it is dicult to see how more accurate depiction
of the basic phenomena as physical objects could have conduced to their
abstraction into general systems. For the dening terms of the systems lay
in conceptual realms ever farther removed from the physical space the art-
ists had become so adept at depicting. ose terms could not be drawn; at
best, they could be diagramed. (Mahoney, 1985, p. 200)
Reasoning about mechanics was already conducted in the language of mathemat-
ics. Mathematical diagrams remained the main form of representing mechanical
relations and were used for reasoning through the Renaissance. But, as Mahoney
remarks, “It is the mind’s eye that is looking here, and it is peering into the struc-
tural relations among quantities belonging to many dierent conceptual (rather
than perceptual) spaces” (p. 209). Mathematics here marks out the dierence in the
source of imagination, from the mind’s eye that both imagines and comprehends
compared to the body’s eye that sees.12
For the economist, exploring the economy by model-making involved repre-
senting the economy in new ways and involved drawing new things. e economic
elements inside the Edgeworth Box: the indierence curves, the contract curve,
the points of tangency and equilibrium, that is, the mathematically expressed ele-
ments, are new, mind’s eye, conceptual elements – not body’s eye, perceptual ele-
ments. Merkies’ description of the Box (his rst quote) accompanies the artist’s
perception, the body’s eye; his description of the ndings with the Box (his second
quote) depends on reasoning in conceptual space, reasoning which cannot be done
with the Artist’s Box (Figure 3.3b), but needs the full mind’s eye version of the
Economist’s Box (Figure 3.3a).
is distinction between conceptual space and perceptual space tells us how
to distinguish when a diagram is doing any work in the argument. If the diagram
is about perceptual space but the argument about conceptual space, the reason-
ing will take place, as Mahoney describes it, “o the diagram”. e diagram – in
this case, the artist’s version – will be, at best, an illustration, rather than a tool
for experimentation and demonstration. In contrast, Merkies’ second quotation
11 And the older drawings of machines were of such inaccuracy that an observer could not see how
the machine parts tted together, nor therefore surmise how the machine might work (in a non-
scientic sense) .
12 On the “mind’s eye”, see Ferguson (1977, 1992).
e World in the Model
106
reports the results of economists’ reasoning with the Edgeworth Box as the
diagram’s conceptual apparatus developed over the period from Edgeworth’s rst
diagram in 1881 until the 1950s and beyond. During that period the conceptual
resources of the diagram provided a highly creative reasoning tool. Humphrey
(1996) reconstructed this history of using the Box diagram, especially its important
role in deriving economic propositions and proving theorems, and its tremendous
versatility to deal with theoretical questions in various domains of economics.
Anyone who ever thought the Box diagram was ‘merely for illustration’ need only
read his account to see how using the model was critical in developing the theo-
retical results of mathematical economics.13 We turn now to the history of how the
diagram itself was made.
5. e History of the Edgeworth Box Diagram – as Told by Itself
e contrast between the artist’s illustrations and the scientist’s conceptual elements
of the Box teaches us something of the content of the economists’ model worlds
and shows that such models cannot be gained only by a process of taking the world
as it seems and subtracting things, for the conceptual content would be lacking.
But that contrast does not show us how the model was created. Nor does the artist’s
sequence of gures – for the artist, Engelen, in showing Albert and Beatrice, cheese
and wine, was representing an image already known to economists, an image that
had long ago established their convention of placing people at corners and lining
up their goods along two sides of a box as if along two sides of a graph.
e historical image sequences of Figures 3.4 and 3.5 show the history of how
the Box was actually developed. ey show how Edgeworth, Pareto, Bowley, and
others created the model that culminated in the modern Box diagram. ese his-
torical sequences suggest that successive economists created the Box diagram by
rst portraying how one individual behaves with respect to one commodity, then to
consider two individuals exchanging two commodities, and then into more com-
plex diagrams. is process of developing the world in the model by starting with
the most simple case and adding details (as a modern treatment would also do)
forms the opposite to the process of beginning with a description of the whole
world and simplifying downwards into a model world (as in Merkies’ account).
ese are well-accepted alternatives in model-making.14
13 Once every economist became familiar with the Box and its results, the diagram’s status in the
profession changed. It became an illustration for earlier results derived using the Box, and so used
as a teaching tool. At the same time, any search of the journals shows that it continues to be used
as a referent, as well as in new forms and ways in some of the most highly ranked journals in the
academic discipline, for it connects to important results derived from other forms of representa-
tion (game theory) and is used in human and computer experiments.
14 On these alternative accounts sometimes known as ‘concretization’ and ‘idealization’, see the dis-
cussions in Hamminga and De Marchi (1984) and in Morgan and Knuuttila (2012); see Chapter 4
on starting complex and making simple.
Imagining and Creating Images 107
ese actual historical sequences involve a number of surprising moves and
can be usefully compared with a reconstruction of that history using equivalent
modernized versions of the Box provided by Humphrey (1996). In reconstructing
his history of using the Box diagram, Humphrey modernized along one dimension
(the diagrams) to tell the history along another dimension (the theoretical results).
is was an eective device, but Humphrey’s set of images, also, could have been
made only by someone who already knew the Box, was familiar with what it could
represent, and with how it could be used.
My question is rather dierent: How did economists actually make this model?15
When we ask this question, it is clear that both the two generic accounts of model-
making (simplifying down or building up) and Humphrey’s reconstruction miss an
important point, namely, that the materials used in the model have to be imagined
before they can be imaged by the economist. Where Merkies’ artist could make an
image, and Humphrey redraw the images, the economists who created the Box rst
had to imagine the small world of the model. is is not just the dierence between
making a model to describe something known and one that has to describe some-
thing opaque. Rather the comparison points to the requirement to develop con-
ceptual clarity about those things that are only dimly perceived. is is where the
economist’s imagination comes in.
In this section, I seek to recreate the unfamiliarity erased by time and usage to
understand how this mathematical model – the Box diagram – came into being,
how economists used their imagination and built images to create that small
world in a model. Recreating this journey takes us from Jevons’ utility curve and
Marshall’s trade diagram (at the start of Figure 3.4), to the extraordinarily com-
plicated and conceptually rich version of the small world created by Leontief (at
the end of Figure 3.5). ese mark the start and end of the historical sequences of
images. is reconstruction of the Box’s development requires cognitive attention
to see just what is in the history (and – especially for economists – not to overprint
into the Box what comes later).
5.i Edgeworth’s Imagination and Image
e Edgeworth Box is named aer Francis Ysidro Edgeworth (1845–1926), an
Irish economist of great originality, whose work in both mathematical econom-
ics and statistics continued to be mined throughout the twentieth century. Like
Ricardo, Edgeworth came to economics from other elds: originally a student of
literature and classics, he trained as a commercial lawyer and taught himself math-
ematics before becoming a political economist. Edgeworth’s version of the Box
15 We might both be interpreted as following Lakatos’ (1976) example in Proofs and Refutations, with
actual history below the line, and reconstructed history above. We chose to reconstruct along dif-
ferent lines. And, while he does not show the original diagrams, Humphrey’s ne analysis reports
many of the historical changes made in the diagrams.
e World in the Model
108
diagram that bears his name – its rst appearance – was introduced in his now
famous Mathematical Psychics (1881), his rst main work of economics, a dense
and dicult book that develops economics into mathematical abstract forms and
applies them to all sorts of questions including those of unionism and coopera-
tives.16 Edgeworth begins his book by arguing for the application of mathematics
to economics and is gently scathing of those who suppose that one can solve argu-
ments by a form of reasoning which is mathematical but without the symbols that
make it mathematical and thus miss the “characteristic advantages of deductive
reasoning.” (Edgeworth, 1881, p. 3).
For Edgeworth, mathematics is both a language, and, because of its special
qualities, a tool or instrument for the expression of economic ideas and for rea-
soning about them. But in Edgeworth’s mind, it is also an instrument of imagi-
nation to capture the evidence and behaviour of “things not seen in the world”
(Edgeworth, 1881, p. 13). His imaginative speculations and descriptions about
economic behaviour were funded by many analogies, ranging from electricity and
magnetism to the Fairy Queen as a charioteer, reecting his erudition in many
elds of learning.17 is is an extraordinary book, perhaps mainly because it does
not t our prejudices of how a mathematical account of the economic world might
be written. Brian Rotman (2000) writes, most refreshingly, about mathematicians
as follows
Let us ignore the usual job description given of mathematics (exercise
of pure reason, pursuit of objective truth, free play of the mind, and the
like) and operate ethnomethodologically. We observe that mathematicians
spend their time scribbling and thinking: writing or manipulating . . . a pro-
digious range of symbols, as well as thinking about all manner of imagined
worlds and the objects/processes within them. (Rotman, 2000, p. 121)
is well describes Edgeworth’s ways of thinking and reasoning about the imagined
world of economics in mathematical terms in which – following Jevons – he con-
ceived an account of man as a pleasure machine.18
Much more might be said about Edgeworth and his many accomplishments,
but the hero of this story is his diagram. So let us dip straight into Edgeworth’s
account of exchange between two individuals as follows:
16 See Keynes’ essay (1926) for an early appreciation of Edgeworth’s work. For an account of
Edgeworth’s economic work on this particular topic, see Creedy (1986). For a new edited and
annotated version of this important 1881 book, see Edgeworth, ed Newman (2003).
17 For an example: “e invisible world of electricity is grasped by the marvellous methods of
Lagrange; the invisible energy of pleasure may admit of similar handling.” (Edgeworth, 1881/2003,
p. 13). For an account of the metaphors and analogies used in Edgeworth, see Newman’s version
of 2003, and Mirowski (1994, Part III).
18 See Edgeworth, 1881, p. 15. Jevons’ original development of utility graphs depended on analogical
thinking (see Maas, 2005, amongst others), and though Edgeworth used physical and psychophys-
ical analogies to present the ‘contract curve’, when it came to the Box diagram, the discussion (as
in Pareto’s treatment, see later) became rmly economic, yet expressed in mathematical forms.
Imagining and Creating Images 109
To illustrate the economical problem of exchange, the maze of many dealers
contracting and competing with each other, it is possible to imagine a mech-
anism of many parts where the law of motion, which particular part moves
o with which, is not precisely given – with symbols, arbitrary functions,
representing not merely not numerical knowledge but ignorance – where,
though the mode of motion towards equilibrium is indeterminate, the posi-
tion of equilibrium is mathematically determined. (Edgeworth, 1881, p. 4,
his italics)
e point at which they should settle to make an exchange is “mathematically
determined”, but the process by which they get there is not known. is is an eco-
nomic rather than a mechanical problem, and so the analogical content fades away
as he begins with his simplest case of two individuals with two goods to exchange
where parties are free to contract only by mutual consent and without competi-
tion from other traders. He denes the locus of points at which exchange might be
contracted as that where, whichever direction a move is made away from that set
of points, one trader gets more and the other less utility. is set of points he terms
the “contract-curve”. He then sets about (pp. 20–8) demonstrating the qualities of
his dened contract curve by a series of mixed mathematical (calculus rather than
geometrical proofs) and verbal reasoning describing these spatial arrangements,
to assure himself that the characteristics of the contract curve are sensibly proved
by dierent approaches. ese mathematical reasonings are analytic or general
in character, and are conducted in the language of mathematics: “let two individ-
uals. . . . Consider P – F(xy) = 0 as a surface” and so forth, but these do not quite
settle the questions that interest him about the range of indeterminancy and how
that might be overcome.
At a certain point in his mathematical discourse, Edgeworth moves into
one of his imagined worlds, and the original version of the Box appears as his
gure 1 (see Figure 3.4c) encased in the following text: (my underlinings, his
italics):
It is not necessary for the purpose of the present study to carry the
analysis further. To gather up and x our thoughts, let us imagine a sim-
ple case – Robinson Crusoe contracting with Friday. e articles of con-
tract: wages to be given by the white, labour to be given by the black.
Let Robinson Crusoe = X. Represent y, the labour given by Friday, by
a horizontal [sic] line measured northward from an assumed point, and
measure x, the remuneration given by Crusoe, from the same point along
an eastward line (See accompanying gure 1 [Figure 3.4c here]). en any
point between these lines represents a contract. It will very generally be in
the interest of both parties to vary the articles of any contract taken as ran-
dom. But there is a class of contracts to the variation of which the consent
of both parties cannot be obtained, of settlements. ese settlements are
represented by an indenite number of points, a locus, the contract-curve
(a) (b)
(c)
(d)
(e)
Figure 3.4. Historical Sequence of Original Box Diagrams Part I.
(a) Jevons’ Utility Curve (1871).
Source: William Stanley Jevons, e eory of Political Economy, 1871, London: Macmillan & Co.,
g. 4 p. 49.
(b) Marshall’s First Trade Diagram (1879).
Source: Alfred Marshall, “Pure eory of Foreign Trade”, 1879, gure 1. Marshall Library,
Cambridge. (Reprinted, London: London School of Economics and Political Science Reprints of
Imagining and Creating Images 111
CC′, or rather, a certain portion of it which may be supposed to be wholly
in the space between our perpendicular lines in a direction trending from
south-east to north-west. is available portion of the contract-curve
lies between two points, say η0x0 north-west, and y0ξ0 south-east; which
are respectively the intersections with the contract-curve of the curves of
indierence for each party drawn through the origin. us the utility of
the contract represented by η0x0 is for Friday zero, or rather, the same as if
there was no contract. As that point he would as soon be o with the bar-
gain – work by himself perhaps. (Edgeworth, 1881, pp. 28–9, his italics,
underlining added)
us Edgeworth imagines his Robinson Crusoe and Friday at right angles to each
other in the same plane, shoulder to shoulder, as bets those who must mutually
agree before exchange can take place. Edgeworth’s (x, y) space is a plane, and the
indierence curves are projections from three-dimensional utility surfaces; thus he
imagines and makes his image accordingly (and so he correctly wrote that for his
gure 1 we draw the Y-axis horizontally northwards). e individuals, Crusoe and
Friday (X and Y), are not fully and separately distinguished on the diagram from
those things that they have to exchange (x and y).
It seems so natural to economists nowadays to represent the two goods for
exchange along these two axes, but it was not so in the late nineteenth century
when economic diagrams were still in their infancy. Edgeworth’s reference two
pages earlier to Marshall’s 1879 trade diagrams, which use this convention, pro-
vides the likeliest clue to their provenance. In Marshall’s diagrams, such as in the
second of our historical series, Figure 3.4b (another one was shown in Chapter
1), the oer curves depict the amounts oered for exchange at dierent prices by
sellers of English cloth in exchange for German linen and vice versa, one oer
curve for each of the two countries. e two goods are represented on the two
axes and the whole of the space between is open for trade between two coun-
tries. Edgeworth depicts two individual traders alongside their goods in a similar
Scarce Tracts in Economics, No. 1, 1930). Reproduced with thanks to Marshall Library of
Economics, Cambridge.
(c) Edgeworth’s Exchange Diagram (1881).
Source: F. Y. Edgeworth, Mathematical Psychics. London: C. Kegan Paul & Co., 1881, g. 1,
p. 28.
(d) Pareto’s “Optimum” Box Diagram (1906).
Source: Vilfredo Pareto, Manuale di Economia Politica. Milano: Societa Editrice Libraria,
1909 Edition, g. 16, p. 138.
(e) Pareto’s “Improvement” Box Diagram (1906).
Source: Vilfredo Pareto, Manuale di Economia Politica. Milano: Societa Editrice Libraria,
1906, g. 50, p. 262.
Figure 3.4. (Cont.)
e World in the Model
112
arrangement, and includes Marshall’s oer curves, seen as the two internal dotted
curves on Edgeworth’s diagram (Figure 3.4c).19.
Edgeworth’s rst invention is to draw an indierence curve – the outer dotted
lines – for each individual in this trading space: the individual is indierent
between points along their curve, for they represent ones of equal utility to him.
is is usually regarded as a critical step forward in the history of neoclassical
economics, in which Edgeworth takes Jevons’ 1871 “pleasure machine” graph in
Figure 3.4a (also discussed in Chapter 4) showing sensations of utility experienced
by an individual from consuming one good and develops it into a utility map rep-
resenting the utility of combinations of two goods to the individual (Figure 3.4c).
And while it seems initially that the whole space is open for trade as in Marshall’s
Figure (3.4b), Edgeworth’s Figure (3.4c) draws the indierence curves through
the origin, that is, points at which utility is equivalent to that obtained from zero
exchange. is rules out some areas of the 90-degree total space. As he drew in
these curves it became clearer that this representation of the problem of exchange
restricts the space in which contracts might be made compared to Marshall: the
range of indeterminancy of exchange is not the whole plane, but only the area
within the indierence curves and the contract curve.
e contract curve: CC′, the second of Edgeworth’s innovations – represents the
line of most desirable contracts for exchange that Crusoe and Friday might make with
each other. As they bargain from the origin point, they can move northeastwards to
points where either or both are better o up to the points on the contract curve.
Once settled there, no variation is possible without making one of them worse o.
Edgeworth’s analysis showed the range of bargaining, but exactly where they settle
depends on the bargaining strength of each of the two individuals: “is simplest case
brings clearly into view the characteristic evil of indeterminate contract, deadlock,
undecidable opposition of interests” (Edgeworth, 1881, p. 29). And so Edgeworth
indicates the role for industrial arbitration “for instance, Robinson Crusoe to give
Friday in the way of Industrial Partnership a fraction of the produce as well as wages,
or again, arrangements about the mode of work” (Edgeworth, 1881, p. 29).
So far, Edgeworth uses the diagram to demonstrate – neatly and eectively – his
abstract concepts and spatial reasoning. en he begins to develop the diagram as
19 It is not immediately clear from Edgeworth’s 1881 diagram what his two middle curves are. ey
cannot be indierence curves, because the contract curve is a locus of points at which the indier-
ence curves are at tangency with each other. Edgeworth’s footnote, p. 27, noted the close but not
identical concepts of Marshall’s treatment of instability in trade compared to his own treatment of
instability of contract (and he referred to Marshall’s gures 8 and 9 – which is consistent as a refer-
ence to Marshall, 1879 [1930]). In Edgeworth’s 1891 similar diagram, these are Marshallian oer
curves, and the consensus of the literature (see Creedy, 1992) is that they are indeed oer curves.
I am indebted to Chiara Baroni for her research assistance and translation of various Italian art-
icles of the 1890s which show Edgeworth (1891) repeating the basic elements of his 1881 diagram,
and making some comparison with other diagrams of the period, in the context of a commen-
tary on Marshall’s trade diagrams. A history of these oer curve diagrams is given by Humphrey
(1995), who also discusses other diagrams by Edgeworth from the 1880s. See also Cook (2005)
and De Marchi (2003).
Imagining and Creating Images 113
an instrument of enquiry to consider what happens with more than two traders: this
is the case of ‘imperfect competition’ (which had previously failed to yield to math-
ematical analysis). He works with the gure to reason through the process by which
agreements might be made and then broken as more traders enter the market.20 e
uncapped axes that he inherited from Marshall’s trading diagrams put no limit on
the amount of resource that can be exchanged. is enables him to represent agree-
ments at greater (and lesser) exchange amounts as the process of imperfect compe-
tition goes ahead. Just as Ricardo had found unexpected insights from developing
and using his model farm, Edgeworth gained new understanding from developing
his model of exchange contracting and then from his reasoning with it.
Edgeworth was so impressed by the way his own diagram enabled him to gen-
erate insights about the process (rather than the outcome) of what happened when
additional traders joined the market, that he wrote (1881, pp. 36–7, underlining
added) that “the gure 1, page 28, is proved to be a correct representation,” and
that reasoning with it provides “an abstract typical representation” of the process
that “will go on as long as it is possible to nd a point x′y′ with the requisite prop-
erties. . .”. In continuing this argument, he notes that this process arrives at the point
ηξ on his gure 1 (our Figure 3.4c), where the price ray from the origin will be at a
tangent to both indierence curves (not shown on his diagram, but shown on the
equivalent modern diagram, Figure 3.6b), which is also where the oer curves meet
at the contract curve (shown on both). is point, Edgeworth notes, is the limit
point to the case of increasing numbers of traders, namely the point obtained when
full competition is in place.
It is not the primary aim of this chapter to go into the way that models such
as the Edgeworth Box are used (see rather Humphrey’s 1996 account) or how
economists reason with them in general (see my later chapters). But because of my
world-making claims, I need to delve a little further into how Edgeworth viewed
this episode. From the beginning of his book, we see Edgeworth arguing for math-
ematics in economics, imagining how the economy could be described in mathe-
matics and representing the economic world in mathematical terms and models.
He arrived at his diagrammatic mathematical model – his gure 1 – by imagining
a particular case he took to embody the typical exchange problem and making an
image to represent it.
Having made his model to represent two parties in an economic situation, he
then used it to demonstrate his previous claims, and to explore and explain other
aspects of exchange behaviour that could be represented in his diagram. In this, he
was following a pattern of representing trading situations: not only Marshall’s dia-
grams of exchange between England and Germany, but recall also from Chapter 2,
Ricardo’s earlier arithmetic example of trade between Portugal and England. As we
20 At this stage, Edgeworth does not even bother to deal with the case of perfect or market compe-
tition since he claims that the results and nature of the equilibrium outcome are well understood
from the work of Jevons, Walras, and Marshall.
e World in the Model
114
shall see in Chapter 9, models made to represent situations form a continuing and
important tradition in economic modelling. And while such diagrams represent
specic situations, by providing convincing demonstrations of a logical kind that
might well t typical cases they seem to acquire broader relevance.
Edgeworth understands the powerfulness of such reasoning with cases, as we can
see in his discussion of non-numerical forms of mathematical argument. Although
he applauds mathematics because its “very genius is generalisation, [which,] without
dipping into particulars, soars from generality to generality” (p. 86), he also claims
that mathematics can get general results from arguing single particular cases:21
Indeed, the nature of the subject is such that a single instance – by a sort
of ‘mathematical induction,’ as it has been called – a single ‘representa-
tive-particular’ authenticated instance of mathematical reasoning without
numerical data is sucient to establish the general principle. (Edgeworth,
1881, Appendix I, “On Unnumerical Mathematics,” p. 83, his italics)
is claim about “ a sort of mathematical induction” using a “single ‘representative-
particular’ instance” is an apt description of his reasoning about Robinson Crusoe
and Friday and what happens to their exchanges when you add traders into their
isolated island market, that is, to their economic world in the model. If we take his
description “an abstract typical representation” as a good one for something we
would now denote ‘a model’, along with his equally interesting description of his
mode of reasoning with it as: “a single ‘representative-particular’ instance of math-
ematical reasoning”, then we have an appealing combination of denitions of mod-
els and model reasoning.
But there is also an appeal to generality in Edgeworth’s reasoning: he claimed
mathematics could establish a “general principle” by working with a single instance,
a particular representative case, a diagram created from his imagination.22 is
sounds rather grand, and perhaps untenable. Yet the same thing occurred with
our parallel example from the last chapter. Ricardo’s enquiry into his little arith-
metic model of the exchange of cloth and wine between Portugal and England – a
very simple and particular case – also produced an outcome that has been taken
21 It appears to be in the nature of geometric reasoning that particular cases are taken to provide gen-
eral proofs; see Arnheim, 1969, chapter 10, for an interesting discussion of this, and Netz (1999)
for an account of the origins of such reasoning in Greek mathematics. For much of the nineteenth
century, geometry was the exemplar of the mathematical method and the way to establish truths
via mathematical argument (see Richards, 1988, and Weintraub, 2002 for its relevance for econo-
mists in that period). Edgeworth’s views might be contrasted with those of Marshall, whose claims
for the inductive role of diagrams rested on the possibility of drawing out all the possible cases
(see De Marchi, 2003). I suggest however, in Chapter 10, that their two positions can be seen as
consistent once one understands how the scope of model ndings is extended across cases via
mathematics.
22 is seems close to C. S. Peirce’s views: “Mathematical truth is derived from observation of cre-
ations of our own visual imagination, which we may set down on paper in the form of diagrams”
(C. S. Peirce, Collected Papers, 1932, Vol. 2, Para 77).
Imagining and Creating Images 115
as demonstrative not just for the world in his model, but for a general principle,
namely, for the law of comparative advantage.23 e question of how economists
reason with such abstract typical representations and representative-particulars
will reappear later in Chapter 10, when I explore how such arguments with cases
support claims that might best be described as generic rather than general.
5.ii Pareto’s Imagination and Images
Vilfredo Pareto (1848–1923), an Italian contemporary of Edgeworth, was an
equally important character in the development of mathematical economics, but
his creation of a small economic world in a mathematical model proceeds very
dierently. Pareto’s Manual of Political Economy (1906 [1971]) uses two types of
mathematical reasoning; the primary one in the text develops through a series
of arguments in which diagrams are the main mathematical form, and another,
relegated to a long appendix, oers a more general treatment using algebra and
calculus (like Marshall, he places some of his mathematical treatment in the
background). Like Edgeworth, he relies on general arguments to introduce the
specic diagrams, but unlike Edgeworth, these arguments are not analogical in
character and he relies on the diagrammatic form much more extensively to work
out his arguments and explanations of the economic behaviour of individuals.
He portrays individuals as having particular tastes and seeking to do the best for
themselves, but they are faced with and constrained by ‘obstacles’. Individuals
must take various paths to get around the obstacles, a trial-and-error, wandering,
process reected in the various diagrams he uses. Indierence curves between
two goods are interpreted as contour lines on a map, for, as with Edgeworth, they
are projections from an imagined (but not imaged) three-dimensional utility sur-
face, with equal levels of utility along each contour. So an individual reaches an
equilibrium when they have succeeded in getting around the obstacles and they
have reached the highest point on their contour map. His description is extremely
graphic.
Amongst a plethora of diagrams, the two that move Edgeworth’s diagram for-
ward are the rst appearance of it as a box: his gure 16 (our Figure 3.4d), and his
gure 50 (our Figure 3.4e) in which the diagram is used to develop the notion of
what is known as a ‘Pareto improvement’. e former gure 16 creates a box from
Edgeworth’s open axes, and reorientates it (by ninety degrees), with the two indi-
viduals at opposite corners, each with a whole set of indierence curves (rather
than the single one for each individual drawn in by Edgeworth). e latter, gure
50, is similar but shows only two indierence curves for each individual. One of
23 While this law remains as a general foundational tenant of economic science, its ability to account
for our observations of the world is more doubtful. Indeed, its failure to explain trade patterns has
lead to the development of other trade ‘principles’, or general claims, some of which were devel-
oped through reasoning with the Edgeworth Box.
e World in the Model
116
these individuals is represented as located with axes 0x and 0y and indierence
curves labelled with t, so that as that person moves further away from their origin
at 0, they are at successively higher levels of utility or pleasure (Pareto’s “ophelim-
ity”), they are moving uphill in Pareto’s terminology. e other has axes ωα and
ωβ and indierence curves labelled with s, moving uphill as they go away from ω
towards 0. ey appear with the following theorem and commentary on it:
We have the following theorem:
For phenomena of Type 1, when equilibrium takes place at a point where
the indierence curves of the contracting parties are tangent, the members
of the collectivity under consideration enjoy maximum ophelimity [utility].
(Pareto (1906[1971] Chapter 6, Para 34, p. 261, his italics)
For phenomena of Type I, we know that the equilibrium point must be
at a tangency of the indierence curves of the two individuals. Let c be one
of these points. If we move away from it following the route cc′, we ascend
the rst individual’s hill of pleasure and descend that of the second; and
conversely, if we follow the route cc′′. Hence, it is not possible to move away
from c helping, or harming, both individuals at one and the same time; but
necessarily, if it is agreeable to one, it is disagreeable to the other.
It is not the same for points, such as d, where two indierence curves
intersect. If we follow the route dd′, we increase the satisfaction of both
individuals; if we follow the line dd′′ we decrease it for both. (Pareto,
1906[1971], Chapter 6, Para 35, pp. 262–3)
Type I phenomena are those in which neither individual tries to alter the mar-
ket terms of exchange, that is, where the two individuals’ indierence curves meet
at a tangency with the price ray (the ratio of exchange between the goods, repre-
sented by a straight line) so the equilibrium is at point c as in his gure 16, a point
that comes to be called ‘a Pareto optimum’.24 Type II phenomena appear when indi-
viduals do have some power to alter the price ratio, and as Pareto argues, at their
likely equilibrium point d, there are possibilities for both parties to gain utility by
moving in direction d′, and for the collective utility therefore to rise: that enquiry,
with his new setup in the diagram, lead to the fundamental notion now known as
a ‘Pareto improvement’. But still the nal point of exchange is indeterminate, and
here Pareto muses regretfully about the impossibilities for economists – if only they
were as lucky as chemists – to conduct experiments with individuals in exchange
situations to further these investigations. Several decades later, his wish came true,
and an example of such experiments with individuals in the situation depicted in
the Box is reported in Chapter 8.
24 Point c will be a point on Edgeworth’s contract curve: the set of points where the indierence
curves are tangencies to each other (which is not shown in Pareto’s diagram). When two indif-
ference curves meet back to back at the price ray (that is, where the price ray is a tangent to both
indierence curves as at point c) that point comes to be called a ‘Pareto optimum’ – a notion
mentioned by Merkies.
Imagining and Creating Images 117
For Pareto, as for Edgeworth, the essential and important reasoning is done
with the diagram, not o the diagram, though in the case of Pareto, the diagram is
taken as oering neither a typical case nor grounds for a mathematical induction.
For Pareto, the reasoning just is diagrammatic. His series of specic cases – each one
shown in a diagrammatic model – represents his mathematical economic world
within which he builds up his arguments. While his ‘sketch’ account (using his g-
ure 50 diagram) is strong enough to carry the detail required to convince, Pareto,
like Edgeworth, argues that rigorous proofs of his theorems can be given only by
mathematics (in his Appendix). For both it seems, general analytical treatments are
not necessarily of greater importance than the economic reasoning with diagrams
in the text. For both, the diagrammatic models provide the arguments for the two-
good, two-traders world, and they are sucient for demonstrating results and gain-
ing conviction about that small economic world in the model.25
e Box diagram is, however, an extremely deceptive object. It looks like
a very constrained world in the model: What can it possibly have to say more
broadly? First, as we saw in Merkies’ arguments, despite its small scale and appar-
ently limited scope, Edgeworth’s and Pareto’s demonstrations with the Box reach
towards some fundamental and general results in mathematical economics such
as Pareto optimality and so to the “First Fundamental Welfare eorem” in mod-
ern economics (see Blaug 2007). Second, as we know from its later history (see
Humphrey, 1996), although this small-scale world was built to represent specic
exchange situations, it turned out to have great exibility over a range of similar
trading situations as well as in other domains of economics such as in production
and welfare economics. ird, although the Box is a two-dimensional object on
paper, the number of things it can represent does not seem to be unduly con-
strained by that dimensionality. Edgeworth manages to enlarge his small world
to argue the case with more traders and, even as early as Pareto’s time, the Box
represents two individuals, each with two goods in exchange, along with equilib-
rium points and price rays: that is, it already shows relations among six economic
elements.26
Given these kinds of exibility, it is perhaps not so surprising that for both
Edgeworth and Pareto, diagrammatic models played an important role in their
making a new version of the world for economic science, one that could be rea-
soned with mathematically. In creating their mathematical diagrams, they followed
a process of imagination and image-making. ese visualizations embedded new
conceptual materials for economic analysis (indierence curves, contract curves,
and Pareto improvements). A further historical sequence of diagrams also supports
25 Of course, when economists nd models too small and limited in dimensionality, and seek to
generalize to bigger worlds (e.g., to cases of more goods and more traders), they may look to other
kinds of mathematical demonstrations, perhaps to the general equilibrium account of Walras (and
the method of mathematical postulation and proof; see Chapter 1).
26 Lancaster (1957) claimed that later boxes show relations among twelve economic variables, pos-
sibly he was including the production elements as well.
e World in the Model
118
deeper and broader claims about newness. For this I return to questions about
representation.
6. e World Newly Made in the Model: Questions
of Representation?
6.i Visualization
As we observed in discussing the picture sequence within Merkies’ text, model-
making is a creative process; but the actual historical sequence of visualization
observed in Figures 3.4 and 3.5 is very dierent from that of his artist illustrating
an already well-accepted model diagram. When economists rst make an image of
the economy, it is not that they already know how the world works and subtract
elements from it to isolate certain parts. Rather it is that they use their imaginations
about the hidden workings of the economic world to make representations of those
workings in equations or diagrams. Gradually over time, other economists add fur-
ther elements to the representation. e historical development of the Edgeworth
Box model enables us to explore some detailed questions about this process of
model-making and to answer certain earlier questions about the representation:
Why is it a box? Why are the individuals in an antagonistic stance? And so forth.
Here the relevant comparisons are not between the historical sequence and
the artist’s pictures, but between the historical sequence and an economist’s mod-
ernised versions of the Box. If we start with the modern Box representation (as
seen already in Figure 3.1), we nd two adjacent sides of the Box denoting a xed
amount of the two goods or services or resources available so that the Box repre-
sents a world with given and xed resources. e two antagonistically placed origin
points mark the direction of stance of two traders, each with their own two axes
(the adjacent ones), and on which their own shares of resources by endowment and
by exchange can be marked.
But this was not how Edgeworth imagined the economic world. Our compari-
son reveals that the most striking thing in this historical sequence of diagrams,
evidenced in our second series Figure 3.5a–f, is that Edgeworth’s 1881 diagram
is not a box at all, but an open plane, in which the quantities of goods at issue are
not xed but expandable (in Figure 3.5a).27 It is equally striking that Edgeworth’s
individuals line up side by side: each trader measures o his resources for exchange
27 Economists are now so habituated to the modern diagram that some have diculty in seeing what
imaginative leap was required and what was new about Edgeworth’s diagram. My experience in
giving this chapter as a seminar paper was that some economists found it dicult to believe that
Edgeworth did not conceive of a box – despite his diagram; others argued that he must have fully
conceived all the conceptual contents and outcomes before he drew it, that is, that the diagram was
“merely illustration” to his argument – despite the textual evidence (quoted above) which suggests
otherwise.
(a) (b) (c)
Figure 3.5. Historical Sequence of Original Box Diagrams Part II.
(a) Edgeworth’s Exchange Diagram (1881).
Source: F.Y. Edgeworth, Mathematical Psychics. London C. Kegan Paul & Co., 1881, g 1 p. 28.
(b) Bowley’s Box (1924).
Source: Arthur Lyon Bowley, e Mathematical Groundwork of Economics, An Introductory Treatise. Oxford: Clarendon Press, 1924, g. 1, p. 5.
Reproduced with permission from Oxford University Press.
(c) Lenoir’s Box (1913).
Source: Marcel Lenoir, Études sur la Formation et le Mouvement des Prix. Paris: M. Giard & É. Brière, 1913, g. 22, p. 21.
(d) (e) (f)
Figure 3.5. (Cont.)
(d, e) Scitovsky’s Extending Box 1941.
Source: T. De Scitovszky (1941), “A Note on Welfare Propositions in Economics”, e Review of Economic Studies, 9:1, 77–88, g. 1 diagram 1 on p. 80
and g. 1 diagram 2 on p. 81. Reproduced with permission from Wiley-Blackwell.
(f) Leontief’s Box 1946.
Source: Wassily Leontief (1946), “e Pure eory of the Guaranteed Annual Wage Contract”, Journal of Political Economy, 54:1, 76–79, g. 1 on p. 77.
Reproduced with permission from University of Chicago Press.
Imagining and Creating Images 121
along one axis only – one trader X is trying to make a contract by trading his own
x for some y oered by Y. What might now be taken as the irreducible shape of the
Box – namely a closed set of two amounts of exchangeable items represented by the
sides of the Box, and two traders at opposite corners, each with two axes of poten-
tial commodities to trade with – are not there from the beginning. In Edgeworth’s
imagination and diagram, the world is represented very dierently from that found
in the modern version.
It was Pareto in 1906 (in French in 1909), who without comment, imagines and
places the individuals at the SW and NE corners (this new orientation becomes
the standard one). By placing them opposite each other and making the diagram
into a Box as we saw in his gure 16 (Figure 3.4d), he represents a xed quan-
tity of both goods, but, by extending the axes beyond the rectangle, invites the
possibility of extension. Marcel Lenoir (1913), who was familiar with Edgeworth
and Pareto’s work, picked up the latter’s formulation of the Box, and seems to have
anticipated Bowley’s innovation of moving the starting point for trade inside the
Box (Figure 3.5c). Apparently Pareto’s contribution was not immediately known in
the English-language literature, and this perhaps explains why Bowley’s 1924 image
(Figure 3.5b) follows Edgeworth in orientation (i.e., potentially NW–SE), while he
too presents the two traders at opposite corners. And though he presents almost
a box, it remains open, or rather, unclosed, and his axes appear exible in length.
Bowley puts numbers on his sequence of indierence curves: he thinks of them
as representing nonmeasurable, but ordered, sensations of satisfaction, where the
numbers are like readings of heat on a thermometer, except that “e thermometer
is calibrated; the imaginary vessel of sensation is not” (Bowley, 1924, p. 2).28
Lenoir’s and Bowley’s most important image change then is moving the starting
point for trade – the point from which trading commences according to the indif-
ference curves, and that we now call ‘the endowment point’ (the point representing
how much each trader is endowed with) – into the middle of the Box.29 By con-
trast, Edgeworth had pictured Crusoe and Friday starting exchange from a posi-
tion where each owned only the full amount of his own resources. is imaginative
move has consequences, for while the indierence curves can be drawn fully inside
the Box (as Humphrey shows in our Figure 3.1), the oer curves for the traders
must be drawn from their initial endowment point: every change in endowments
alters the bargains they are likely to agree to, and thus the range of the solutions.
28 is habit relates to a debate over the cardinality or ordinality of utility measures (and so of indif-
ference curves) and the broader relation between psychology and economics – see Coats (1976)
for an historical account of these issues.
29 Historians of economics have argued over whether Edgeworth’s original diagram can properly be
called a box and over the relative contributions of Edgeworth, Bowley, and Pareto to its genesis
and development (see particularly Creedy, 1980; Tarascio, 1980; and Wetherby, 1976). Lenoir’s
contribution was unknown until recovered by Chaigneau and Le Gall (1998). In the British lit-
erature, the Box is sometimes known as the Edgeworth-Bowley Box, possibly because, in his con-
tinuation of Edgeworth’s work, Bowley added these two specic innovations of double axes and
endowment points.
e World in the Model
122
Much of neoclassical economics’ use of the Box follows this lead of starting from an
initial point inside the Box and using that point to address questions of eciency
and optimum outcomes, but these will be optimum only given that initial endow-
ment of goods. So, by assuming the endowment point is already given, questions
about welfare and equity in the initial distribution of wealth are closed o. Merkies’
lecture was concerned with such equity issues, which, as we can now see, became
masked by the historical development of moving the endowment point into the
Box. Lenoir’s and Bowley’s version of the diagram thus proved a highly signicant
move in the history of welfare economics.
As we have seen, the diagram was originally developed to analyse the exchange
outcomes of two individuals. e question that Edgeworth inherited from Jevons’
utility map of pleasure and pain for one individual was to picture what happened
with just two individuals – not market exchange with many traders on both sides.
He portrays an isolated island economy – of Crusoe and Friday – to provide an
imaginative focus for considering how two such individuals would bargain and
where they will end up making an exchange. He argues that the exchange point
between these two will rest on the contract curve, but exactly where will depend
on their relative bargaining power. Pareto develops the Box to dene which moves
towards an exchange point within the area of possible points are improvements for
both. Bowley uses his Box diagram (Figure 3.5b) to argue that the area of bargaining
is not on the contract curve, but dened by the range of exchange points bounded
by Marshall’s oer curves and the contract curve: Bowley’s Q1QQ2 (if B sets the price
ratio, the solution will lie at Q 1 and if A controls the prices, at Q2). For both Pareto
and Bowley then, the exchange outcomes are dependent upon the original endow-
ment point, as well as upon the relative bargaining power of the traders in nego-
tiation as Edgeworth had argued. Leontief (Figure 3.5f) uses the diagram to label
another two points – his points e and f, equivalent to Edgeworth’s boundary points
on the contract curve (points C and C′ on the modern image Figure 3.6a) – as the
solution points for ‘perfectly discriminating’ monopolists in contrast to Edgeworth’s
earlier location of the point of perfect competition.
e Box edges might seem unimportant, but this aspect of the image too is
an element to be carefully considered. While Bowley’s two axes continue but do
not meet, Scitovsky (1941) (our Figure 3.5d), like Pareto, extends his axes beyond
the Box, as indeed does Lerner (1933/52), who, by simply substituting factors of
production for goods to exchange, and production maps for utility maps, made
his Box represent production, not exchange. We see the importance of whether the
Box is joined up, and so resources xed, or not in the work of Scitovsky. He uses his
diagrams to establish what would happen if the Box grew in size. e critical point
of his article is the dierence in judging allocative eciency between situations in
which the total resources in the economy are xed – denoted by a xed size Box,
and those in which the resources change – denoted by a change in Box size. e
representation of the eect of this change proves to be quite dicult to under-
stand for the modern user of boxes: it is an imaginative and cognitive diculty.
Imagining and Creating Images 123
It is tempting for the viewer of the model to suppose that by expanding the Box,
there are just longer axes, more cheese and wine to be exchanged for a given indif-
ference maps (representing tastes, which have no reason to alter). But of course,
these indierence contours are in conceptual space inside the box, and increasing
the total resources eectively expands the box from the middle. As the axes are
lengthened, perceptual space expands, but so does the conceptual space, so that the
contract curve on his rst diagram becomes the two dotted lines on the second (see
Scitovsky’s 1941, Figure 1, Diagrams 1 and 2, our Figure 3.5d and 3.5e). Changing
the resources by increasing one axis and reducing the other creates even more dis-
sonance for the modern economist.
Each of these moves, each new addition, each change in shape or content, or
reconstruction of the Edgeworth Box diagram – each new image – was prompted
by a process of economists’ imagining how individuals come to make economic
exchanges. We see the results of this process of imagination and image-making by
following the original historical sequence of diagrams (Figures 3.4 and 3.5). is gives
an impression of a model that begins quite modestly and evolves to stabilize in form
around the early 1950s. We see the addition of elements and growing complexity of
the diagrams as economists get more condent in visualizing exchange questions
and demonstrating answers within this model. At the beginning of the history, as
can be seen when comparing some of these original gures with Humphrey’s mod-
ernized version in Figure 3.1, there is a substantial dierence between the originals
and the modern version. Aer Leontief (1946) (Figure 3.5f), the original diagrams
are virtually the same as Humphrey’s. At that point, we might say the representation
became ‘modern’ and Leontief indeed describes the diagram as “conventional”.
If we were to make the reverse comparison, and look at the full sequence of
modernized diagrams given by Humphrey to represent these changes compared to
the real historical sequence, we would nd that sometimes he subtracted elements
to focus on what is new, sometimes added elements, and sometimes made extra
versions of the Box, to make his modernist form provide the required represen-
tative power, arguments, and explanations of the earlier diagrams. His additions
and changes are not necessarily because the earlier diagrams lack the resources
to show the elements; on the contrary in some ways they are more eective. In
part these changes are because the balance between words and diagrams in explan-
ation and argument alters over the period. Earlier users are more economical with
their diagrams (perhaps they had to be for printing reasons). For example, com-
pare Leontief’s diagram with Humphrey’s version of his diagram in Figure 3.6a.
ey are drawn to represent the same concept set: the indierence maps, the con-
tract curve, the oer curves, and the discriminating monopolist exchange points.
e same main points are labelled on both, but notice the incredible complexity
of Leontief’s diagram compared to Humphrey’s. is is because Leontief uses only
one diagram to explain all the elements and theoretical results to date, whereas
Humphrey, by this stage in his text, is using his ninth diagram. For another part, it
is because once the Box has become stabilized into its current closed form, it is not
e World in the Model
124
so easy to make it represent things in the same way as in the older boxes. As can
be seen in Figure 3.6b, Edgeworth, with his open (unboxed) plane of competition,
can represent the process of imperfect competition in his one diagram, possibil-
ities that cannot be shown on Humphrey’s modernized format in which the Box is
already closed and so the total resources of the economy xed and predetermined.
Humphrey needed an additional four diagrams to show what he takes to be the
equivalent process.30 For another example, see the (above) discussion of the Box by
Scitovsky (1941), which Humphrey cannot easily represent because the xed size of
the modern Box does not allow it. His modern reconstruction required Humphrey
to rethink the images, but not to re-experience the imaginative leaps of the original
modellers.
It is the combination of this economy of representation and the exibility in
representational space found in earlier diagrams that makes some of them di-
cult to understand for modern users. Once the diagram had stabilized in form
and content, some of this exibility disappeared, though at the same time, the
range of spaces the Box was taken to represent expanded to include production
Figure 3.6a. Matching the Modern Economist’s Diagrams to the Original Box Diagrams.
On le: Source: Wassily Leontief “e Pure eory of the Guaranteed Annual Wage Contract”,
(1946) Journal of Political Economy, 54:1, 76–79, g. 1 on p. 77. Reproduced with permission
from University of Chicago Press.
On right: Source: Tom Humphrey “e Early History of the Box Diagram” (1996) Economic
Quarterly, 82:1, 37–75, gure 9. Reproduced with permission from the author, Tom Humphrey,
and e Federal Reserve Bank of Richmond.
30 To be fair to Humphrey’s account, Edgeworth does then use a second gure (his gure 2, p. 40) –
to give a ‘close-up’ view of how increasing traders moves toward the market solution point.
Imagining and Creating Images 125
and international trade domains alongside the original exchange and welfare ones.
Economists continued to nd new uses for the diagram and turned it into a means
of enquiry into other economic realms. e imaginative use of the diagram does
not seem to have stopped even though the main image stabilized in form.
Figure 3.6b. Matching the Modern Economist’s Diagrams to the Original Box Diagrams.
On top: Source: F. Y. Edgeworth, Mathematical Psychics. London: C. Kegan Paul & Co., 1881,
g 1, p. 28.
On bottom: Source: Tom Humphrey “e Early History of the Box Diagram” (1996) Economic
Quarterly, 82:1, 37–75, gures 2 and 4. Reproduced with permission from the author, Tom
Humphrey, and e Federal Reserve Bank of Richmond.
e World in the Model
126
Perhaps for the non-economist, the strangest element about the history of the
Box is the ciphering of the individuals and the conation that occurs between their
identity and that of the goods that they own and come to exchange. Remember in
Merkies’ lecture how the colour coding for the goods – cheese and wine – suddenly
morphed to represent the individuals. ese conated elements appear as a set of
preference lines in the indierence maps; that is, people are represented both by their
origin or endowment points and in their preferences in terms of the two goods. But
they have little personality: their indierence maps are drawn to behave according
to the ‘wishes’ of the economist (as Merkies expressed himself). Albert and Beatrice
appear as letters on the axes or at the origins: in Bowley’s diagram, people A and B
trade goods 1 and 2, while in Leontief’s paper, people a and b trade goods A and B.
In Scitovsky’s diagram, we have people A and B, with indierence lines labelled a and
b and trading goods x and y! is is pretty confusing, and the lack of any consist-
ency here indicates how unimportant their identities are. ese are symbols without
any symbolism, without any special meaning, for neither people nor goods in the
Box have any particular character worth mentioning. It might have seemed from
Merkies’ pictures that the individuals and their goods shown around the edge are the
most important things in the model. In Edgeworth’s Box, they still have characters:
Robinson Crusoe and Friday; but by Pareto’s time, they really are the shadows they
become in the Artist’s pictures. I discuss how individuals turn into these shadowy
people in economics in Chapter 4; but here it is the conceptual apparatus depicting
their exchange behaviour inside the Box that matters and is being imagined, imaged,
and so modelled, without much attention to their personalities.
6.ii Newness
Although economists fail to express visually the full particulars of Albert and Beatrice,
or their cheese and wine, the diagrams are critical for Edgeworth, Pareto, and the
other users of the Box because the Box enables them to place their symbolised indi-
viduals into a dierent form of relationship, and to say dierent things about that
relationship, than in the verbal economics they supplant. e act of representation
here involves the direct visualization of the economic world into mathematical sym-
bols and other forms of nonverbal denotation to create a substantial new world in the
model. Along with the new forms came substantial new conceptual content.31
e contents of the Box traced through the historical model sequence. Figures 3.4
and 3.5 show how the new conceptual elements associated with the model were devel-
oped into an analytical apparatus. Edgeworth (1881) made a substantial development
of both Jevons’ (1871) individual utility graph and Marshall’s (1879) trade diagrams
31 is relation between new forms of expression and new content echoes Weintraub’s (1991) account
of how the construction of economic theories about dynamics into mathematical form changed
the substance of those theories. For other examples of imagistic reasoning in scientic discovery
in relation to innovations in concepts, see Nersessian (1990), Griesemer and Wimsatt (1989), and
Toulmin (1953, chapter 2), who also uses Crusoe and Friday to focus his discussion.
Imagining and Creating Images 127
in commodity space for two traders (countries) by mapping utility concepts into the
commodity space: namely by adding an indierence curve for each trader and their
contract curve (see Creedy, 1986). ese indierence curves and the contract curve
are the critical conceptual innovations that Edgeworth developed, and they are rep-
resented for the rst time in his diagram. Pareto provides indierence maps, and
shows the trading range in which welfare improvements can be negotiated in relation
to price rays. Bowley introduces the possibility of initial endowments inside the Box
and shows the oer curves from this new ‘origin’ point clearly on the same map to
indicate an alternative bargaining range. Scitovsky develops an analysis of what hap-
pens to the utility maps when the size of the commodity space changes. Leontief puts
together all the conceptual elements of the indierence map, oer curves, the contract
curve, and price rays onto the same diagram. Although some of the ideas associated
with these elements have a longer history, the conceptual apparatus is not something
that existed before and outside of the model; rather, the conceptual elements are new
with the representation and developed inside and alongside the model.
As a test of this proposition of newness, imagine giving a translation of Leontief’s
diagram in words with a suciently exact description so that all the parts, and
their relations to each other, are made clear. Such a description could be given, but
only by using economists’ now habitual mathematical and spatial terms expressing
these economic concepts. But these same concepts and terms depended for their
denition and their development on the creation of the diagram and on economic
reasoning with it. us, economists can translate (with some diculty) their math-
ematical model world back into verbal terms, but it is a new world being expressed,
one that they could not have expressed before they made that diagrammatic world.
A similar trial of imagination and cognition is made when an economist of today
tries to explain the Table a u Économique of Chapter 1. ere is an incommensura-
bility in these cases that comes from both the newly conceptualized materials and
from their mode of expression.
I should be careful here to point out that when the Edgeworth Box is described
as a mathematical model, it is not made of only mathematics. Recall also from
Chapter 1 that model-making, in giving more exact form to intuitions about the
economic world, at the same time provides rules for reasoning with that model.
is is best illustrated (and speaks indirectly to the newness claim) by considering
the allowable movements or manipulations that can be made in the Box model. e
notion that the two traders will be at some kind of optimum when their indier-
ence curves meet at a tangency makes use of mathematical concepts and logic. But
the apparatus of oer curves, indierence curves, and so, for example, the spaces
in which trade is ruled out, depend on understanding the new economic concep-
tual content of the elements in the model. Bowley’s movement of the origin into
the Box has implications for welfare arguments, which depend on the economic
content of the Box. Scitovsky’s diagram showing the implications of increasing the
resources requires manipulations of the diagram that are determined by the eco-
nomic meaning of these new curves, which were derived from three-dimensional
e World in the Model
128
maps and so do not follow the rules or logic of two-dimensional diagrams. Both
mathematical and subject matter conceptual knowledge go into forming the details
of the representation, and so reasoning with the model depends not only on the
mathematics but also on economic subject information to dene the allowable
rules of manipulation.32 From this point of view, there would be as much diculty
in ‘translating’ the Edgeworth Box into ‘just mathematics’ with no subject content
as into ‘just words’ with no mathematical content.
A more general sense of what it means to say that we have a new model version
of the world is suggested by Michael Lynch (1990) in his discussion of diagrams in
social theory. ere he remarks, of one example, that it “is a diagram that does not
obviously perform an independent representational function. If it were removed
from the text, it would not be missed because it adds very little to what the sur-
rounding text says” (Lynch, 1990, p. 5). is is a stronger version, if you like, of
Mahoney’s observation about “reasoning o the diagram”, because of the additional
focus on independence, and echoes James Griesemer’s parallel argument (of 1991)
that diagrams may be ineliminable with respect to other forms of representation
in the text. ese suggestions about the independence of diagrammatic reason-
ing support claims about the autonomy of models, namely that it is their indepen-
dence in functioning that gives models such a potentially powerful epistemic role
in science (see Morrison and Morgan, 1999). Here with the Edgeworth Box, that
potential rests on its independent representational content. And, as we have seen in
the preceding discussion, that content is conceptual. e Edgeworth Box diagram
carries new conceptual apparatus that could not be represented, or manipulated, in
verbal form and indeed cannot be entirely expressed in purely (ie subject-matter
free) mathematical terms. is is how it comes to carry an independent represen-
tational function, and why the Edgeworth Box has had such a long lifespan as an
autonomous model able to represent not only individuals in exchange, but also
many other elements and relations.
As we saw in Merkies’ account, reasoning with the conceptual elements devel-
oped with the Box has had such a general reach in economics that we may even
see the Edgeworth Box as a shorthand version of modern neoclassical economics:
demonstrating – with two consumers, two producers, two factors of production,
and two goods – ecient production, maximum utility (consumption), Nash equi-
librium outcomes, and Pareto optimality. ese are the essential building blocks
and main results of neoclassical economics contained in a nutshell. e Edgeworth
Box acts as both a scale model or miniature version of neoclassical economics and as
a perfect ‘logo’ or role model for such economics.33
32 See Weintraub’s (2002) chapter 5 (with Ted Gayer) on Patinkin and Phipps for a good example of
how mathematicians and economists can talk past each other because they fail to see this point.
33 I am indebted to Tim Hatton, who suggested this ‘logo’ aspect (see Chapter 10). See Baden-Fuller
and Morgan (2010) on the distinction between scale and role models in a discussion of how cer-
tain real rms act as ‘business models’.
Imagining and Creating Images 129
7. Seeing the World in the Model
I return now to the importance of the particular language of representation in the
history of economics. e pioneering mathematical economists wanted to express
their economics in new ways, and in this respect, the move from sentences to dia-
grams may be associated with a somewhat more radical change than that from sen-
tences to algebra. e basis for this claim can be found in the analysis by Larkin and
Simon (1987, p. 66), who point to the dierences in the way arguments work when
a problem is expressed in a “sentential” representation (sentences or algebra) com-
pared to a diagrammatic representation. e diagrammatic form expresses location
and spatial relational aspects of a problem; the sentential forms express the tempo-
ral and/or logical relations.34 e relatively greater change required to move from
the representational forms of sentences to diagrams (as opposed to from sentences
to equations), and their dierent possibilities, might be one reason why diagram-
matic models played such an important creative role in making a new version of
economics through mathematization for the rst generation of model-makers in
the late nineteenth century.
But as I argued in Chapter 1, form also dictates certain aspects of the reasoning
rules used with models, or, as Larkin and Simon express the point: “the distinctions
between representations is not rooted in the notations used to write them, but in the
operations used on them” (Larkin and Simon, 1987, p. 68). From the point of view
of how we use a model, it matters little if we denote a person as A or Albert, but the
discussion of his relationships and exchange equilibrium works very dierently with
the Edgeworth Box diagram than when working with a set of sentences, or even a
set of equations. Edgeworth found it both very inecient and extremely dicult to
analyse the imperfect competition exchange problem (of an increasing number of
traders) verbally or by seeking a general analytical mathematical formulation of the
process, yet it yielded to his diagrammatic “abstract-typical” case approach. is
returns us to my argument at the beginning of this chapter about the importance of
choices of form or language in making new versions of the world in models.
Diagrammatic reasoning may also benet from a certain cognitive advan-
tage compared to sentential or algebraic representation. It is notable that Larkin
and Simon discuss an economics example, the supply and demand Marshallian
cross: “the great utility of the diagram arises from perceptual enhancement, the
fact that it makes explicit the relative positions of the equilibrium points, so that
the conclusions can be read o with the help of simple, direct perceptual opera-
tions” (Larkin and Simon, 1987, p. 95).35 e general point to take here is that this
34 I am grateful to Marcel Boumans who points out that of course, these sentential forms are not
reducible or easily translatable to each other, a stronger version of my point about the ‘formal
equivalence’ of representations in Section 1.
35 e primacy of the visual sense in communication and intelligibility has oen been asserted. See
Arnheim (1969) for the stronger thesis that thinking is perceptual and Tue (particularly 1983
and 1997) for a series of books celebrating both views.
e World in the Model
130
perceptual element helps solve the cognitive problem of understanding and using
the conceptual spaces of the diagram only once that diagram is already conceived.
Once the model has been created, perceptual elements may be helpful in reasoning
with the Box model, and constructing argument chains with the diagram, as we
shall see with the Marshallian cross diagram (in Chapter 7). But it is the creation
and development of the Box diagram that allowed the economists involved to open
up those new conceptual spaces and resources in economics.
Let me put these bits of argument together in a more general way: the abil-
ity to take cognitive advantage of the dierent perceptual possibilities of dierent
forms of model is determined by the choices the scientist makes in portraying
the economic world in the model, both the choice of representational form and
within that, the choices of how elements and their relations are represented. I can
communicate the importance of this aspect of models by relating it explicitly to
an analogous change in visual representation. Ivins (1953), in writing about the
introduction of printmaking techniques, gives us an analogy for how economists
make models in the rst place. He asks: How do etcher-engravers make their visual
representations? Much like economic model-makers it seems, for, as Ivins wrote
of the former,
e competent and honest observer and recorder, however, had his very
distinct limitations. In the rst place, he could only draw a selected and
very small part of the things he did observe. More than that, courageous
and sharp-sighted as he might be, he had learned to see in a particular way
and to lay his lines in accordance with the requirements of some particular
convention or system of linear structure, and anything that way of seeing
and that convention of drawing were not calculated to catch and bring out
failed to be brought out in his statement. For shortness’ sake I shall fre-
quently refer to such conventions as syntaxes. (Ivins, 1953, pp. 60–1)
Ivins thus takes us straight back to language and conventions. For the earliest engrav-
ers, dierent visualizing conventions developed in dierent locations. Apparently,
the Italian etchers aimed for three-dimensionality and concentrated on represent-
ing the outlines of objects in relation to space, while the Germans paid relatively
more attention to representing the textures of the objects. Ivins suggests the eect
of this – namely that “even the greatest of them [the Germans] saw objects located
in a space that was independent of them and unrelated to their forms, whereas
the greater Italians saw that space was merely the relation between objects” (Ivins,
1953, p. 64).
e analogical material here echoes my claims for mathematical economics.
A new kind of representation – mathematical models – leads economic scientists
to see in a particular way; and each dierent form of visualization, such as arith-
metic, algebra or geometry, diagrams or even machines, leads to a focus on dierent
aspects of the economic elements represented in their models. Portrayal and cog-
nition are intimately linked and both these, in turn, to conception and perception.
Imagining and Creating Images 131
Economists do not start out by perceiving the world clearly and describing it in
their model but by visualizing how the economic world might be and portraying
that intuition in their model – imagining and imaging. In the process of such mod-
elling, economists develop new concepts and so they – and we – come to perceive
new things in the economic world (a point I return to in Chapter 10). A new way
of looking at the familiar problems of exchange led to a new sense of what the phe-
nomena entailed.
8. Conclusion
I argued earlier that models play an important role in the process of the mathema-
tization of economics, rst because economists could not make their mathemati-
cal version of the economic world all at once and second, because they needed to
generate both the new vocabulary and new forms for thinking about the world,
just as etchers had to learn the means and develop a language to make new forms
of pictures. e history of the Edgeworth Box diagram provides an exemplar for
these claims in economics. It suggests how the process of making a new world,
a world of mathematical economics, was accomplished gradually by a process of
developing mathematical models or representations which stabilized over time. A
mathematical economic version of exchange relations in the world was not there
to be read o: the situations and processes of exchange had to be imagined and
imaged; they had to be visualized into a new representation: the Edgeworth Box.
At the same time, the independent representational content and function of
this particular model helped to create the elements for a broader mathematically
made version of economics. Creating this Edgeworth Box model and using it as
a means of enquiry generated some of the important concepts of mathematical
economics, concepts that turned out to be more generally relevant for the fur-
ther mathematization of economics and so helped delineate the representations
and reasoning claims that were allowable in the disciplinary eld. ese concep-
tual elements – indierence curves, contract curves, and so forth – have lived a
longer life than their initial enclosure within the Edgeworth Box might suggest.
Far from being prisoners of a particular model, they proved remarkably free to
travel into other models and even to completely dierent modes of doing econom-
ics. Indierence curves, for example, became standard representative devices in
microeconomics in general. e range of the contract curve in which settlements
would be made within the Box was reconstituted in 1959 as “the core” an important
concept in game theory by Martin Shubik (who will turn up as one of the heroes
of Chapter 8). ‘Lab’ experiments have investigated people’s exchange behaviour by
designing experiments to match the Box situation (as we also nd in Chapter 8).
Such conceptual content that travels free from its initial model formulation is par-
ticularly important for it forms a generic vocabulary, far more useful than technical
terms tied to a specic time and purpose. When we nd such abstract conceptual
e World in the Model
132
elements that are rst developed in models and then become more deeply rooted
in economics, we begin to understand how and why modelling grew so luxuriantly
in modern mathematical economics and why mathematical economics became so
dependent on modelling.36
us, to go back to my original claims for the importance of modelling in rela-
tion to both the history of economics and the nature of the science it became, it
is not just that (as economists have long argued) mathematics is more exact in
expression, or a more ecient workhorse, or more rigorous in argument. e point
is that economics did not start with a mathematical version of the economic world;
rather, economists imagined how the economic world worked, and made images,
or models, of it: a joint process of guring it out and lling it in. ese mathe-
matical models represent something dierent from verbal accounts, they involve
dierent concepts, and use dierent kinds of arguments. ey represent some-
thing independently of the text; that something has conceptual content not (easily)
expressible in words, and it is this quality that made models such good building
blocks for a mathematically made version of the economic world. us models
became constitutive – rather than illustrative – of modern economics.
Acknowledgement
is chapter was written for the ECHE conference on “Economic Science and Visual
Representation”, Montreal, March 2002. It was given a preliminary airing at the Measurement
Group in Physics and Economics at CPNSS, LSE in October 2001, and was later presented
at seminars at Cambridge, Queen Mary College London, UC Davis, and Pittsburgh; and
to the History of Economics Society Annual Conference and at the ANU-Toyota Public
Lecture Series 2005 at the National Museum of Australia. My thanks go particularly to
Roy Weintraub, Neil De Marchi, Charles Baden-Fuller, Harro Maas, Marcel Boumans, Paul
Teller, Tom Humphrey, Tony Lawson, John Davis, Margaret Schabas, Mike Mahoney, Chris
Ritter, Robert Leonard, Yves Gingras, Bert Mosselmans, Bob Breunig, Tim Hatton, Paul
Frijters, and u Nguyen and many others for their helpful comments. I thank my history
of science hosts at UC Berkeley and University of Pennsylvania during 2000–01 when I
was reading and thinking about visualization; and to the British Academy for originally
funding this research. Part of the paper was given at the PSA in November 2002 (and pub-
lished as Morgan, 2004), and I thank the symposium participants: Mauricio Suaréz, Bas van
Fraassen, Andrea Woody, and Ronald Giere (and the anonymous member of Wisconsin’s
judiciary who came from the courthouse across the road!) for their useful comments. Very
special thanks go to Arnold Merkies and Koen Engelen for permission to use their text and
36 is is not to imply, of course, that such conceptual content comes only with modelling. Ingrao and
Israel’s account of the invisible hand notions of equilibrium and the development of general equilib-
rium theory provides a parallel account for conceptual and mathematical developments that are pri-
marily non-model based. As an aside to their main story, they note the development of small-scale
modelling in this eld in the work in the mid-twentieth century, which they interpret as economists
copying physics’ use of the modelling method. My account in Chapter 1 suggests a dierent chronol-
ogy, and a more important role for models much earlier in the mathematization process.
Imagining and Creating Images 133
pictures and to Ada Kromhout for text translation; to Tom Humphrey for permission to use
his diagrams; and to Till Gruene and Chiara Baroni for research assistance.
References
Arnheim, R. (1969) Visual inking. Berkeley: University of California Press.
Baden-Fuller, Charles and Mary S. Morgan (2010) “Business Models as Models”. Long Range
Planning, 43:2–3, 156–71.
Baigrie, B. S. (1996) [ed] Picturing Knowledge: Historical and Philosophical Problems
Concerning the Use of Art in Science. Toronto: University of Toronto Press.
Blaug, Mark (2007) “e Fundamental eorems of Modern Welfare Economics, Historically
Contemplated”. History of Political Economy, 39:2, 184–207.
Boumans, M. (1993) “Paul Ehrenfest and Jan Tinbergen: A Case of Limited Physics Transfer”.
In N. De Marchi (ed), Non-Natural Social Science: Reecting on the Enterprise of More
Heat an Light (pp. 131–56). Annual Supplement to History of Political Economy, Vol.
25. Durham, NC: Duke University Press.
Bowley, A. L. (1924) e Mathematical Groundwork of Economics. Oxford: Clarendon Press.
Chaigneau Nicolas and Philippe Le Gall (1998) “e French Connection: e Pioneering
Econometrics of Marcel Lenoir”. In Warren J. Samuels (ed), European Economists of the
Early 20th Century, Vol. 1 (pp. 163–89). Cheltenham: Edward Elgar.
Coats, A. W. (1976) “Economics and Psychology: e Death and Resurrection of a Research
Programme”. In S. Latsis (ed), Method and Appraisal in Economics (pp. 43–64).
Cambridge: Cambridge University Press.
Cook, Simon (2005) “Late Victorian Visual Reasoning and Alfred Marshall’s Economic
Science”. British Journal for History of Science, 38:2, 179–95.
Creedy, J. (1980) “Some Recent Interpretations of Mathematical Psychics”. History of Political
Economy, 12:2, 267–76.
(1986) Edgeworth and the Development of Neoclassical Economics. Oxford: Blackwell.
(1992) Demand and Exchange in Economic Analysis: A History from Cournot to Marshall.
Aldershot: Edward Elgar.
Daston, Lorraine and Peter Galison (1992) “e Image of Objectivity”. Representations, 40,
81–128.
De Marchi, Neil (2003) “Visualizing the Gains from Trade, Mid 1870s to 1962”. European
Journal of the History of Economic ought, 10:4, 551–72.
Edgeworth, F. Y. (1881) Mathematical Psychics. London: Kegan Paul, London. (New anno-
tated edition. In Peter Newman (ed), F. Y. Edgeworth’s Mathematical Psychics and
Further Papers on Political Economy (pp. 1–174). Oxford: Oxford University Press for
the Royal Economic Society, 2003.
(1891) “Observations on the Mathematical eory of Political Economy, with a Special
Reference to the Principles of Economics by Alfred Marshall”. Giornale degli Economisti,
March, 233–45.
Ferguson, Eugene S. (1977) “e Mind’s Eye: Nonverbal ought in Technology”. Science,
197:4306, 827–36.
(1992) Engineering and the Mind’s Eye. Cambridge, MA: MIT Press.
Fisher, I. (1892/1925) Mathematical Investigations in the eory of Value and Prices. New
Haven, CT: Yale University Press.
Goodman, N. (1978) Ways of Worldmaking. Indianapolis: Hackett.
e World in the Model
134
Griesemer, James R. (1991) “Must Scientic Diagrams Be Eliminable? e Case of Path
Analysis”. Biology and Philosophy, 6, 155–80.
Griesemer, James R. and William C. Wimsatt, (1989) “Picturing Weismannism: A Case
Study of Conceptual Evolution”. In M. Ruse (ed), What the Philosophy of Biology Is
(pp. 75–137). Dordrecht: Kluwer.
Hamminga, B. and N. De Marchi (1994) Idealization in Economics. Amsterdam: Rodopi.
Homan, M. (2004) “How to Get It: Diagrammatic Reasoning as a Tool of Knowledge
Development and its Pragmatic Dimension”. Foundation of Science, 9, 285–305.
Hughes, R. I. G. (1997) “Models and Representation”. Philosophy of Science, 64, S325–36.
Humphrey, T. (1995) When Geometry Emerged: Some Neglected Early Contributions to
Oer-Curve Analysis”. Federal Research Bank of Richmond. Economic Quarterly, 81:2,
39–73.
(1996) “e Early History of the Box Diagram”. Federal Reserve Bank of Richmond.
Economic Quarterly, 82:1, 37–75.
Ingrao, B. and G. Israel (1990) e Invisible Hand. Cambridge, MA: MIT Press.
Ivins, W. M. (1953) Prints and Visual Communication. Cambridge, MA: Harvard University
Press.
Jevons, W. S. (1871) e eory of Political Economy. London: Macmillan.
Keynes, John M. (1926) “F. Y. Edgeworth”. Economic Journal, 36, 140–53.
Lakatos, I. (1976) Proofs and Refutations. Cambridge: Cambridge University Press.
Lancaster, Kelvin (1957) “e Hecksher-Ohlin Trade Model: A Geometric Treatment”.
Economica, 24, 19–35.
Larkin J. H. and H. A. Simon (1987) “Why a Diagram Is (Sometimes) Worth Ten ousand
Words”. Cognitive Science, 11, 65–99.
Latour, B. (1986) “Visualization and Cognition: inking with Eyes and Hands”. Knowledge
and Society, 6, 1–40.
Le Gall, Philippe (2007) A History of Econometrics in France. London: Routledge.
Lenoir, Marcel (1913) Études sur la Formation et le Mouvement des Prix. Paris: M. Giard &
É. Brière.
Leonard, Robert (2003) “Mini-Symposium on Economics and Visual Representation”.
European Journal of the History of Economic ought, 10:4, 525–686.
Leontief, W. W. (1946) e Pure eory of the Guaranteed Annual Wage Contract”. Journal
of Political Economy, 54, 76–9.
Lerner, A. P. (1933/1952) “Factor Prices and International Trade”. Economica, 19, 1–16.
Lynch, M. (1990) “Pictures of Nothing? Visual Construals in Social eory”. Sociological
eory, 9:1, 1–21.
Lynch, M. and S. Woolgar (1990) [eds] Representation in Scientic Practice. Cambridge,
MA: MIT Press.
Maas, Harro (2005) William Stanley Jevons and the Making of Modern Economics. Cambridge:
Cambridge University Press.
Mahoney, M. S. (1985) “Diagrams and Dynamics: Mathematical Perspectives on Edgerton’s
esis”. In J. W. Shirley and F. D. Hoeniger (eds), Science and the Arts in the Renaissance
(pp. 198–220). Washington: Folger Books.
Marshall, A. (1879/1930) e Pure eory of Foreign Trade; e Pure eory of Domestic
Valu es. Reprints of Scarce Tracts in Economics, No. 1 (London: London School of
Economics and Political Science) and in J. K. Whitaker (ed), e Early Economic
Writings of Alfred Marshall 1867–1890, Vol. 2 (1975) (pp. 111–236). New York: Free
Press
Merkies, A. H. Q. M. (1997) “Zo” Afscheidscollege, September, 1997, Vrije Universiteit,
Amsterdam.
Imagining and Creating Images 135
Mirowski, P. (1989) More Heat an Light. Cambridge: Cambridge University Press.
(1994) Edgeworth on Chance, Economic Hazard, and Statistics. Lanham, MD: Rowan &
Littleeld.
Morgan, Mary S. (1996) “Idealization and Modelling”. Journal of Economic Methodology, 3,
131–48.
(2004) “Imagination and Imaging in Model-Building”. Philosophy of Science, 71:5,
753–66.
Mary S. Morgan and Tarja Knuuttila (2012) “Models and Modelling in Economics”. In
U. Mäki (ed), Handbook of the Philosophy of Economics (one volume in Handbook
of the Philosophy of Science. General Editors: Dov Gabbay, Paul agard, and John
Woods). Amsterdam: Elsevier/North-Holland. Available at: http://papers.ssrn.com/
sol3/papers.cfm?abstract_id=1499975
Morrison, M. and M. S. Morgan (1999) “Models as Mediating Instruments”. In Mary S.
Morgan and Margaret Morrison (eds), Models as Mediators: Perspectives on Natural
and Social Science (pp. 10–37). Cambridge: Cambridge University Press.
Nersessian, Nancy (1990) “Methods of Conceptual Change in Science: Imagistic and
Analogical Reasoning”. Philosophica, 45:1, 33–52.
(2008) Creating Scientic Concepts. Cambridge, MA: MIT Press.
Netz, Reviel (1999) e Shaping of Deduction in Greek Mathematics. Cambridge: Cambridge
University Press.
Pareto, V. (1906/1971) Manual of Political Economy. Translated by A. S. Schwier. London:
Kelley/Macmillan.
Peirce, C. S. (1932) Collected Papers, Vol. 2: Elements of Logic. Cambridge, MA: Harvard
University Press.
Richards, Joan (1988) Mathematical Visions: e Pursuit of Geometry in Victorian England.
Boston: Academic Press.
Rotman, B. (2000) Mathematics as Sign: Writing, Imagining, Counting. Stanford, CA:
Stanford University Press.
Scitovsky, T. (1941) “A Note on Welfare Propositions in Economics”. Review of Economic
Studies, 9, 89–110.
Tarascio, V. J. (1980) “Some Recent Interpretations of Mathematical Psychics: A Reply”.
History of Political Economy, 12:2, 278–81.
Toulmin, Stephen (1953) e Philosophy of Science. London: Hutchinson.
Tue, E. R. (1983) e Visual Display of Quantitative Information. Cheshire, CN: Graphics
Press.
(1997) Visual Explanations. Cheshire, CN: Graphics Press.
Weintraub, E. R. (1991) Stabilizing Dynamics: Constructing Economic Knowledge. Cambridge:
Cambridge University Press.
(2002) How Economics Became a Mathematical Science. Durham, NC: Duke University
Press.
Wetherby, J. L. (1976) “Why Was It Called an Edgeworth-Bowley Box? A Possible
Explanation”. Economic Inquiry, 14:2, 294–6.
136
4
Character Making: Ideal Types, Idealization,
and the Art of Caricature
1. Introduction 136
2. Characterizing Economic Man: Classical Economists’
Homo Economicus 138
3. Concept Forming: Weber’s Ideal Types and Menger’s
Human Economy 141
4. Symbolic Abstraction: Jevons’ Calculating Man 145
5. Exaggerating Qualities: Knight’s Slot-Machine Man 150
6. Making a Cartoon into a Role Model: Rational Economic Man 153
7. e Art of Caricature and Processes of Idealization 157
8. Model Man’s CV: De-Idealization and the Changing Roles of
Economic Man 164
1. Introduction
Economics is about people and their actions. But economists have found that it is
as dicult to gure out the economic motivations and behaviour of individuals as
to make an analysis of the whole economy. And, though each person is only one
small unit in the overall economy, the individual cannot be neglected for his or her
behaviour creates exchange, markets, and the aggregate economy. When we search
for accounts of the individual’s economy, we quickly nd that over the past two
centuries economists have created a series of economic man portraits, a veritable
gallery of economic heroes, each fashioned to t the style and content of the eco-
nomics of their day. Whereas early characters appear as descriptions with recognis-
able human passions, later characters became more shadowy for their design was
more clearly driven by the needs of economists’ theories. ese successive models
of economic man were represented initially in verbally drawn sketches, and later
in terms that were informed by and tted to mathematical notions. During the
process, economists began to refer to these model people with symbols, and, as we
have learnt from the last chapter, labelled them anonymously and interchangeably
Ideal Types, Idealization and Caricature 137
as X and Y, or A and B. We can treat these as models inasmuch as each one oers a
well dened portrait of individual motivations or behaviour strictly limited to the
economic sphere. We are dealing here, not with the development of a small world,
but with a model person, someone who in some respects appears thinly described
but in others appears a caricature: an economic man, not a full man.
ese model men may not be workable or manipulable in quite the same way
or to the same degree as other models in economics, but they can be reasoned with.
ese economic men are objects that economists both enquire into and enquire
with. ey enquire into them to explore the content and full implications of their
ideas about man’s economic behaviour. ey explore with these models of economic
man in the sense that each one provides a comparator or benchmark for taking to
the real economic behaviour found out in the world, or more recently, in the class-
room-laboratory of economic experiment. But economists also explore with these
models in another rather interesting sense. Economists learnt, during the twenti-
eth century, to refer to their economic man as an “agent” – a term to take seriously
when we think about his role in economic reasoning. Economic model man may
be thinly characterized, but he has agency: he motivates. He is the actor who shapes
the possibilities and outcomes in other economic models such as the exchange sit-
uation represented in the Edgeworth Box (Chapter 3) or the Prisoner’s Dilemma
game (Chapter 9). In other words, enquiries with such economic models depend on
the characteristics – particularly his knowledge, ambitions, and preferences – of a
model economic man who inhabits those small worlds. Dierent characterizations
of economic man (whether he is selsh or cooperative), or dierent formulations
(whether he is mathematically described or verbally), will provide dierent rules
for his behaviour and so create dierent outcomes when using those models for
reasoning. So, while economic man may be the smallest unit in economists’ toolbox
of models, he is a very powerful one: his behaviour has all sorts of consequences in
other economic models and thus for the rest of economics.
e making of a portrait of economic man is one in which economists have
a special entree – for all of us are economic actors, able to observe ourselves and
those we interact with in the economy. So, as a starting point, it seems reason-
able to think that by observing themselves and others, economists can come to a
view of what is important in economic behaviour. And having done so, they can
subtract everything else, leaving behind just those elements that make a portrait
of economic man. While this process of ‘idealization’, as philosophers like to call
it, may provide a good description of the early-nineteenth-century processes of
making economic man portraits, it simply does not cover what happened later. If
we follow the history of economists’ accounts of model man, we nd a combina-
tion of processes going on, not just subtracting, but abstracting, concept formation,
and even adding and exaggerating certain of his features. Nevertheless, in making
models of man, economists are making models of people who might be themselves,
and so the process has oen been the subject of signicant and interrogative com-
mentary on the content and nature of economic models. ose reections have
e World in the Model
138
provided two appealing, and especially social science, notions about the making of
such models – the creation of ideal types and of caricatures – that I explore in the
course of this chapter.
2. Characterizing Economic Man: Classical Economists’
Homo Economicus
e classical economists from Adam Smith to Karl Marx were very particular in giving
accounts of economic behaviour, but few of them created models of economic man.
is is certainly so for Smith, the Scottish moral philosopher and founder of classi-
cal economics, whose description of economic behaviour in his Wealth of Nations
(1776) is much too well-rounded a portrait to work as a model. Smith characterized
economic behaviour as coming from a complex mixture of instincts (the propensity
to exchange as much as self-interest), talents, motivations, and preferences. All of
these traits are vital to Smith’s account of how wealth is created and spread through
the nations. Economic man is “thickly” described, to use a phrase that has haunted
both recent historiography and anthropology. Yet this was not considered a realistic
portrait by his contemporary scholars, such as omas Reid, who regarded it as a c-
tional device to motivate a virtuous story about commercial society.1
Fictional character or not, Smith’s characterization of economic behaviour does
not constitute a model man. Why not? e character is simply too complicated to
reason with. Smith linked man’s individual motivations with particular outcomes
(e.g., his prudence with investment) but it is not so easy to trace the full outcome of
all of his character traits together at the same time because they interact with each
other and link up with so many other characteristics and are dependent upon so
many circumstances. Nor is it easy to use his account of man to enquire into the
economy as a whole, for though Smith’s description suggests that causal power lies
at the level of the individual, it is the eects of actions in aggregate that create the
laws of nineteenth-century political economy such as the subsistence wage thesis
or Marx’s thesis of capitalist cycles. ese laws emerge as the unintended conse-
quences of individuals’ actions at the level of groups, and the individuals themselves
are powerless in the face of them.2 We saw just this diculty in Ricardo’s attempts
to work out the laws of distribution by starting with individual farmers, and how he
managed to wriggle through to a solution by having his model farm represent both
the individual farm and the aggregate farm at the same time (see Chapter 2).
1 As such, Smith’s account began by persuading us that the fundamental propensity to truck, barter,
and exchange was a natural given as a way to draw us into his commercial world picture. I thank
Harro Maas for his helpful discussion of this point. (For a history of the actual emergence of a
“commercial man”, see Bhimani, 1994.)
2 at is, even if Smith’s description of the individual economic actor had formed a model, he would
have had great diculty in using it to enquire into the workings of the economy.
Ideal Types, Idealization and Caricature 139
Classical political economy was not a science in which a model man could
easily function, yet there are examples where he did. omas Malthus, a parish
priest and great friend of Ricardo, worried about the fast growing population of
his day. In his account of 1803, he supposed that this problem arose because of the
interaction between man’s two primary motives: his self-interest being more than
oen overwhelmed by his natural proclivity to create children. He also proposed
two simple laws of natural reproduction to be always at work (namely that human
populations grow geometrically but food supplies only arithmetically). ese two
motivations, in conjunction with the two laws, would create cycles in the lives of
the working poor swinging from poverty with vice to satisfaction at subsistence
level. And in accordance with classical ideas about the laws of economics, Malthus
supposed that these hypothesized cycles might not be observed because of interfer-
ence from the other disturbing features in the world.
Malthus’ character does form a model man in the sense that he was thin enough
in characterization to reason with. He has simple economic and demographic
motivations, from which a sequence of population and economic outcomes were
derived. In addition, Malthus enquired into the outcomes of his behaviour by a
counterfactual thought experiment, that is, by conceiving that the characteristics
of his model man might be otherwise and seeing what dierence this would mean.
So Malthus tells us that if man used his foresight and reasoning power to restrict
his family, the law of human population growth would be dierent (and so Malthus
lauds the benets of education). e arguments that Malthus constructed were
important for the development of Darwin’s theory of evolution in the later nine-
teenth century, and continue to resurface periodically whenever the problem of
population growth becomes a signicant political issue.
In Malthus’ work, we nd the portrait of a man who functions as a model in
economics, that is (as I argued in Chapter 1) whose formulation gives us resources
to reason with – both about economic laws and to enquire into the real economy.
His model man has direct descendants in modern economics. ey reappear with
more sophisticated statistical clothing, and amongst many thousands of similar,
virtual, people, in Orcutt’s computer-based microsimulation model of population
dynamics (discussed in Chapter 8). More immediately, Malthus’ model man pro-
vided an exemplar for John Stuart Mill’s only slightly later claims about the require-
ment for a thinly modelled man to make economics a viable science. Mill, though
best known as one of the great philosophers of the nineteenth century, was also a
political economist. He dened the science of economics as dealing with an explic-
itly restricted range of man’s motivations and propensities, namely his economic
ones, for he argued that only by both delimiting the scope of the subject domain of
economics, and dening more narrowly the characteristics of individual economic
behaviour, could economists construct a scientic account.
Signicantly, Mill’s model man character sketch therefore comes intertwined
with his denition of economics as:
e World in the Model
140
. . . the science which treats of the production and distribution of wealth, so far
as they depend upon the laws of human nature. (Mill, 1836, pp. 318, 321–2)3
And, despite the fact that both Mill and Malthus were members of the same broad
school of classical economics, the content of Mill’s portrait is markedly dierent
from Malthus’ one. e motivations of Mill’s economic man consist of one con-
stant positive motivation, namely, a desire for wealth, accompanied by only two
“perpetual” negatives: the dislike of work and the love of luxuries (he downgrades
the Malthusian sexual drive to an important, but nonperpetual, motivation):
It does not treat of the whole of man’s nature as modied by the social state,
nor of the whole conduct of man in society. It is concerned with him solely
as a being who desires to possess wealth and who is capable of judging of
the comparative ecacy of means for obtaining that end. . . . It makes entire
abstraction of every other human passion or motive; except those which
may be regarded as perpetually antagonizing principles to the desire of
wealth, namely, aversion to labour, and desire of the present enjoyment of
costly indulgences. ese it takes, to a certain extent, into its calculations,
because these do not merely, like [our] other desires, occasionally conict
with the pursuit of wealth, but accompany it always as a drag, or imped-
iment, and are therefore inseparably mixed up in the consideration of it.
(Mill, 1836, pp. 321–2, italics added)
In Mill’s homo economicus (as his character is known), we have the portrait of a
lazy, miserly, but entirely eective, Scrooge. Mill made his thinly characterized eco-
nomic man very powerful within his account of the economic system, not in the
sense of Malthus’ model in giving us specic outcomes (about population), but by
arguing for the breadth of his impact. For example, the laws on property – accord-
ing to Mill – also ow from this primary desire to possess wealth, for such institu-
tions are designed by man to further his success in accumulating wealth.
Both Malthus and Mill followed processes that enabled them to limn the con-
stitution of economic man according to their own chosen hierarchy of economic
motives. eir strategies might be described as rst focus then simplify: rst pick
out the economic aspects believed to represent economic motivations and actions
and then subtract away all the non-economic aspects. Yet Mill portrayed his def-
inition as being the result of a process not of subtraction or simplication but of
“abstraction” (as we see above). For him, political economy was an “abstract science”
(1836, p. 325), like geometry, a science of denition, assumption, and deduction.
Hamminga and De Marchi (1994) discuss this notion of abstract science in the more
general context of laws rather than of homo economicus. ey suggest that the classical
authors’ understanding of “abstract” was that it oered a more generalized account.
3 ere are two edition of this essay: On the Denition of Political Economy: in 1836 and 1844 with
some minor dierences between them. e 1844 edition is reprinted in Mill’s Collected Works,
Vol. IV (1967), with the changes since 1836 indicated in square brackets.
Ideal Types, Idealization and Caricature 141
But, as they point out, this in turn is open to at least two further interpretations,
which are equally relevant in thinking about homo economicus. For some classical
authors, it meant that such a character has general descriptive or explanatory reach
so that he is applicable almost everywhere (with minor exceptions) – and perhaps
this would be so for Malthus, for while neither his population laws, nor the cycles
he proposed, could be directly observed in the world, his economic man’s behaviour
could be found there. For other authors, Mill included, it meant that the character is
not applicable directly anywhere in the real world – because nowhere is such a person
to be found. As Mill claimed of his economic character, no “political economist was
ever so absurd as to suppose that mankind are really thus constituted” (1836, p. 322).
However, this does not mean that his homo economicus was not relevant for explain-
ing economic behaviour. Quite the opposite. In Mill’s view, economics was not only
an abstract science, but at the same time a science of tendency laws, wherein general
laws might be applied to the concrete cases of the world provided they are always
modied by an account of the many specic and disturbing causes that occur there.4
Mill tendency laws hold for all of us. So, despite this diculty of application, his
abstraction, homo economicus, was relevant for explaining everyone’s behaviour (not
just that of some types of people) with allowances for other causes.
3. Concept Forming: Weber’s Ideal Types and Menger’s
Human Economy
“Abstract” has many connotations, and the process of abstracting in the history of
economics became associated not just with generalizing, but also with conceptual-
ising, with creating a kind of concentrated notion, encapsulating or reducing (in the
cookery sense) some aspects of well-considered phenomena.5 is kind of concept-
forming abstraction creates “ideal types” in the social sciences, a label – indeed a
concept in itself – most closely associated with the work of the great German social
scientist of the early twentieth century, Max Weber.
4 “at which is true in the abstract, is always true in the concrete with proper allowances. When
a certain cause really exists, and if le to itself would infallibly produce a certain eect, that same
eect, modied by all the other concurrent causes, will correctly correspond to the result really
produced” (Mill, 1836, pp. 326–7). is became the standard defence of why the laws of classical
analysis are dicult to validate. On tendency laws in Mill and their modern counterparts in eco-
nomics, see Cartwright (1989) and Hausman (1992). On Mill’s economic man, see Persky (1995).
5 We see this occasionally in the classical school. A good example of what I mean is given by Smith
when he attributes an abstract character to labour, the labour that features so strongly in classi-
cal economists’ labour theory of value, in order to nesse an explanation of how dierent kinds
of labour that cannot easily be compared can nevertheless be understood to determine exchange
values:“e greater part of people, too, understand better what is meant by a quantity of a par-
ticular commodity than by a quantity of labour. e one is a plain palpable object; the other an
abstract notion, which, though it can be made suciently intelligible, is not altogether so natural
and obvious.” (Smith, 1776, Book I, Chapter V, para 5)
e World in the Model
142
Weber’s ideal types are generalizations constructed from the “facts of
experience”, yet in the process, creating abstract concepts that he described as “pure
ctions”.6 One of the economists whose work Weber respected and found congen-
ial to his way of thinking was Carl Menger, the late-nineteenth-century founder
of the Austrian school of economics.7 Menger’s economic man portrait is located
in his concept of the individual or ‘human economy’ (in contrast to the “national
economy” of his contemporaries in the German historical school of economics). In
his 1883 work, Menger starts from what he takes to be the most vital elements of
human economy, namely,
. . . premeditative activity aimed at satisfying our material needs. . . . e
direct needs of each economic subject are given in each case by his individ-
ual nature . . . e goods available to him are strictly given by the economic
situation of the moment. . . . us, the starting point and the goal of every
concrete human economy are ultimately determined strictly by the economic
situation of the moment. (Menger, 1883/1985, p. 217, his italics)
Menger’s economic man was one who aimed and acted to satisfy his or her needs
by choosing between alternative goods, given the constraints of his or her sit-
uation of the moment. (We return to the importance of ‘situation’ in this def-
inition later in this chapter, and more seriously in Chapter 9.) For Menger, all
humans had many dierent needs: for example, man needs water – to drink, to
wash, to give to his horse or dog, and so forth, which he wants to satisfy, as well
as needs for dierent goods – food, clothing, heat, and so forth, all of which he
also wants to satisfy. Menger represented this in a schedule in his 1871 Principles
(our Figure 4.1) showing an individual’s personal rating of the dierent goods
(Roman numbers, horizontally) and dierent degrees of satisfaction from each
of these goods (Arabic numbers, vertically) and suggested that humans choose
quantities of each good, and of dierent goods, in such a way as to satisfy those
needs in a particular order, with necessities rst, then less important needs, up to
a point where the satisfactions gained from consuming each element of the var-
ious goods are equal.
In reecting on how he arrives at such a conceptual account of human econ-
omy, Menger writes about his aim as follows:
. . . to ascertain the simplest elements of everything real, elements which
must be thought of as strictly typical just because they are the simplest.
It strives for the establishment of these elements by way of an only par-
tially empirical-realistic analysis, i.e., without considering whether these
in reality are present as independent phenomena; indeed, even without
6 See Weber (1904); and for the two quoted phrases, his 1913, p. 98 and 1917, p. 44. See Zouboulakis
(2001) on a comparison of Menger’s versus Weber’s notions of abstraction.
7 See Weber (1908 [1975]). e historical relationship between Weber and Menger is nicely drawn
in Bruce Caldwell’s recent book (2004) on Hayek.
Ideal Types, Idealization and Caricature 143
considering whether they can at all be presented independently in their
full purity. In this manner theoretical research arrives at empirical forms
which qualitatively are strictly typical. It arrives at results of theoretical
research which, to be sure, must not be tested by full empirical reality (for
the empirical forms under discussion, e.g., absolutely pure oxygen, pure
alcohol, pure gold, a person pursuing only economic aims, etc., exist in
part only in our ideas). (Menger, 1883/1985, pp. 60–1, his italics)
In his political economy work of 1871, Menger successively composed these “real
simplest” elements into an account and explanations of economic man’s reasoning
and behaviour contingent upon his situation. Where Mill had picked out – had
abstracted – from the full description of man’s motivations what he took to be man’s
main economic motivations, Menger composed his concept of human economy by
sequencing together the denitions of the simplest elements to build up his abstract
notion of typical economic behaviour.8
We can gain further insight into Menger’s economic man as an ideal type if
we recognise that he is neither ideal nor a type in the common meanings of those
terms. Machlup (1978, p. 213) suggests that, consistent with the community notions
of his time and place, ‘ideal’ refers not to some elements of perfection, but as the
adjectival form of ‘idea’; and ‘type’ refers not to a classicatory kind we meet in the
world, but to a ‘mental construct’.9 ese are helpful observations for understand-
ing Austrian school economists like Menger. For example, he believed that it is
another important part of the character of being human to have limited knowledge,
Figure 4.1. Menger’s Consumption Schedule.
Source: Carl Menger, Grundsätze der Volkswirtschaslehre, Wilhelm Braumüller,
Vienna,1871, p. 93 (Reprinted facsimile, London: London School of Economics and Political
Science Reprints of Scarce Tracts in Economics, No. 17, 1934.)
8 is composing notion does not refer to the “compositive denitional mode” that Bruce Caldwell
(2004) suggests is the way Austrians economists arrive at aggregate accounts.
9 Fritz Machlup (1978) follows the notion of ideal types from the German-speaking communities’
discussions of the later nineteenth century into more recent times.
e World in the Model
144
and so that feature is found in his portrait of economic man. Menger’s ideal type
economic man is an abstract portrait, but its critical feature is that it oers a con-
ceptual model of economic behaviour, neither an idealized character nor a specic
natural kind in the world.
Menger thought that by a process of introspective observation and thought-
ful, logical method, he could obtain the general or exact laws of the “phenomena
of abstract economic reality” but not of the “real, in part extremely uneconomic,
phenomena of human economy” (Menger, 1883/1985, p. 218, italics his).10 at
is, since his economic man was painted in abstract conceptual terms, the account
could not be applied to the world, even with diculty, which speaks to the dierent
notion of ‘abstract’ we nd compared with Mill’s portrait earlier. What then is the
function of such abstract conceptual – or ideal type – models? Weber’s answer goes
as follows:
e ideal type concept will help to develop our skill in imputation in
research: it is no “hypothesis” but it oers guidance to the construction of
hypotheses. It is not a description of reality but it aims to give unambiguous
means of expression to such a description. . . . It is a conceptual construct
(Gedankenbild) which is neither historical reality nor even the “true” real-
ity. It is even less tted to serve as a schema under which a real situation or
action is to be subsumed as one instance. It has the signicance of a purely
ideal limiting concept with which the real situation or action is compared
and surveyed for the explication of certain of its signicant components.
(Weber, 1904 [1949], pp. 90 and 93, his italics)
So Weber suggests that an ideal type fosters understanding of the social scientist’s
world, not because it can be directly applied, but as a benchmark device against we
can enquire into the world; not because it is a hypothesis, but because it enables us
to formulate such hypotheses. Ideal types function neither as theories nor empir-
ical descriptions, but as independent instruments or tools that enable the social
scientist to support enquiries into both domains.11 In other words, they carry the
same function we attributed to models as instruments of enquiry in economics in
the discussion of Chapter 1. And, like these ideal types, economists’ abstract con-
ceptual models form instruments of a subtle and sophisticated kind.
10 Machlup interprets Menger as distinguishing between “strict” (ideal) types and “real” types, sug-
gesting a further distinction between economic man as a strict type with no counterpart real types,
and other ideal types like “free market price”, which have corresponding real types in observ-
able, regular phenomena (1978, pp. 255–6; see also his commentary on pp. 230–32 and Menger
(1883/1985, Appendix VI). (See also Mäki, 1997.) Machlup reports the vehemence of contem-
porary arguments over whether the ideal type may also be, or is in contrast to, a real type and
whether it is possible to regain the concrete from the ideal type. See also Hempel’s (1965, chapter
7) discussion of the purpose of ideal types.
11 Ideal types don’t necessarily form usable scientic models, just as not all analogies do. Once
again – as in the Malthus case earlier – it comes down to whether the ideal type is exactly and sim-
ply enough formed to be useful in economic reasoning.
Ideal Types, Idealization and Caricature 145
We have already found two notions of abstraction in our history of economic
man. For Mill’s way of making his portrait, the term suggests something like the
process of making a reader’s abstract: not so much shortening and simplifying,
but distilling out the main economic characteristics so that they stand out from
the detail of the whole. is contrasts with the notion of abstracting we found in
Menger’s work: a concept-forming activity, which is not so easy to describe but that
clearly involved a more constructive process than subtracting one. Marx Wartofsky
suggests we may think of concept forming in science as a process in which the
scientist turns perceptions into more abstract mental images.12 Such perceptions
are presumably not literally observations, but rather intuitions and understand-
ings, and the scientists use their cognitive and imaginative talents to turn these into
concepts or abstract ideas. Menger’s analysis of typical economic behaviour and his
creation of an ideal type portrait, work he described (above) as theoretical work
to get at the typical empirical form, does indeed seem to fall under this notion of
abstracting as concept forming.
But when, as Wartofsky suggests, these abstractions create concepts that can be
represented in symbolic form, this opens up all sorts of new possibilities, for con-
cepts transformed into symbols can be manipulated, reasoned with, and extended
into dierent contexts than the original source. In this sense, the most signicant
dierence in the abstracting process behind Menger’s human economy compared
with Jevons’ calculating man is in their language of representation. ough the por-
traits were contemporaries of each other, and both involved concept-forming work,
it was Jevons who, as we see next, moved the portrait from the symbolic languages
of verbal expression rmly into those of mathematics, opening up ideas about indi-
vidual economic behaviour to a dierent, and more powerful, mode of manipula-
tion. More important perhaps, Jevons’ mathematical prortrait could travel easily
into many new contexts.
4. Symbolic Abstraction: Jevons’ Calculating Man
William Stanley Jevons’ (1871) economic man is a calculating consumer, his moti-
vations and actions are dened in psychological terms that are fundamentally
unobservable.13 Like Mill, Jevons explicitly deals only with the economic motiva-
tions of man; but whereas Mill’s portrait rests upon the classical laws of production
and distribution, for Jevons, the main base was the economic laws of consumption.
Jevons’ portrait is inspired by the economistic moral principle of utilitarianism:
Economics must be founded upon a full and accurate investigation of the
conditions of utility; and, to understand this element, we must necessarily
12 See Wartofsky (1968, chapter 2).
13 ere is a wonderfully rich literature on Jevons, see particularly Maas (2005a), Schabas (1990), and
Peart (1996). On Mill versus Jevons, see Maas (2005b).
e World in the Model
146
examine the wants and desires of man. . . . it is surely obvious that economics
does rest upon the laws of human enjoyment. (Jevons, 1871, p. 102)
is is a move away from Mill’s man’s desire to accumulate wealth in the form of
goods or money, towards man gaining enjoyment or utility from consumption of
goods, thus replacing the constant positive motive found in Mill’s homo economicus
with one of his negative motives.
Jevons’ portrait was painted in the formal language of mathematics. Calculation
and psychology go along together here, for Jevons’ economic man is a pleasure seeker –
he ‘maximizes utility’ from consumption, where utility is conceived of in a uniform
way.14 Jevons begins with Jeremy Bentham’s psychologically based account of util-
ity, with its seven dimensions: intensity, duration, certainty/uncertainty, propinquity/
remoteness, fecundity, purity, and extent.15 Jevons regards the last three as being rele-
vant for moral theory, but not relevant for the “simple and restricted problem which
we attempt to solve in economics” (p. 95). He transforms two of the remaining four
“circumstances” – intensity and duration – into quantities, so that each experienced
value of pleasure (or its negative value, pain) could be plotted as Cartesian coordi-
nates in a two-dimensional space. is diagrammatic representation enables him to
depict how man gains pleasure from consuming a good and how that pleasure – or
utility – declines with successive units of the good consumed based on the physiolog-
ical principle of satiation. While the basic idea has much in common with Menger’s,
Jevons interpreted the intensity of pleasure (or utility) as varying continuously with
its duration (or amount of the good), an abstraction consistent with the mathematical
conception of economic man and his behaviour. is can all be seen in Jevons’ gure
4 (our Figure 4.2), which charts the amount of good consumed along the horizontal
axis and intensity of pleasure from such consumption on the vertical.
Where Malthus and Mill had earlier reduced the broad classical portrait given
by Smith to a simple set of economic motivations in order that they could reason
about man’s behaviour more easily, Jevons reduces the dimensions of Bentham’s
utility analysis not just to make it tractable, but to mathematize his treatment of the
consumption feelings and decisions of economic man. By transforming Bentham’s
verbal ideas into mathematical conceptions and symbols to represent economic
man’s behaviour, Jevons characterizes that man’s behaviour with a new level of
exactitude. It also enabled him to take his newly created portrait into the labo-
ratory of mathematics and to investigate his economic model man’s motivations
and feelings with mathematical forms of reasoning. As argued in Chapter 1, such
rules of enquiry come with the form of the model: because his economic man is
14 In this respect, Jevons’ conception of utility is narrower than that of his contemporary, J. B. Clark
(1899), who had utilities associated with forms, places, time, etc.
15 Bentham’s (1789/1970) scientic claims involved a reductionist theory of mind that sensations
(pleasures/pains) lead to mental associations and that pleasure is homogeneous and quantiable.
Although he used mathematical metaphors: “felicic calculus”, “axioms of mental pathology” etc.,
he did not formulate these ideas mathematically.
Ideal Types, Idealization and Caricature 147
mathematically dened, so are the rules governing his behaviour in the model.
us Jevons used mathematical rules to dissect his economic man’s feelings, using
calculus to measure his total amount of utility from consumption (represented by
an area on the diagram), and the ‘nal degree’ of utility from consuming successive
“marginal units” of the good as marked out along the line of the curve.
e mathematical rules of reasoning used by Jevons to describe the behaviour
of the model man are then imputed as the rules of reasoning followed by the man
in the model for he implies that real man makes such calculations for himself using
the same kind of reasoning and mathematics (as Jevons presents). at is, man
makes his economic decisions by weighing up, comparing, and deciding how to
maximize his utility from consuming:
Now the mind of an individual is the balance which makes its own compar-
isons, and is the nal judge of quantities of feelings. (Jevons, 1871 p. 84)
For example, when faced with choice between two goods, Jevons represents his
consumer as mentally weighing the utility from successive degrees of consump-
tion of the dierent goods until they are equal, where they can be exchanged at the
margin (and this gives exchange ratios or relative ‘prices’ for that individual). By
portraying his economic man as thinking in terms of these mathematical notions,
he revealed his deep sense that this is how economic behaviour is determined.
Jevons dened utility not as a quality within goods, but as “a circumstance of
things arising from their relation to man’s requirements” (Jevons, 1871, p. 105), that
is, as a relation between goods and man, so that the utility valuations of his calculat-
ing man, – preferences and weighings – are neither observable nor measurable. So,
despite the exactitude depicted in the graphs and mathematics of man’s behaviour,
Figure 4.2. Jevons’ Utility Curve.
Source: William Stanley Jevons, e eory of Political Economy, 1871, London: Macmillan
& Co., g. 4 on p. 49.
e World in the Model
148
the terms these symbols represent are fundamentally internal and known only
to the subject. Whereas Mill’s picture of homo economicus still seems to refer to
observable behaviour that might be accessed objectively by a commentator, Jevons’
calculating man is an introspective character, whose subjectively registered feelings
such a commentator could not access.16 It was only literary licence that allowed
Dickens to give us access to Scrooge’s wealth seeking (Mill’s economic man) from
his external behaviour and to see him weighing past and future pleasures against
pains (Jevons’ economic man) in his Christmas dreams!
From Jevons’ point of view, in contrast to that of Mill, the material of econom-
ics is mathematical, so, naturally, economists’ portrait of economic man should also
be written in the language of mathematics and its methods of analysis must also
be mathematical. is move into mathematics turned out to be highly signicant
and was subject to much debate at the time. McMullin (1985) writes about similar
kinds of arguments over Galileo’s earlier use of mathematics in the natural sci-
ences, arguments that go back in various forms to dierences of opinion between
Aristotle and Plato. is dierence depends upon whether we understand the Book
of Nature for economic science to be written in mathematics or not. If the Book of
Nature for economics is not written in mathematics, Jevons’ mathematization of
the portrait imposes a particular kind of abstraction, or idealization for purposes
of convenience:
Mathematical idealization is a matter of imposing a mathematical formal-
ism on a physical [for us, economic] situation, in the hope that the essen-
tials of that situation (from the point of view of the science one is pursuing)
will lend themselves to mathematical representation. (McMullin, 1985,
p. 254)
at is, we might interpret Jevons’ reduction and transformation of Bentham’s ideas
on utility into two-dimensional geometry and dierential calculus as mathemati-
cal forms imposed for convenience of the representation and its subsequent usage,
rather than because mathematics is the form in which economic man’s behaviour
is best and most accurately represented. Yet both Jevons here, and Edgeworth as we
saw in Chapter 3, took it for granted that economists’ Book of Nature was written
in mathematics (see Schabas, 1990), just as:
Galileo took for granted that his geometry provided the proper language of
space and time measurement, and that arithmetic would suce for gravità.
(McMullin, 1985, p. 253, his italics)
Regardless of whether economic man lent himself naturally to a mathematical
portrait, or whether his nature was constrained into the mathematical form, this
move to mathematical abstractions and concepts was highly signicant for the sub-
sequent career of economic model man. e combination of attributes in Jevons’
16 Until, that is, recent developments in neuroeconomics (see Section 8 later).
Ideal Types, Idealization and Caricature 149
portrait: the psychophysical treatment of motivations, economic man’s calculating
mentality, and the mathematical nature of Jevons’ depiction – all had longer-term
implications for the way economists go about the task of abstracting. is is why
Jevons is oen lauded as one of the founders of modern economics (see Maas
2005a). By his kind of work, methods of creating models of economic man became
inextricably linked with ‘formalizing’. is entailed changing the language of eco-
nomics, from the informal and hugely nuanced possibilities of expression found
in our verbal languages (but with their limited reasoning possibilities) to the more
constrained but more exact and rule-bound symbolic forms of mathematics (with
their greater reasoning powers, as discussed in Chapter 1). Aer Jevons, economic
man was generally characterized in ways consistent with a mathematical treatment
of his qualities.
Where does this mathematically drawn calculating model man sit in relation
to the rest of economics? In Jevons’ newly formalized conception of man in mar-
ginal economics, and in the neoclassical economic theory that grew out of it, the
individual seems to have gained causal power for the laws of economics operate at
the level of the individual, not the aggregate as in classical economics. As Chapter 3
records, Edgeworth took Jevons’ calculating man into a small-world model – that
became the Edgeworth Box – to enquire how his utility maximizing behaviour
would enable him to reach exchange decisions with a limited number of other cal-
culating individuals. And, as that chapter also records, Pareto taking advantage of
his symbolic abstract form, investigated how such an economic man – an X or a Y,
an A or a B – found his or her way around the obstacles on the path to the top of
his hill of pleasure. Once formed – as with other models before and since – Jevons’
model man was used by other economists to think with and to reason about human
economic behaviour in other situations. It was Edgeworth who named Jevons’ cal-
culating man an economic ‘agent’, a motivating agent for plugging into other mod-
els and setting the reasoning going. As we shall see (in Chapter 9), his ospring live
up to that agency role particularly in modern game theory.
Jevons’ model man was not so eective as a model for enquiries into the world,
not at least until the advent of experimental economics 100 years later (see Chapter
7) and perhaps neuroeconomics even more recently. It is not just that calculating
man’s calculations are unobservable, but that, as Jevons carefully explains when he
laid out his mathematical theory of marginal utility:
e laws [of individual economic man’s behaviour] which we are about to
trace out are to be conceived as theoretically true of the individual; they
can only be practically veried as regards the aggregate transactions, pro-
ductions, and consumptions of a large body of people. But the laws of the
aggregate depend of course upon the laws applying to individual cases.
(Jevons, 1871, pp. 108–9)
is is not the same aggregation problem of classical economics, as perceived by
Malthus or Mill: of disturbing causes covering up, in the aggregate, the behaviour
e World in the Model
150
that might be found by the addition of lots of individuals following similar courses
of action. e problem here follows from the combination of the actions of individ-
uals following the same laws of behaviour but with dierent preferences for goods,
subjectively judged. For the ‘marginalists’, Menger as much as Jevons, each and
every valuation decision freely made by the individual economic man can make a
dierence to the aggregate outcome.
We saw this directly in Chapter 3, when Edgeworth (1881) stressed the ability
of each individual, each with dierent tastes and desires, like Robinson Crusoe and
Man Friday, to contract freely in the market place. Equally, we can see the power
of each individual calculating model man in the formal mathematical account of
general equilibrium by the French marginalist Leon Walras. Dening economic
behaviour in terms of individual maximizing of utility turns out to mean that if
the preferences for just one good by just one of all the calculating consumers in
the economy changes, the demand for that product changes, and the prices of all
the other products may also change because of the way these calculating individ-
uals are linked together into the overall market account. is makes it well nigh
impossible to think of going back from any individually isolated behaviour to the
real world as Mill had proposed. is makes the model man an important feature
of neoclassical economics, powerful as a motivating device for other models, and in
theorizing. But it creates considerable diculty, for, to make economic man tract-
able en masse, later economists must decide whether they really are all the same
and might be represented by one particular ‘representative agent’, or need to have
their variability characterized explicitly.17
5. Exaggerating Qualities: Knight’s Slot-Machine Man
It was the main American exponent of neoclassical economics, Frank Knight (in
his thesis of 1915, published in 1921) who worked out the details that allowed cal-
culating man to play his full role in the formal neoclassical theory of the econ-
omy. Menger had argued that, unlike his account of ‘human economy’, it must be
assumed that the economic subjects used in price theory do not act in error nor
without information about the situation (1921, p. 71). Knight’s move was a much
more positive one. He argued that only by endowing calculating man with full
information about everything in the economy (rather than the limited information
Menger assumed for his human economy), and with perfect foresight about the
future (rather than the uncertainty that Jevons had le aside from his calculating
man portrait), could the individual person make the necessary calculations that
would allow him to judge accurately what actions to take in buying and selling
and consuming. ese exaggerations are necessary not for understanding man in
actual economic life but in order that economic man could play the part required
17 See Hartley (1997) and Kirman (1992).
Ideal Types, Idealization and Caricature 151
of him in the overall mathematical theory of the economy being constructed by the
neoclassical economists.18
Knight was the rst to admit that a world peopled by such individuals was no
longer a simplication, but an “heroic” abstraction.
e above list of assumptions and articial abstractions is indeed rather a
formidable array. e intention has been to make the list no longer than
really necessary or useful, but in no way to minimize its degree of articial-
ity, the amount of divergence of the hypothetical conditions from those of
actual economic life about us. (Knight, 1921, p. 81)
While the classical economists had pared down to homo economicus, neoclassical
economists such as Knight exaggerate certain of his characteristics (his calcu-
lating ability and his ‘perfect knowledge’). Like Mill, he argues that scientic eco-
nomics places severe limitations on the treatment of man. But in order to arrive
at denite analytical results about the workings of markets and the economy as a
whole, Knight argues that economic science requires a fully idealized economic
man, not just a simplied or abstracted man. Knight’s portrait is very dierent
from Mill’s. e model man Knight creates was specially designed to live in the
highly idealized mathematical world of neoclassical economic theories: a crea-
ture of artice. Only by assuming that there were innitely many of him, and that
each acted independently of the others, could neoclassical analysis depict the
perfectly competitive economy and equilibrium outcome that maximized aggre-
gate utility. is model man was an idealized mathematical character designed
to behave perfectly in an idealized mathematical world of neoclassical economic
science.19
e issue of knowledge is a critical one for Knight. Despite, or rather because
of, all that information and foresight that he was endowed with, Knight argues that
his model economic man has no intelligence:
With uncertainty absent, . . . it is doubtful whether intelligence itself would
exist in such a situation; in a world so built that perfect knowledge was
theoretically possible, it seems likely that all organic readjustments would
become mechanical, all organisms automata. (Knight, 1921, p. 268)
Weber had pinpointed this same question of information as a requirement of act-
ing in a “logically ‘perfect’ way” in the context of a discussion of what it meant to
18 See Giocoli (2003) on the way in which Weber foresaw this requirement. Knight’s denitions are
verbal despite the mathematical role that the character played.
19 is portrait of economic man was strongly embedded as the central character of formal math-
ematical theorizing of neoclassical economics. As Knight pointed out in his thesis way back in
1921, and as Arrow has argued more recently (1986), this economic man is one leg of a three-
legged stool. He has to be combined with two other basic tenets – perfect competition and general
equilibrium theorizing – to get the strong formal results that characterized the middle part of
twentieth-century economics, but even there, he was pretty helpless on his own, for each element
also depended on the others.
e World in the Model
152
act rationally, but he did so to establish what real people would do by comparison,
rather than as a requirement of a broader theoretical aim (1917, p. 42). For Knight,
the point is not to establish what real people would do, but what this model man
would do inside an economic theory. Knight (later) portrays this idealized eco-
nomic man as a slot machine:
e Economic Man neither competes nor higgles . . . he treats other human
beings as if they were slot machines (Knight, 1947, p. 80),
not even a one-dimensional man, but a purely impersonal utility maximising agent
(as economists now say), a pleasure machine that experiences none of Jevons’
man’s pain or pleasure, nor satises his needs as Menger’s man does; he has no
Malthusian vices, virtues, desires, or children, nor Smithian propensities, talents,
or preferences.
Knight insisted that this ideal gure of economic science – his slot-machine
model man – does not help to describe actual economic behaviour, and so can-
not be used for socially useful economic analysis or policy interventions. Unlike
Mill’s economic man portrait that he thought held true of everyone at some level,
Knight’s model man was not to be used in analysing behaviour in the real economy.
Indeed, as part of his commitment to liberal democracy, Knight wrote moral com-
mentaries describing man’s actual economic behaviour as being driven by compe-
tition but acting according to the rules of the social game. He explicitly denied that
the rational economic man of his analytical work had any realistic import.20
e kind of economic man that Knight created for neoclassical economists’
theorizing, slot-machine man as I have labelled it (for it would seem odd to refer to
a machine by a personal pronoun), was heaped with important extra information
and foresight, qualities accentuated by Knight to enable him to play the central role
in the neoclassical system. Weber had already recognised this kind of exaggeration
in thinking about the market economy:21
Substantively, this construct [an exchange economy] in itself is like a
utopia which has been arrived at by the analytical accentuation of certain
elements of reality. . . An ideal type is formed by the one-sided accentua-
tion of one of more points of view and by the synthesis of a great many
diuse, discrete, more or less present and occasionally absent concrete
20 Although these two domains of his economics were largely separate, Knight created a second eco-
nomic man character in his portrait of the American economic way of life (see Emmett, 1994).
ere, we nd Knight portrays competition as a human urge or instinct to motivate his descrip-
tion of human behaviour (see Knight, 1923). is characterization of real economic man moti-
vated by some very powerful basic instinct is similar in kind to Smith’s propensity to truck, barter,
and exchange or Malthus’ evolutionary imperative. Knight was following in the same path as the
American marginalist J. B. Clark, whose economic man might be called ‘social man’ (in contrast to
the isolated individual usually assumed) and who also had two kinds of economics, one for theo-
rizing and one for describing for the world (see Morgan, 1994).
21 Machlup (1978) suggests that Comte also noted the use of exaggerations in this way; see his p. 228.
Ideal Types, Idealization and Caricature 153
individual phenomena, which are arranged according to those one-sidedly
emphasized viewpoints into a unied analytical construct (Gedankenbild).
In its conceptual purity, this mental construct (Gedankenbild) can not be
found anywhere in reality. It is a utopia. (Weber, 1904, p. 90, his italics)
Weber’s account of this process of exaggeration, or one-sided emphasis in the
development of an ideal type is unlike Menger’s ideal type human economy, which
depended on locating what is typical of real behaviour at its simplest level. e exag-
geration we nd here is also of a qualitatively dierent kind than the miserliness
le aer Mill’s abstraction from other motivations. Recall that earlier versions of
economic man were arrived at by processes of focussing on economic motivations
and subtracting or abstracting in the sense of ‘to abstract’ (of Malthus and Mill) or
by the rather dierent concept-forming abstraction (of Menger and Jevons), all of
which suggest, in some way, the ling away of extraneous elements.
If Knight had only taken away uncertainty, as Jevons did when he omitted
the uncertainty that Bentham had thought relevant to decisions about utility, this
would t the usual analogical example of the frictionless plane, used as a standard
example to illustrate the notion of model-making by idealization in physics. But
Knight’s slot-machine man is a model arrived at through the addition of ctions or
falsehoods. He did not just ignore uncertainty or set it at zero, but chose to dene
its absence as the presence of perfect knowledge.22 And perhaps it came as a sur-
prise to nd that the addition of perfect knowledge – in Knight’s terms – means his
character has no need of intelligence, and thus we get to the slot-machine model
of man, for an automaton does not think. It is this kind of addition that makes
the economic man we see in Knight’s characterization into the pure concept that
Weber remarks upon, for Knight had created the economic model man of neoclas-
sical economists’ utopia. Knight’s slot-machine man could be used by economists
to learn about the idealized (theoretical) economy, and it could do so because it
enabled them to explore, within their theories, the economic behaviour of man and
its consequences in its most exaggerated form.
6. Making a Cartoon into a Role Model:
Rational Economic Man
Just as nineteenth-century classical economics supported dierent models of
economic man’s character, so too did twentieth-century neoclassical economics.
22 Philosophers of economics, such as Cartwright (1989) and Mäki (1992), usually reserve the term
“idealization” for these false statements – and have in mind the kind of under- or overstatements
dened by limit cases (such as setting some factor at zero or innity) in contrast to leaving a
factor out (termed ‘abstractions’ by Cartwright and ‘isolations’ by Mäki). But there is a dier-
ence between setting something (ignorance) to zero and lling in what its opposite – for example,
knowledge – might mean. See also the parallel discussion of various kinds of ceteris paribus c ondi-
tions by Boumans in Boumans and Morgan (2001).
e World in the Model
154
We have just seen how Knight’s model of economic man was well clothed with
articial assumptions about his knowledge and foresight, even while his underlying
character had become decidedly less human, for Knight had black-boxed Jevons’
enquiries into what happened inside real man’s head and replaced economic man
by a wonderfully endowed automaton. A dierent kind of black-boxing went on
in an alternative refashioning of economic man in which he gained the adjective
‘rational’. Rational economic man seems to have somewhat more the qualities of
a cartoon: he is decidedly two-dimensional in character, and while regarded with
aection by economists, he is regarded as a gure of fun by other social scientists.23
But despite these cartoon qualities, rational economic man came to function as a
role model for rational behaviour
e process by which economic man gained the label ‘rational’ is complex
indeed, but my aim here is not to unravel this process, only to sketch in enough to
indicate another historically important version of economic man in my gallery of
portraits.24 To this end, I oer just one path through the historical maze, beginning
with the distinction between the economic man portraits of Jevons and Menger.
Jevons’ mathematical analysis of calculating man was concerned with how he made
such decisions to maximize utility from consumption assuming that utility was all
one kind of stu, so the nature of man’s choices between dierent kinds of things
received little attention. More of a good is better than less up to the point where
the extra (marginal) unit no longer gives him pleasure but pain, but beyond that,
Jevons’ account was limited: his calculating man has no way of choosing between
two equal utility-valued goods – he is simply indierent between them. Edgeworth
followed this strand when he expressed the series of points of equal utility valua-
tions for combinations of the two goods as indierence curves in his discussion
of Crusoe and Friday (see Chapter 3). In Menger’s account, man is an economizer
rather than a maximizer. His subjective valuations (based on introspection) are
concerned with choices at the margin between satisfying dierent needs given his
circumstances, rather than with assessing standardized units of pleasure from con-
suming dierent goods as Jevons’ calculating man does. It is in this Austrian mar-
ginalist tradition in the late nineteenth century that we nd an economic man who
considers how to choose between things.25 On the other hand, it was Jevons’ and
Edgeworth’s mathematical formulation of economic man that provided the means
of description for rational economic man.
23 Exaggerations of certain features (as noted here in this chapter) have led other social scientists
(and critical economists) to make fun of these economic man portraits in ways that reect these
cartoon qualities. For example, J. M. Clark observed that the marginal man of Jevons’ variety was
“absorbed in his irrationally rational passion for impassionate calculation” (1918, p. 24).
24 I thank the referee who oered me eight dierent alternative readings of the main elements of
rational choice theory! Each no doubt has a history that is mutually entwined with that of the oth-
ers. See note 26 for further references.
25 His was not the only account that focussed on individual economic choosing. J. B. Clark (1899),
the American marginalist, relied on an account of choice inuenced by the social group.
Ideal Types, Idealization and Caricature 155
is history of what happened to economic accounts of behaviour aer Menger
and Jevons has been told in various ways, but they mostly agree that this refocus-
ing of the portrait involved two separate moves. On the one hand was a process of
stripping away the underlying psychology from both Menger’s picture of satisfying
needs and from Jevons’ picture of maximizing utility that led to the psychological
thinness of the new characterization.26 On the other hand, it involved lling in the
notion of what it meant for economic man to be “rational”. Historically, economists
have used two main notions: one relates to reasoning behaviour, the other to choos-
ing behaviour as Herbert Simon (1976) pointed out. In the early neoclassical eco-
nomics of Knight, rational meant ‘reasoned’, goal-directed, activity, a notion that
hardly diers from the ecacious pursuit (of wealth) that we found in Mill’s homo
economicus. It was rational in the second ‘choosing’ sense more associated with
Menger that became closely linked to mid-twentieth-century neoclassical econom-
ics, and the birth of this man was, as with Mill, closely associated with a change in
the denition of economics.
Once again, Weber makes an interesting pointer, taking Menger’s concern with
satisfying needs given his circumstances into a more general idea:
Specically economic motives . . . operate wherever the satisfaction of even
the most immaterial need or desire is bound up with the application of
scarce material means. (Weber, 1904, p. 65, his italics)
is comes close to the standard twentieth-century neoclassical denition of eco-
nomics as: “the science of the ecient use of scarce resources”, for as Lionel Robbins
announced in 1932, economists were no longer concerned with “the causes of mate-
rial welfare”, or the creation and distribution of wealth as were the eighteenth- and
nineteenth-century classical economists, but with “human behaviour conceived as
a relationship between ends and means” (p. 21).27 e situation of scarcity, noted
by Weber and announced by Robbins as dening economics, was one in which
choices have to be made.
is change in the base denition of economics had great consequences for
the portrait of economic man for it places his ability to make choices central to his
conception. In the marginalists’ conception, whether of Jevons or Menger, model
man’s desires or his needs (respectively) are the primary components of the portrait.
26 A. W. (Bob) Coats (1976) recounts how the late-nineteenth-century attempts to provide psycho-
logical underpinnings to economic behaviour gave way in the twentieth century following attacks
by pragmatic philosophers in the U.S. and the failure of measurement programmes in the U.K.
Using a similar cast of economists that includes Fisher, Pareto, and more, Nicola Giocoli (2003)
writes of an “escape from psychology”. For a recent dissenting voice, at least as far as some of the
story about psychology goes, see Hands (2010). e rise of behaviourism and positivism are also
thought to be important factors (on the latter, see Hands, 2007), as are discussions about altruism
(see Fontaine, 2007).
27 Robbins references the Austrian tradition, and Caldwell (2004) discusses that relationship though
Howson (2004) suggests local roots to his ideas. See Backhouse and Medema (2009) on the accep-
tance of the new denition and Maas (2009) on the Weber-Robbins comparison.
e World in the Model
156
ese were pared away in twentieth-century rational economic man, for whom it is
assumed that his desires can be maximized or satised only by ‘rational’ decisions
and choices. Characterizing this rationality then became the main object of the
portrait. is commitment to a new denition of economic man, and throwing out
of the old, was expressed by Lionel Robbins:
e fundamental concept of economic analysis is the idea of relative valu-
ations; and, as we have seen, while we assume that dierent goods have
dierent values at dierent margins, we do not regard it as part of our
problem to explain why these particular valuations exist. We take them as
data. So far as we are concerned, our economic subjects can be pure ego-
ists, pure altruists, pure ascetics, pure sensualists or – what is much more
likely – mixed bundles of all these impulses. e scales of relative valua-
tions are merely a convenient formal way of exhibiting certain permanent
characteristics of man as he actually is. (Robbins, 1932, p. 95)
As Robbins took pains to point out, this did not exclude individuals making rela-
tive valuations on the basis of their feelings of all kinds, including “virtue or shame”,
or even an interest in “the happiness of my baker” (Robbins, p. 95, a reference to
Smith’s self-interest in exchange argument); it is just that these motivations were
no longer of interest to the economist.28 It is this loss of personality as well as of
psychology that create the sense of two-dimensionality, and so the cartoon-like
character, that this new ‘rational economic man’ exhibits.
By making choices dominant over desires, mid-twentieth-century economics
eectively allowed economic man to have any type of character he liked provided
he behaved ‘rationally’. Rational economic man was named so because he chose
rationally: he wished to maximize his utility (as in Jevons’ account) but did so by
making choices that were logically consistent over a set of goods (rather than by
introspectively following by his pleasure or his needs).29 Here rationality is instru-
mental – economists working in this neoclassical tradition claimed nothing about
the underlying feelings of people, as in marginal economics of Jevons and Menger,
nor about their motives as in the classical economics of Malthus and Mill; and, as
Robbins implies, economists did not even care. e person in the model ceased to
have any explanatory power over the causes of economic behaviour.
Economic man had already became a shadowy gure in the early-twentieth-
century Edgeworth Box, labelled with an X or a Y; or as J. M. Clark remarked, “He
has become a symbol, rather than a means of description or explanation” (1936,
p. 9). When he then acquired propensities to behave rationally, economists used
28 “It is not from the benevolence of the butcher, the brewer, or the baker that we expect our dinner,
but from their regard to their own interest. We address ourselves, not to their humanity but to
their self-love, and never talk to them of our own necessities but of their advantages” (Smith, 1776,
Book I, Chapter II, Para 2).
29 Choices must be ‘consistent’ and ‘transitive’ over a number of goods (i.e., if A is preferred to B and
B to C, then A must also be preferred to C).
Ideal Types, Idealization and Caricature 157
him to enquire into the nature of rational behaviour and to reason with him by
asking what constitutes rational behaviour in any given circumstance or situation
such as in the situations of game theory (see Chapter 9). Because of his charac-
ter he came, on the one hand to be seen as oering an account of the rationality
of outcomes of economic behaviour in the economy: rational economic man was
“designed for interpreting observed consequences of men’s actions”, not for inter-
preting the actions themselves (Machlup, 1978, p. 281). On the other hand, he was
also seen as oering a model for how real man should behave:
e rational man of pure theory is an ideal type in the sense not only of
being an idealization where the theory holds without qualication but also
of being a model to copy, a guide to action. In pointing out the way to sat-
isfy a given set of ordered preferences, the theorist gives reasons for action.
(Hahn and Hollis, 1979, p. 14)
Here, the “reasons for action” are not in the initial feelings of the subjects, but are
rationalised (or reasoned backwards) by the economist from looking at the conse-
quences. Model man in this sense is no longer a perfectly distilled, that is, abstracted,
version of real man’s economic behaviour, or even of the observed consequences of
his actions, but for some economists at least, a normative model of behaviour for
real economic actors to follow. Economic man became a role model that dened
rational behaviour.
7. e Art of Caricature and Processes of Idealization
Let me return here to my larger agenda – the problem of understanding how mod-
els are made, for this was the question for the rst part of this book. By peering into
the history of economic man we have seen how successive generations of econo-
mists created their accounts of individual economic behaviour. We have also seen
why economists created these model men, for, as they stated quite clearly, they
needed a distilled notion of human economic behaviour in order to make econom-
ics viable as a science. Making a model of the individual was to create a more care-
fully limited account of economic man’s character, and of the way he behaves, into
a form that could be used for reasoning with, either in theorizing or in enquiries
into the world.
Various terms have been used here to describe the model-making processes
used by these economists: focussing, simplifying, subtracting, reducing, abstract-
ing, isolating, conceptualizing, symbolizing, idealizing, composing, exaggerating,
and so forth. Other terms have been used to describe the outcomes: model man as
abstractions, utopias, conceptual devices, symbolic abstractions, ideal types, autom-
ata, and cartoons. Some of these terms were used by the economists themselves,
and others came from my attempts to capture the process they were using or to
characterize the outcomes they obtained. We have seen, for example, that Malthus
e World in the Model
158
and Mill made their economic man portraits in a relatively straightforward way:
they focussed on, or abstracted, only the elements they considered most impor-
tant. At rst sight, such a description seems to be equally relevant for Menger
and Jevons. But in these latter cases, it is by no means a sucient account. eir
kinds of abstraction meant that other processes were involved too. Menger’s man
was made by a process of composing from simplest typical elements and involved
abstractions and concept forming in making his ideal type. Jevons used processes
of reduction and transforming into symbolic form as well as picking out the salient
characteristics for attention and setting others aside. In other words, we quickly
nd that it is quite dicult to select exactly the right set of terms to capture –
with the required nuances – the way that any one economist created his particular
model man, and that it is even more dicult to generalize about these processes.
It is tempting at this point to turn to philosophy of science for a way to orga-
nise these materials. But when we do so, we face a similar problem. e generic
label used by philosophers of science for all these processes is ‘idealization’, but
they do not all share the same understanding of exactly what this term entails, and
to add to the confusion, they use the term idealization to refer to both the process
and to the end product.30 is lack of agreement may be partly based on dier-
ences in philosophical standpoint, but it is also because it really is dicult to gen-
eralize across the dierences in the processes that scientists use in model-making.
e history of science is usually messier than philosophers would like it to be, and
while we can fashion an account that ts well for one process of making an eco-
nomic model man, it is dicult to pick one process of idealization that generalizes
for all the economists, and for their model men who have peopled this chapter. It
is not that ideas from philosophy of science are not relevant – for aer all, I have
been using them during this chapter. e point is rather that clean-limbed philo-
sophical analysis does not so much organise our sprawling historical experience
as stumble over it.
Missing from these accounts of idealization is that model-making is a creative
activity, as I suggested in my Chapter 3 account of model-making as world– making.
A comparison between scientists’ processes of making a model and the artists’ of
making a character portrait invites us to consider where that creative element lies
in these complicated and mixed processes of idealization.
To start with, let us go back to the striking example of Knight’s slot machine
man, whose portrait relied on a particular choice of exaggeration. While the notion
of exaggeration had been discussed by Weber (above), it was just such exaggerations
30 In addition, their debates juggle a set of additional terms: causal versus construct idealization
(see note 40), mathematical idealization, concretization, and isolation (of horizontal and ver-
tical kinds). For discussions of this idealization literature with many references (including the
Poznań approach to idealization) in the philosophy of economics, see the essays and references in
Hamminga and De Marchi (1994, discussed in Morgan, 1996); and Morgan and Knuuttila (2012).
See footnote 38 on the process/outcome conation.
Ideal Types, Idealization and Caricature 159
that gave rise to the terminology of models as “caricatures” used by Gibbard and
Varian, (1978) to describe the modelling practices of neoclassical economics.31
A caricature relies on the artist taking a subjective view in the sense that it relies
on distorting or exaggerating certain characteristics beyond the point of objective
description. So the kind of representation that just extends a nose or eyebrows so
that we can put a name to the character is not what is meant here. e Spitting
Image puppet of the past British Prime Minister, John Major, is more the kind of
thing I have in mind.32 Major could be recognised in cartoons by his grey suit (as
Margaret atcher was by her handbag), but when the puppeteers presented Major
as grey, not only in his habitual clothing, but in skin and body colour right through,
the exaggeration captured an immediately recognisable double set of qualities in
the politician: he was boring, and utterly reliably so, even – given his occupa-
tion – to the point of trustworthiness! It is exactly this exaggeration of a particular
characteristic that enable us to recognise an additional ‘something’ inherent in the
person’s character. us the insight we gain from caricature comes from compar-
ing that representation with our knowledge of the original in which we must rst
recognise the similarity in features before we can go on to recognise the additional
new understanding these exaggerations or distortions bring.33
is art of caricature is reputed to have begun with Annibale Caracci, the Italian
artist of the late sixteenth century, who is also credited with introducing the word:
Is not the caricaturist’s task exactly the same as the classical artist’s? Both
see the lasting truth beneath the surface of mere outward appearance. Both
try to help nature accomplish its plan. e one may strive to visualize the
perfect form and to realise it in his work, the other to grasp the perfect
deformity, and thus reveal the very essence of a personality. A good carica-
ture, like every work of art, is more true to life than reality itself. (Quoted
in Gombrich & Kris, 1940, pp. 11–12)
Caracci’s notion of caricature can help us understand economic portraiture too.
Mill’s Scrooge portrait of a man driven overwhelmingly by the motive to gain
wealth, as he pointed out, was not intended as a realistic description, but rather
to suggest that inside every person there was something of this economic man.
By contrast, Knight’s slot-machine man is a creature of economic science not of
the real world, it was by exaggerating the most extreme characteristics assumed of
importance in neoclassical economics that Knight gave the professional economist
as the audience (not the general reader) insight into the implications for their the-
ories of adopting a character of full information and foresight – for example, that
31 It is signicant that this term emerged from one of the earliest philosophical studies of models in
economics, rather than in another scientic eld.
32 I refer here to the political satire TV show that appeared in Britain in which political gures
appeared as rubber puppets during the atcher and Major eras, 1984 and 1996.
33 is argument, about similarity supporting new insights, parallels the way new insights are gained
from analogical models to be found in Chapter 5.
e World in the Model
160
such a man is one of no intelligence. As Weber noted of his ideal types, caricatures
are not descriptions of reality, but allow the economist-scientist to express such
descriptions and to explicate the signicant elements of their materials. ese are
sophisticated portraits fashioned in sophisticated ways.
Simple or more daring as these dierent model outcomes were, like caricatures,
they have, as Caracci argued, the potential to be sources of truthful insight into
the motivations of economic man or into economists’ theoretical accounts of his
behaviour. Again, we must rst recognise the accurate portrayal of similar qualities
in model man and actual man to recognise the additional insight oered in these
economists’ portraits. Mill’s Scrooge character, Malthus’ man driven by his pas-
sions, Menger’s careful chooser, and Jevons’ calculating man can all be understood
as caricatures – character sketches in which certain inherent characteristics have
been featured and emphasized over others in such a way that the viewers – of each
time period – were able to recognise the signicance of those characteristics. We
can view Malthus’ and Mill’s portraits as caricatures for classical economics just as
Knight’s character plays the same role for neoclassical economics.34
How does this caricature notion speak to our problem of understanding the
process of making economic portraits? In other words, what processes are involved
in the art of creating a caricature? One of the most famous political caricatures in
history was the mid-nineteenth century depiction of Louis Philippe of France as
a pear. In defending himself in court, the artist, Charles Philipon, drew a series
of sketches showing four stages in his caricaturization process (shown here as
Figure 4.3).35 He claimed that he was not representing the King as a pear: his
defence hinged on the argument that although the rst drawing was indeed Loius
Philippe, it gave no sign that he was the King, and the fourth drawing was a only
a pear (also, in French, meaning a fathead or dupe). In creating the caricature,
the artist must use her or his creativity to overcome the cognitive hurdle for the
observer who must recognise Loius Philippe both as King and as pear to gain the
insights about the King that came from the meanings of a pear. And once we have
gained the insight of the King as a pear, it is not possible to go back and lose that
recognition, as was proved by the actions of the French populace who drew pears
to refer to their king.36 ough the artist lost his case, Petrey (1991) recounts the
history of how this caricature of the King as a pear rapidly spread through France,
and details the ever more ineective actions of the French state to ban all refer-
ences to pears!
34 Even Adam Smith’s portrait discussed at the beginning of this chapter, though not a model, appears
to have been viewed as something of a caricature to his contemporaries (see note 1).
35 e set shown here come from Gombrich and Kris (1940, p. 20, reproduced in Gombrich, 1960).
is 1834 set diers slightly from the original set of 1831 reproduced by Petrey (1991) in his
semiotic analysis and history of this caricature. Charles Philipon was editor of the journal La
Caricature, later Le Charivari, and the employer of the great nineteenth-century French caricatur-
ist Honoré Daumier.
36 Chapter 9 describes a similar situation, namely that economists see Prisoner’s Dilemma models
at work in the world, while Chapter 10 discusses the more general claim that economists see their
models, including rational economic man, everywhere around them.
Ideal Types, Idealization and Caricature 161
It is a wonderful story, but let us not be distracted from how this relates to
model-making. Philipon’s sequence of drawings shows a process of losing the fea-
tures of the real person (Loius Philippe) at the same time as gaining features of the
caricature of him (the pear). But we can see that it is not just a process of selecting
some features in and others out, or even of adding or extending features, but of
creatively transforming a description of a person into an insightful representation
of that person in another form. Descriptions of this process of caricaturization in
terms of generalization, subtraction, abstraction, addition and, of course, exaggera-
tion – are all relevant, but no single one of these notions of idealization (taking that
as the generic term) fully captures the creative process of transformation going on in
these sketches, though in combination they come close to it. It is this same complex
combination of processes that Philipon uses in making his caricature that we have
seen going on in scientic model-making in economics.
Figure 4.3. Philipon’s Art of Caricature (1834).
Source: E. H. Gombrich & E. Kris, Caricature, Harmondsworth : Penguin, 1940, gure 11, p. 20.
Reproduced with permission from Leonie Gombrich, Anton O. Kris and Anna K. Wol.
e World in the Model
162
Model-making understood as the art of caricaturing – a process of selecting,
synthesizing, and transforming elements for an already existing person or account –
can be understood as a series of idealizations (used in its generic sense).37 is
comparison with the art of caricaturing suggests an important point about scien-
tic model-making by idealization. It is an obvious point, easy to overlook, that
scientists can apply such processes of idealization only to some quite well-formed
materials they already have in hand.38 Scientists, like caricaturists, can simplify only
from a more complicated description and exaggerate from a representation already
available; they can only pick out, reject, and transform elements from the versions
of the world that they already have. ese are not newly made versions of the world
(as the Edgeworth Box of Chapter 3); they are re-made versions of a world we know
much about and have already described.
Where do these initial versions come from in the sciences? is is where the fact
that economists are modelling economic man becomes important, for by observing
themselves and others, economic scientists have a considerable observational base
of knowledge of economic man.39 And they have other versions in hand as well –
in previous theories about economic behaviour and motivations. Economists can
use the model men made by earlier economists as the descriptions from which, by
further processes of idealization, they come to new models. us, the moves from
Jevons’ calculating man to Knight’s slot-machine man or to rational economic man
can be interpreted as cases in which economists have been applying their idealiza-
tions to already existing models of man rather than to earlier verbal descriptions,
or even to their own observations of man’s motives and behaviour.40
37 is begins to sound a little like Boumans’ (1999) recipe account of model-making applied to
Ricard’s model farm (see Chapter 2). e dierence is that idealization processes are carried out
on an already existing object or account (e.g., in physics, the pendulum is an object that lends itself
to description and then idealization of the description; see Giere, 1988 and Morrison, 1999) rather
than being a newly created or imagined account.
38 It is one of the oddities of the idealization literature that this point is overlooked. It may happen
because there is an easy slippage, and sometimes conation, between an idealization as an outcome
and the process of idealization. To idealize (verb), we must already have some kind of description
of the world, and then set some bits at zero or ignore them in order to make a tractable model, that
is, to arrive at an idealization (noun).
39 Evidence from experimental economics suggests that economists are made by part nature and part
nurture. at is, economics students already think and behave more like economic model men
than other students, but they come to resemble those models more closely from their economics
training. is casts an interesting light on the reexivity of economists in relation to the models
of economic man.
40 McMullin (1985) makes a distinction between “construct” versus “causal” idealizations depending
“on whether the simplication is worked on the conceptual representation of the object, or on the
problem-situation itself” (p. 255, and see Suárez, 1999). Usually, causal idealizations are designed
to simplify the problem situation by taking away causes, as Mill did when he assumed only three
constant causes at work in order to make his model man more tractable. Another example of
causal idealization is Malthus’ suggestion that we might rethink his portrait of economic man
to include education and reasoning power – this proposal takes us back to the world level and
asks us to rethink the main causes at work in a new idealization producing a slightly dierent
portrait. A move from Mill’s homo economicus either to Jevons’ calculating man, or to Menger’s
Ideal Types, Idealization and Caricature 163
Although this caricature-making account nicely conveys how model-making
involves a complex combination of processes of idealization, it does not tell the
economist exactly which items to pick out and which to jettison from amongst
the many characteristics that are available, nor how to transform them to make a
model portrait. e scientist must play the role of the artist here – responsible for
choosing some elements and leaving behind others, working with some of these
and leaving others untouched, and for fashioning them all together into the cari-
cature. Whereas two eyes, a nose, and a mouth in particular places within a circle
might be sucient to provide a representation of a face to a growing child, the art-
ist has to do more than this to present the King-as-a-pear to the French population
of the 1830s: both the King and his representation as a pear must be recognisable
at the same time. Similarly, any particular economist’s portrait of economic man
depends on that scientist selecting, transforming, and synthesizing his materi-
als in creating a model of economic man and his behaviour that are recognisable
within his economic tradition and that still maintains some sense of the real eco-
nomic man.
But while the art of caricaturing provides an account of the process of creating
models of economic man, it does not give much insight into how and why his por-
trait has changed in such radical ways over time. e economic tradition within
which an economist works shapes, in a strong way, the choice of elements and
kinds of idealizations made. And, since these models of man provide the objects
that economists use to represent man’s behaviour in their theories, the elements
chosen and their mode of transformation into a new portrait will be dierent
between economic traditions. So, for example, an Austrian school economist of
the early twentieth century would not have created, by mathematical idealiza-
tion, Knight’s portrait of perfect knowledge – this is a spurious possibility since
Austrian school economists both eschewed mathematics and believed that being
human entailed having limited knowledge. Each model man representation, and
his process of creation, have to be consistent with and coherent within his broader
scientic tradition not only of content, but of form and style as well as scientic
practice.
is is just as would expect from our comparison of the way models and cari-
catures are developed. Earlier caricatures were represented in ne detail in eigh-
teenth-century engravings and nineteenth-century newspapers and their insights
into political character are oen lost to us now. Twentieth- and twenty-rst-century
choosing man, was also a causal idealization. It meant, as we have seen, a return to the real-world
object – man – and taking a new direction of simplication and abstraction, to a dierent account
of economic man with dierent attributes and so causal capacities. In a construct idealization,
the scientist alters one or some aspects of an already modelled man rather than going back to the
original object. us the move from Jevons’ calculating man to Knight’s slot-machine man could
be understood as idealizing on the already conceived mathematical model of man as a pleasure
machine to turn it into slot machine. is distinction between causal and construct idealization
claries the historical moves made between models.
e World in the Model
164
caricatures come to us as cartoon sketches and speak to us by caricaturing matters
of our own day.41 e same dynamics are at work in prompting the successive cari-
catures of economic man. We nd a parallel change in style in economics: whereas
Malthus’ economic man was drawn with quite a detailed verbal account and it is
dicult to understand the milieu in which he made sense, economic man of our
own day is created in the abstract formal style of modern economics and is designed
to speak to economists’ changed scientic concerns about the modern economy.
ese changes in model man go along with changes in contents, methods, and
modes of doing economic science. As schools of economics rise and fall, they cre-
ate new portraits, new caricatures that pick out the features that economists of that
time and place nd most interesting and salient to the analysis of that school. ese
radical changes in economic man portraits were not so much driven by paradigm
change – as exemplications of them. And if the portrait of economic man is an
indicator of more general changes, we seem now to be the midst of another para-
digm change.
8. Model Man’s CV: De-Idealization and the Changing
Roles of Economic Man
Looking beyond the details, we can discern two major shis in the three-phased
career of economic man. In the rst phase, economists treated model man as an
observational sketch. e second took model man into the centre of economic the-
ory. ese two phases of idealizations of various kinds provided the materials for
this chapter. e third phase, indicated only briey here, takes him back to some-
thing of an observed character sketch, via processes which might best be described
as ones of de-idealization.
In the rst phase, we began with the relatively straightforward characters
of the classical economics of Malthus and Mill and thence described the more
abstract conceptual versions in Menger’s ideal type and in Jevons mathemati-
cal form. During this historical process, the basic character of model economic
man went through several mutations. Malthus portrayed him as driven by phys-
ical appetites, Mill as a wealth seeker. Jevons changed him into a man seeking
to maximize pleasure or utility from consumption, while Menger presented him
as satisfying needs though sensible choices. But these were all model men com-
pared to the rich descriptive portrait we nd in other works of social science. Each
41 According to Gombrich and Kris (1940), it was only around the turn of the eighteenth to nine-
teenth centuries that caricatures became associated with the comparative simplicity of cartoon
representations, though there were certainly masters of the art before that time. (See Levy and
Peart [2010] on nineteenth-century cartoons and caricatures with economic content.) As we have
seen, economic man portraits involve a drastic level of simplifying on the grounds of scientic
functionality, that is, they have the qualities of cartoons, which is another reason why the notion
of caricature models is particularly apt for economics.
Ideal Types, Idealization and Caricature 165
model man was made to reduce the complexity of dealing with all human feelings
and emotions and actions that ow from them and, at the same time to focus the
attention on the explicitly economic aspects of man’s behaviour. is sequence
of model men was the nineteenth-century economists’ answer to the problem of
dealing with human behaviour in a scientic way. In each case, model man was
taken to represent real man, but pared down to focus on the picture of economic
behaviour in its simplest, purest, or most abstract form, unaected by other con-
siderations and so oered the possibilities of analysis within this narrowed frame-
work. Taken literally he was regarded as a ctional character, but one whom it
still seemed possible, by processes of self or other observation (and perhaps by
processes of imagination), to compare back with real man. Each of these dierent
models seemed to their economist-creators a sensible scientic strategy compared
to the alternative social science approaches in the nineteenth century of studying
the real behaviour of man directly with all his feelings and amongst his family,
community, or nation.
Jevons’ economic man marks a signicant turning point into the second phase
in this history of such portraits, for his character can be understood both by look-
ing forward from the early-nineteenth century standpoint of classical economics
and by looking back at him from the later twentieth-century neoclassical econom-
ics. When we trace from Jevons’ calculating man, through Knight’s depersonalised
slot-machine man, to the rational agent of the mid-twentieth century, we can see
how certain dierent economic qualities became exaggerated. He was endowed with
calculating power by Jevons, given extraordinary amounts of economic knowledge
and certainty to analyse the fullest eect of economizing behaviour by Knight, and
he became extremely rational in the neoclassical economics of the mid-twentieth
century. ese economic men were ‘idealized’ in the sense that they were endowed
with more perfect economic qualities according to the theory of the day. In these
traditions, economic man was no longer taken to represent real man, but to be
an articial character created by economists for their mathematical laboratories in
which the model man is investigated using model reasoning.
e third phase in the career of economic man may be understood as a series of
de-idealizations – processes of adding back elements and bringing the portraits of
economic man closer to descriptions of real behaviour. e reputation of neoclassi-
cal economic men was at a height in the 1970s. Since then, economists have moved
from the all-knowing portrait of Knight’s slot-machine and his thinner cartoon
partner, rational economic man, to portraits that have more scope for application
to the behaviour of people in the real economy. Following attacks in the 1970s – on
rational economic man’s consistency by Amartya Sen, and on his maximizing abil-
ity by Herbert Simon – economists have found good reasons to think about the var-
ious ways in which these two central features of economic man’s rationality might
be limited or “bounded”.42 Behavioural economics, a re-splicing of economics and
42 See Sen (1976), Simon (1976), and Klaes and Sent (2005).
e World in the Model
166
psychology, analyses man’s abilities to make economic decisions.43 Economists
have replaced Knight’s assumption of a man with perfect foresight to investigate
“strategic man”, one who thinks strategically as in game theory; others have chal-
lenged his selshness by considering his possibilities for altruistic behaviour.44 Still
others have become concerned with the information that economic man knows,
chipping away at another of the character traits of Knight’s model to rethink model
man’s ability to act with only limited information; “contractual man” – the ability to
make and keep contracts – being one outcome of this rethink.45 ese widespread
recent developments in the portrait of economic man began by taking neoclassi-
cal economic man as the benchmark ideal and then asking what might happen to
modelling outcomes if he were not so perfectly knowledgeable or so rational or so
selsh as he was painted. Old models, like old habits, die hard.
While these new portraits of economic man typically start with the models of
economic man inherited from neoclassical economics, their refashioning comes
in large part from the new ways that they investigate him, that is, the new por-
traits emerge once again because of changes in the scientic practices of economics.
Experimental work investigates individual’s economic behaviour in dierent kinds
of situations such as markets or games (see Chapters 7 and 9); simulations use
role playing and other kinds of experiment (see Chapter 8); survey work has been
investigating how people feel about things economic, and whether they are ‘happy’;
and neurological investigations (neuroeconomics) seek to trace the physiological
aspects of economic behaviour. In conducting experiments with him and observ-
ing whether he behaves the same or dierently from the benchmark or idealized
model man of earlier theories, economists have come to treat economic man more
like a laboratory rat than a mathematical construct. But by conducting experiments
upon man to map his model portrait via his brain waves, they seem to be in the
process of creating a new biological model organism, one more like the labora-
tory mouse than the laboratory rat. All these new forms of scientic investigation
eectively entail processes of de-idealization, not only to make the portrait more
complex, but to make him more descriptively accurate and less driven by theoret-
ical requirements. ese modes of investigation and processes of refashioning are
fast creating a very dierent portrait – indeed, a set of portraits – of economic man,
ones very dierent from the verbally and mathematically described models that
economists are used to.
ese new economic models of man are fast taking economists away from
their highly idealized characters of the last two centuries. He is becoming a more
rounded and more interesting ‘fatter’ character – a man who can learn, bargain,
act strategically, has memory, and may even be happy. is would be a far cry from
the dismal science portrait given us by Malthus, whose economic man suered
43 See Sent (2004).
44 See Giocoli (2003) on strategic man, Fontaine (2007, and 2012 forthcoming) on altruism.
45 See Pessali (2006).
Ideal Types, Idealization and Caricature 167
from cycles of starvation and the ill eects of vice. Yet, like Malthus’ conception,
these modern approaches suggest a return to a biological or physiological analysis
of man’s behaviour, spliced perhaps with a new cognitive science or psychological
account that might be compared to Jevons’ conception. His portrait is being radi-
cally reconstructed in many dierent ways.
ese three broad phases in the characterization of economic man can be asso-
ciated then with the long run changes in the ideas, theories, questions, and practices
of economic science – in themselves contingent upon many other currents in sci-
entic, political, economic, and intellectual histories. As the focus of enquiry and
explanation for economic man’s behaviour has changed, these three phases of por-
traiture have been associated with dierent functions for economic man within eco-
nomic sciences. e causal capacities associated with earlier manifestations of model
economic men, pictured by Malthus, Mill, and even by Jevons, were the capacities
that they thought to be at work in the world. e motivations of Malthus’ working
man, the character of Mill’s wealth-seeker, and even Menger’s human economy were
understood by economists to be the motives that create changes in the real econ-
omy, which is why these portraits were oen more useful in reasoning about the
world than in theory building. Jevons’ man is once again a crossover point. His feel-
ings (eventually) registered in prices in the market place, but his character proved
more valuable as a subject for investigation in the mathematics laboratory of the
economist (exactly as we saw in Chapter 3 in the Edgeworth Box). From Knight’s
slot machine, through the twentieth-century history of rational economic man, eco-
nomic man has lived primarily inside economic theories, representing a set of causal
capacities inside a mathematical model account of the world. He plays the role of the
individual in whatever problem, situation, or events are portrayed in economists’
models of the world: he is the thin person inhabiting those small worlds. Indeed,
we meet this character again in Chapter 9, playing his due role in another model.
Only in the last few decades, when new, less idealized and more recognisably human
versions of economists’ model man have grown up, have the causal capacities asso-
ciated with economic man’s character come to be seen once again as representing
primarily something active in the world as well as a model for theorizing with. ese
new model men are manipulated not just in mathematical models but also in experi-
mental situations, and as a consequence are once again becoming usable to enquire
into the world, though in radically new ways.
Acknowledgement
is chapter draws on one of the earliest papers on models that I wrote as part of the outcome
of the Wissenschaskolleg in Berlin group on modelling in 1995–6. I am grateful to Margaret
Morrison for prompting me to explore the question and for the support of the Kolleg during
that year. at paper’s 1997 publication under the title “e Character of ‘Rational Economic
Man’ ” in DIALEKTIK. e topic turned out to be critical for my project on modelling – for
what was the small world without a thin man in it? So I resurrected the story here rst for a
e World in the Model
168
talk at Nancy Cartwright’s sixtieth birthday celebrations in June 2005 at LSE, and then added
to it for my Presidential Address to the History of Economics Society also in June 2005
(see Morgan, 2006) at the University of Puget Sound and nally into chapter form – which
has the benet of a much extended section on caricatures. I thank Sheldon Steed for his
ever-patient research assistance. My thanks go particularly to Harro Maas, Roger Backhouse,
Mauricio Suaréz, Bruce Caldwell, Margaret Schabas, Emma Rothschild, and others for their
helpful comments. I also thank participants at various seminars in Australia: at University of
Sydney (History and Philosophy of Science Department) and University of New South Wales
(Economics Department) in October 2005, and at Australian National University (Research
School in Social Sciences, Philosophy Group) in November 2005.
References
Arrow, K. (1986) “Economic eory and the Hypothesis of Rationality”. Journal of Business
59(4). Reprinted in J. Eatwell, M. Milgate and P. Newman (eds),e New Palgrave,
Vol. 2 (pp. 69–75). London: Macmillan.
Backhouse, Roger E. and Steven Medema (2009) “Dening Economics: e Long Road to
the Acceptance of the Robbins Denition”. Economica, 76, 805–20.
Bentham, J. (1789/1970) An Introduction to the Principles of Morals and Legislation. In J. H.
Burns and H. L. A. Hart (eds), e Collected Works of Jeremy Bentham, 2, 1, Principles
of Legislation. London: Athlone Press, 1970.
Bhimani, Alnoor (1994) “Accounting and the Emergence of ‘Economic Man’”. Accounting,
Organization and Society, 19, 637–74.
Boumans, Marcel (1999) “Built-In Justication”. In Mary S. Morgan and Margaret Morrison
(eds), Models as Mediators: Perspectives on Natural and Social Science (pp. 66–96).
Cambridge: Cambridge University Press.
Boumans, Marcel and Mary S. Morgan (2001) “Ceteris Paribus Conditions: Materiality and
the Application of Economic eories”. Journal of Economic Methodology, 8, 11–26.
Caldwell, Bruce (2004) Hayek’s Challenge. Chicago: University of Chicago Press.
Cartwright, Nancy (1989) Nature’s Capacities and eir Measurement. Oxford: Clarendon
Press.
Clark, J. B. (1899) e Distribution of Wealth. New York: Macmillan.
Clark, J. M. (1918) “Economics and Modern Psychology”. Journal of Political Economy, 26,
1–30; 136–66.
(1936) A Preface to Social Economics. New York: Farrar and Rinehart.
Coats, A. W. (1976) “Economics and Psychology: e Death and Resurrection of a Research
Programme”. In S. Latsis (ed), Method and Appraisal in Economics (pp. 43–64).
Cambridge: Cambridge University Press.
Edgeworth, F. Y. (1881) Mathematical Psychics. London: Kegan Paul.
Emmett, R. B. (1994) “Maximisers versus Good Sports: Frank Knight’s Curious
Understanding of Exchange Behaviour”. In N. De Marchi and M. S. Morgan (eds),
Transactors and eir Markets in the History of Economics (pp. 276–92). Annual
Supplement to History of Political Economy, Vol. 26. Durham, NC: Duke University
Press.
Fontaine, Philippe (2007) “From Philanthopy to Altruism: Incorporating Unselsh Behavior
into Economics, 1861–1975”. History of Political Economy, 39:1, 1–46.
(2012) “Beyond Altruism? Economics and the Minimization of Unselsh Behavior,
1976–1993”. History of Political Economy, forthcoming.
Ideal Types, Idealization and Caricature 169
Gibbard, A. and H. R. Varian (1978) “Economic Models”. e Journal of Philosophy, 75,
664–77.
Giere, Ronald (1988) Explaining Science: A Cognitive Approach. Chicago: University of
Chicago Press.
Giocoli, Nicola (2003) Modeling Rational Agents: From Interwar Economics to Early Modern
Game eory. Cheltenham: Edward Elgar.
Gombrich, E. H. (1960) Art and Illusion: A Study in the Psychology of Pictorial Representation.
Princeton, NJ: Princeton University Press for e Bollingen Foundation, NY.
Gombrich, E. H. and E. Kris (1940) Caricature. Harmonsworth: King Penguin.
Hahn, F. and M. Hollis (1979) Philosophy and Economic eory. Oxford: Oxford University
Press.
Hamminga, Bert and Neil De Marchi (1994) “Idealization and the Defence of Economics:
Notes Toward a History”. In Bert Hamminga and Neil De Marchi (eds), Idealization
VI: Idealization in Economics (pp. 11–40). Amsterdam: Rodopi.
Hands, D. Wade (2007) “A Tale of Two Mainstreams: Economics and Philosophy of Natural
Science in the mid-Twentieth Century”. Journal of the History of Economic ought,
29, 1–13.
(2010) “Economics, Psychology and the History of Consumer Choice eory”. Cambridge
Journal of Economics, 34, 633–48.
Hartley, James E. (1997) e Representative Agent in Macroeconomics. London: Routledge.
Hausman, Daniel M. (1992) e Inexact and Separate Science of Economics. Cambridge:
Cambridge University Press.
Hempel, Carl G. (1965) “Typological Methods in the Natural and the Social Sciences”. In
Aspects of Scientic Explanation (pp. 155–171). New York: Free Press.
Howson, Susan (2004) “e Origins of Lionel Robbins’s Essay on the Nature and Signicance
of Economic Science, History of Political Economy”. 36:3, 413–43.
Jevons, W. S. (1871) e eory of Political Economy. London: Penguin, 1970.
Kirman, A. P. (1992) “Whom or What Does the Representative Individual Represent?”
Journal of Economic Perspectives, 6:2, 117–36.
Klaes, Matthias and Esther-Mirjam Sent (2005) “A Conceptual History of the Emergence of
Bounded Rationality”. History of Political Economy, 37:1, 27–59.
Knight, F. H. (1921) Risk, Uncertainty and Prot. Boston: Houghton Miin.
(1923) “e Ethics of Competition”. In e Ethics of Competition and Other Essays
(pp. 41–75). New York: Harper, 1936.
(1947) Freedom and Reform: Essays in Economics and Social Philosophy. New York:
Harper.
Levy, David M. and Peart, Sandra J. (2010) “Economists, Crises and Cartoons”. Working
paper, available at SSRN: http://ssrn.com/abstract=1547886
Maas, Harro (2005a) William Stanley Jevons and the Making of Modern Economics.
Cambridge: Cambridge University Press.
(2005b) “Jevons, Mill and the Private Laboratory of the Mind”. e Manchester School,
73, 62–9.
(2009) “Disciplining Boundaries: Lionel Robbins, Max Weber, and the Borderlands of
Economics, History, and Psychology”. Journal of the History of Economic ought, 31,
500–17.
Machlup, F. (1978) “Ideal Types, Reality and Construction”; “e Universal Bogey: Economic
Man”; and “Homo Oeconomicus and His Classmates”; all in Methodology of Economics
and Other Social Sciences (pp. 223–301). New York: Academic Press.
Mäki, Uskali (1992) “On the Method of Isolation in Economics”. In Craig Dilworth (ed),
Idealization IV: Intelligibility in Science (pp. 317–51). Amsterdam: Rodopi.
e World in the Model
170
(1997) “Universals and the Methodenstreit: A Re-examination of Carl Menger’s
Conception of Economics as an Exact Science”. Studies in the History and Philosophy
of Science, 28:3, 475–95.
Malthus, T. R. (1803) An Essay on the Principle of Population. P. James (ed), for the Royal
Economic Society (1989). Cambridge: Cambridge University Press.
McMullin, Ernan (1985) “Galilean Idealization”. Studies in the History and Philosophy of
Science, 16:3, 247–73.
Menger, Carl (1871) Grundsätze der Volkswirtschaslehre (English Edition: Principles of
Economics, J. Dingwall and B. Hoselitz [eds]). New York: New York University Press,
1976.
(1883/1985) Investigations into the Method of the Social Sciences with Special Reference
to Economics. Translation (1985) of Untersuchungen über die Methode der
Socialwissenschaen und der Politischen Oekonomie insbesondere (edited by Francis J.
Nock, translated by Louis Schneider). New York: New York University Press.
Mill, J. S. (1836) On the Denition of Political Economy. In J. M. Robson (ed), Collected
Works of John Stuart Mill: Essays on Economics and Society, Vols. 4–5 (1967). Toronto:
University of Toronto Press.
Morgan, Mary S. (1994) “Marketplace Morals and the American Economists: e Case of
John Bates Clark”. In N. De Marchi and M. S. Morgan (eds), Transactors and eir
Markets in the History of Economics (pp. 229–52). Annual Supplement to History of
Political Economy, Vol. 26. Durham, NC: Duke University Press.
(1996) “Idealization and Modelling” (A Review Essay). Journal of Economic Methodology,
3:1, 131–8.
(1997) “e Character of Rational Economic Man”. Dialektik (special issue Modelldenken
in den Wissenschaen edited by B. Falkenburg and S. Hauser), 1, 77–94.
(2006) “Economic Man as Model Man: Ideal Types, Idealization and Caricatures”. Journal
of the History of Economic ought, 28:1, 1–27.
Morgan, Mary S. and Margaret Morrison (1999) Models as Mediators: Perspectives on
Natural and Social Science. Cambridge: Cambridge University Press.
Morgan, Mary S. and Tarja Knuuttila (2012) “Models and Modelling in Economics”. In U.
Mäki (ed), Handbook of the Philosophy of Economics (one volume in Handbook of the
Philosophy of Science. General Editors: Dov Gabbay, Paul agard, and John Woods).
Amsterdam: Elsevier/North Holland. Available at: http://papers.ssrn.com/sol3/papers.
cfm?abstract_id=1499975.
Morrison, Margaret (1999) “Models as Autonomous Agents”. In Mary S. Morgan and
Margaret Morrison (eds), Models as Mediators: Perspectives on Natural and Social
Science (pp. 38–65). Cambridge: Cambridge University Press.
Peart, Sandra (1996) e Economics of W. S. Jevons. New York: Routledge.
Persky, Joseph (1995) “Retrospectives: e Ethology of Homo Economicus”. Journal of
Economic Perspectives, 9:2, 221–31.
Pessali, Huáscar (2006) “e Rhetoric of Oliver Williamson’s Transaction Cost Economics”.
Journal of Institutional Economics, 2:1, 45–65.
Petrey, Sandy (1991) “Pears in History”. Representations, 35, 52–71.
Robbins, L. (1932) An Essay on the Nature and Signicance of Economic Science. London:
Macmillan.
Schabas, M. (1990) A World Ruled by Number. Princeton, NJ: Princeton University Press.
Sen, A. (1976–7) “Rational Fools”. Philosophy and Public Aairs, 6, 317–44.
Sent, Esther-Mirjam (2004) “Behavioral Economics: How Psychology Made Its (Limited)
Way Back Into Economics”. History of Political Economy, 36:4, 735–60.
Ideal Types, Idealization and Caricature 171
Simon, Herbert (1976) “From Substantive to Procedural Rationality”. In S. Latsis (ed),
Method and Appraisal in Economics (pp. 129–48). Cambridge: Cambridge University
Press.
Smith, A. (1776) An Inquiry into the Nature and Causes of e Wealth of Nations. Edited by
R. H. Campbell and A. S. Skinner (1976). Oxford: Oxford University Press.
Suárez, Mauricio (1999) “e Role of Models: e Application of Scientic eories:
Epistemological Implications.” In Mary S. Morgan and Margaret Morrison (eds), Models
as Mediators: Perspectives on Natural and Social Science (pp. 168–96). Cambridge:
Cambridge University Press.
Wartofsky, Marx (1968) Conceptual Foundations of Scientic ought. New York:
Macmillan.
Weber, Max (1904) “‘Objectivity’ in Social Science and Social Policy”. In e Methodology
of the Social Sciences. Translated and edited by Edward A. Shils and Henry A. Finch
(1949), pp. 49–112. New York: Free Press.
(1908) “Marginal Utility eory and ‘e Fundamental Law of Psychophysics’”. Translated
by Louis Schneider in Social Science Quarterly (1975), 56:1, 21–36.
(1913) e eory of Social and Economic Organisations. Translated by A. M. Henderson
and Talcott Parsons, Part I of Wirtsha und Gesellscha (1947). New York: Free Press.
(1917) “e Meaning of ‘Ethical Neutrality’ in Sociology and Economics”. In e
Methodology of the Social Sciences (pp. 1–49). Translated and edited by Edward A.
Shils and Henry A. Finch (1949). New York: Free Press.
Zouboulakis, Michael (2001) “From Mill to Weber: e Meaning of the Concept of
Economic Rationality”. European Journal of the History of Economic ought, 8, 1–30.
172
5
Metaphors and Analogies: Choosing
the World of the Model
1. From Metaphors to Analogical Models 172
2. e Newlyn-Phillips Machine 176
3. e Machine’s Inventors: Walter Newlyn and Bill Phillips 184
4. Inventing the Newlyn-Phillips Machine 187
Step 1: Phillips chooses the analogy for his supply/demand model
(early 1949) 189
Step 2: Newlyn designs the blueprint for a monetary circulation machine
(Easter 1949) 194
Step 3: Phillips and Newlyn build the prototype Machine (Summer 1949) 200
5. Analogical Models and New ings 204
1. From Metaphors to Analogical Models
Money is oen thought of as liquid: it runs through our ngers, it leaks out of our
pockets and we are liable to drown in our debts. e metaphorical use is as exten-
sive and as invasive in the technical language of economics as in our everyday talk.
From David Hume’s eighteenth-century observation that, like connected bodies
of water, the value of money will always come to a common level between places,
to the modern-day “liquid assets” (cash and assets that can easily be turned into
cash) and the “liquidity preference ratio” (our preferences for a certain proportion
of assets held in ready, or easily accessible, money), economists have delighted in
the use of metaphorical language.1 It is not just money that prompts economists’
ights of rhetorical fancy. Leon Walras in 1900 described the tendency of the mar-
ket towards an equilibrium to be “like a lake agitated by the wind, where the water
is incessantly seeking its level without ever reaching it.”2 Mechanical metaphors are
1 I thank Margaret Schabas for discussions about the many metaphorical statements about money;
see David Hume’s “Of the Balance of Trade” in Rotwein (1955).
2 See Walras (1874) Lesson 35, sec 322 in Jaé (1954), p. 380, for the English language translation
quoted here.
Choosing the World of the Model 173
equally invasive: Edgeworth held “the conception of Man as a pleasure machine”
and Knight, as we have seen, described him as a “slot machine”, while orstein
Veblen portrayed the whole business economy of his day as a vast machine in which
rms were as closely connected as cogwheels.3
When metaphors are suggestive about the nature of economic objects and eco-
nomic life, they provide the raw material from which to make substantive analogies,
and analogies may be formed into models. By adopting a metaphor, economists can
portray the workings of the economy in terms of some other already-formed and
known world with which they are familiar, maybe a machine such as a mechanical
balance or a physiological system such as the human body. In doing so, economists
can be said to have ‘chosen’ the world of the model. And from imagining some
aspect of the economy in terms of something else, economists are able to think
anew about the economy from their analogical model.
Turning a metaphor, which begins as a gure of speech and idle likeness, into an
analogical model involves both cognitive and imaginative work. And, as with so many
aspects of making models, cognition and imagination are intimately linked, both in
creatively developing the metaphor into a model, and in making the economic terms
t the analogical world, and the analogical terms t back onto the economic world.
e cognitive issue is one we have already met. Economists don’t know well how
the economic world works. One option, explored in the history of the Edgeworth
Box in Chapter 3, is to imagine how some aspects might be and make an image
of them. Another is to start with the bits that are known, and bring them to t
together, as Ricardo did in his model farming in Chapter 2. Yet another is to sim-
plify and abstract an account from the complications of the real world – as in the
history of economic model man in Chapter 4. e fourth alternative here begins
with metaphors and develops them into analogies with which to explore how the
world might be and how it might work if it were like those analogical worlds.4 In
choosing another object/system on the basis of some aspects of similarity between
that system and beliefs about how the economy works, economists place signif-
icant constraints on the form and content of the model. ey develop the ana-
logical model using these constraints as a way to explore the implications of that
analogy and whether the model can be used to interpret the economy in those
terms (see Morgan and Boumans, 2004). is is a cognitive project in that it is
3 For Edgeworth, see his 1881, p. 15; on Knight, see Chapter 4; for Veblen, see his 1904 account.
ough McCloskey (1990) characterizes metaphors as models in economics, metaphors are really
only a starting point (see Morgan [2001] for discussion of her position).
4 Klamer and Leonard (1994) argue for the importance of the cognitive aspects of metaphors at
three dierent levels. Apart from those that are “pedagogical” (ones that serve to clarify but that
do not aect the argument), they label as “heuristic” those that “serve to catalyze our thinking,
helping us to approach a phenomenon in a novel way. . . . metaphor is cognitive here because its
respective subjects interact to create new meanings” (p. 33); and as “constitutive” those that oer
a “conceptual scheme” to characterize our unknown world (p. 39). In the case of models, I suggest
that the two latter levels collapse: If a metaphor becomes embedded into a model, then it is likely
to have become constitutive too.
e World in the Model
174
one of comparison and translation between the metaphor’s subject matter and the
economics’ subject matter. e activity of lling in the chosen world of the model
presents many questions to answer, and it is in solving these that economists nd
the potential for gaining a new understanding of the economic system.
In discussing how a metaphor becomes a model, Marcel Boumans suggested
that we think of a metaphor as something one-dimensional: to suggest that money
is liquid oers an intriguing possibility; it suggests much, but tells us little. To gain
the benet of invoking the metaphor, a scientist needs to develop its various pos-
sibilities or dimensions into a model.5 To ll in a picture of some economic world
in which money has the property of being a liquid requires the use of imagination.
But rst the economist has to choose that world. Is it like blood circulating around
a body, as Francis Bacon and some of the early Mercantilist economists thought
it?6 Or is it like water in a natural ecology (as Hume suggested), or like a tidal ow
between the oceans and lagoons (as Irving Fisher later suggested)?7 Such a choice
of world is the starting point for a model, and because each of those worlds is more
constrained in its possibilities than the original metaphor (that money is a liquid),
it provides more explicit guidance about the analogical features and suggests how
to depict the properties of the modelled world more exactly. We see this happen-
ing, for example, in Irving Fisher’s move from his lagoon-ocean metaphor to his
analogical model that presented bimetallism as a ow of gold and silver liquids
between laboratory asks (see Morgan, 1999). Only when an economist has used
his or her imagination to ll in the full dimensionality of the model, that is, to
design and create such a model world, do the properties of the analogical model
world become evident and usable to the economist.
Suggesting that the development of a metaphor into a model is a process akin to
a change in dimensionality is itself to use a metaphor. Edwin Abbott’s (1884/1952)
novella Flatland captures the cognitive depth and demonstrates the imaginative
aspects of changing dimensions in a wonderfully direct way. Flatland tells the story
of a mathematically dened ‘person’ (a square) who has lived life in a two-dimen-
sional space yet suddenly nds himself confronting a three-dimensional person and
world – at rst a thoroughly disorientating and even frightening experience. Making
sense of the new dimension, learning to live within it eectively and to act within it
safely, requires a cognitive shi in recognising how things are in a three-dimensional
world rather than a two-dimensional one. e reader shares this experience most
eectively in learning what cannot be seen in a two-dimensional world, and so comes
to understand the potential dangers of living in such an environment. Such recogni-
tion is not just an intellectual exercise, for the dierence between living in worlds of
dierent dimensions is not experienced as a logical dierence, nor one that can be
5 is insight prompted some of our joint work on the Phillips Machine and the idea is developed
in that paper (see Morgan and Boumans, 2004).
6 “If they [the merchants] ourish not, a kingdom may have good limbs, but will have empty veins
and nourish little”. (Bacon 1625 in Pitcher, 1985)
7 Hume reference as previously; and see Fisher (1911), chapter VI.
Choosing the World of the Model 175
bridged by small incremental steps. Rather it depends upon an imaginative leap into
the new world, a transition between dimensions that the reader must also make.
Cognition may be held back by a lack of imagination, just as it was for the inhab-
itant of Flatland, whose imagination was – understandably, given that he had only
known a two-dimensional world – unable to stretch easily into the third dimension
without guidance and interpretation from a three-dimensional inhabitant. Homer
Simpson, a two-dimensional television cartoon character from our modern day,
lacked such guidance when he suddenly found himself alone in a three-dimensional
computer graphics landscape and promptly fell into a three-dimensional hole, but
not before he had discovered his own three-dimensional shape, and its shadow, and
the audience had heard his voice echo around his newly three-dimensional world.8
Imagination and cognition are intertwined in any move from living in one world to
another, just at they are in moving from a metaphor to an analogical model world
in scientic work.
When a model becomes fully naturalised in a eld, the creativity and imaginative
leap that were required to overcome the cognitive diculties in its construction are
usually lost. is is so even for everyday models in economics such as the Edgeworth
Box but it is particularly so with analogical models.9 When an analogical model
becomes well accepted and well used in its new home in economics, then the eco-
nomic scientists no longer notice its analogical status, nor what new insights it brought
to the eld.10 When a later economist comes to study it, those problems of cognition
and imagination arise again in particularly severe form. is has proved exactly the
situation in recent attempts to understand and restore the Newlyn-Phillips Machine,
a working hydraulic model of the economy built in 1949–50.11 is Machine – an
analogical model for the aggregate economy – forms the main object for discussion
in this chapter for it enables us to see what happens when scientists ‘choose’ the world
of the model by working with a metaphor to turn it into a fully dimensional economic
model. And it demonstrates how the two main design aspects of developing an ana-
logical model – the cognitive and imaginative – are intertwined.
Later in the chapter, I discuss how economists learn from analogical models.
According to literary scholars, metaphors lead us to see the two objects joined
8 e Simpsons, Treehouse of Horror VII Series 7, Episode 6. In a discussion of how they had done
this, the animators suggest that they drew their two-dimensional characters into the story and then
made them three-dimensional ones (http://show-links.tv/tv_shows/81760/e_Simpsons_2/7/6/
on January 4, 2008).
9 For example, from my seminar presentations on the history of the Edgeworth Box, it became evi-
dent that some modern economists found it very dicult to see how the Box could ever have been
rst drawn without being a box, even though I showed them the pictures of the original non-box
diagram (see Chapter 3).
10 See Mirowski (1989) for a strong metaphor-led view of the history of neoclassical economics and
how twentieth-century economists lost sight of the physics metaphor that they introduced in the
late nineteenth century. An unnoticed analogy is not quite the same as a dead metaphor because
the model may still provide a good working object and provoke new ndings and uses.
11 For example, see Moghadam and Carter’s account of their 1989 attempts to restore the LSE Machine.
e World in the Model
176
in the metaphor in new ways, and similar claims have been made for analogical
modelling in the sciences, namely that scientists have the potential to nd new
insights about their subject eld, nd new properties in the objects they study, and
develop new theories about their behaviour. is will bring in some comparisons
with Fisher’s earlier use of a mechanical balance model in 1911. ese analogical
models were formed by three of the more unusually inventive gures in the history
of economics: Irving Fisher, Bill Phillips, and Walter Newlyn.
2. e Newlyn-Phillips Machine
e Newlyn-Phillips Machine is a hydraulic machine that represents the macro-
economy. e prototype, built in 1949 by two economists, Walter Newlyn and Bill
Phillips, was rst demonstrated to the faculty seminar in economics at the London
School of Economics (LSE) in November 1949; it was taken to a conference meet-
ing of the AUTE (Association of University Teachers of Economics) in Liverpool,
and arrived at the University of Leeds (which had commissioned it) in early 1950.
It is pictured here (Figure 5.1) with Newlyn in his local newspaper (the Yorkshire
Evening Post, January 20, 1950). A report that appeared soon aer in the national
press described the Machine under the heading “Water keeps running through his
hands just like money”:
Tap-water dyed red runs through the veins of the newest member of the
sta at Leeds University Economics Department – a mechanical professor
with a transparent body and two hearts (ex-RAF electric pumps). He is a
bit fat – ve feet wide as well as ve feet high, but students can learn more
from him in one lesson than from a week of text-books…. Aer talking
about economic theory, the lecturer presses a button and Mr. Five-by-Five
goes into action. While the students watch, they see the theory come to life.
(Daily Mirror, January 26, 1950)
is “mechanical professor” is a working hydraulic machine: it is powered by a
motor (around the back) that pumps red water up the vertical channel, gravity brings
it back down the system, and sensors and valves control the ows. Yet the Machine
is at the same time a model of the economic system, for it is designed so that in use it
represents the stock and ow relations of the life of the whole economy – the macro-
economy. It is an analogical model: the economy modelled as an hydraulic machine.
e photograph (Figure 5.1) shows the prototype model, the Mark I (Newlyn-
Phillips) Machine in its actuality, but to see the analogical features clearly, we
have to look at a diagram of the model both for a clearer representation and for
easier recognition of salient features.12 is drawing (Figure 5.2) of the Mark
12 is is a standard point about scientic illustrations, but still worth making: a salient reference is
provided by Law and Lynch (1990), using the topic of eld guides in bird-watching.
Choosing the World of the Model 177
Figure 5.1. Walter Newlyn Demonstrating the Prototype Machine.
Yorkshire Evening Post, Friday, January 20, 1950. Reproduced with permission from Yorkshire
Post Newspapers Ltd.
e World in the Model
178
II (Phillips-Newlyn) Machine exhibits the circular ow of national income in
monetary terms around the Machine’s economy as ows of water around a series of
Perspex tanks, tubes, and channels.13 Each of these tanks and channels represents
dierent elements of the macroeconomy set up in relation to each other according
to the economic ideas and facts of the day. On the diagram, they are labelled with
the economic elements that each part of the Machine represents. e red water,
representing the ows of money, divides and recombines according to its passage
from national income into expenditure, consumption, savings, investment, and so
forth. In certain places, it gathers into various tanks, each of which represents a dif-
ferent pool of money for dierent uses/users. At various points, these ows are gov-
erned by valves, activated by sensors, and controlled by “slides” that incorporate the
theorized behaviour of economic groups such as investors, savers, consumers, the
government, and so forth. ese economic behavioural relations can be seen on the
diagram as slots cut into rectangular boxes (the slides), labelled with their relations.
A number of the engineering solutions for the sensors and the valves are shown in
enlarged drawings at the foot of the page. In eect, the economic relationships are
to be found represented in the form of the physical arrangements, in the form of the
mechanisms that control the ow of water (money) around the system, and in the
ows themselves. Taken all together they stand for the national economy.
is drawing of the Mark II model – probably from the American marketing
literature – wonderfully manages to conjure up the rushing and splashing involved
so that we can almost hear the noise of the water as it moves around the system.14 A
number of these machines were manufactured by a U.K. engineering rm and sold
around the world to universities (accounts are scanty, but amongst others named
are Cambridge, Harvard, Melbourne, Rotterdam, and Istanbul). Others went to, for
example, the central Bank of Guatamala and one of the main motor manufactur-
ers in the USA.15 At least one other institution, the Free University in Amsterdam,
built its own Machine aer a visit to London by local instrument makers, a task
13 I call the prototype Mark I the Newlyn-Phillips Machine, since Newlyn played an important role
in its invention as we shall see; the Mark II is referred to as the Phillips-Newlyn Machine since it
was primarily Phillips who developed the improvements in the later version.
14 e American labels on this diagram show, for example, the central bank that supplies money as the
Federal Reserve, whereas on the UK diagrams of the Machine, one of the tanks is labelled “sterling
balances” (the overseas-held balances). e exact provenance of this diagram (from the James Meade
Archive, LSE) is not known, but labelling the diagram with both Newlyn and Phillips names tells us
it must be an early one since Newlyn’s name is habitually dropped in later years. It shows the more
well known Mark II Machine, which had a few additional features and is also a bit larger, standing
7 . by 5 . by 3 . and so must be post-1950. It was probably drawn to sell the Machine in the USA
following its demonstration by Abba Lerner to American economists in the early 1950s.
15 One note in the Suntory and Toyota International Centre for Economics and Related Disciplines
(STICERD) archive mentions Ford, but there is correspondence from someone at General
Motors (Andrew Court, who wrote articles on hedonic pricing) that indicates that they acquired
a Machine. e total number produced is not known. Estimates vary from about 15 (in LSE-
STICERD records, when an eort was made to trace those sold) to more like 60 (Newlyn’s esti-
mate). (is latter may be an overestimate, but a recent Internet query about the Machine brought
out at least one response from an economist in Istanbul who had one in his oce cupboard and
had not known what it was!)
Choosing the World of the Model 179
FOREIGN HELD
BALANCES
FOREIGN HELD
BALANCES
SURPLUS
BALANCES
SURPLUS
BALANCES
Figure 5.2. Drawing of the Mark II Machine.
Source: James Meade Archive, LSE. Reproduced with permission from estate of James Meade.
e World in the Model
180
requiring ingenuity, and one to be proud of achieving.16 Such worldwide interest
points to the fact that the Machine was designed to be exible to a range of factual
situations (such as institutional arrangements found in dierent countries) as well
as to dierent theories about how the economy works.17
In use, certain parts of the Machine’s controls can be set such that some ele-
ments can be disconnected, or so that dierent initial states of the world can be
represented, while the functional relations that govern the valves can be chosen
to represent dierent behaviours in specic parts of the system. For this reason,
the Machine has also been understood to be a programmable analogue computer,
able to solve directly the system of (potentially) nonlinear relations posed in the
governing slides and thus show the outcomes for certain variables of this dynamic
economic system from each “run” of the Machine as the settings are varied.18 At the
top of both the diagram and the photograph, we can also see some charts where the
state of national income (and some other key variables) are automatically drawn
out on a scaled graph each time the Machine is used.
e eect of the Machine in action is quite extraordinary. It manages to be, all
at the same time: an object whose basic workings everyone can appreciate, a seri-
ous scientic model demonstrating obscure arguments in macroeconomics, and a
wonderful conceit that amuses both expert and layperson alike when they see it. As
a press report in the U.K. said at its launch in Leeds,
e general logic of the thing is simple enough to be understood by any-
body, but the machine has scope to illustrate complicated points of eco-
nomic theory. You can set the basic adjustments such as national income,
rate of exchange and rate of interest in accordance with the facts and see
what should happen. Or, if you want to be wildly theoretical, you can set
them in accordance with the ideas of Dr. Hugh Dalton [ex-Chancellor of
the Exchequer, and sometime lecturer at LSE] and see what shouldn’t be
allowed to happen. (Gordon, Yorkshire Evening Post, January 20, 1950, p. 7)
One of the favourite teaching uses, outlined in the training manual that came with
a purchase of the Machine, was to put dierent students in charge of dierent ele-
ments of the Machine and ask them to coordinate their policies to achieve a certain
outcome.19 At the LSE, where two Machines could be linked together to represent
16 I thank Marcel Boumans for this information; see Langman, 1985, which contains a picture of the
instrument makers.
17 It provides a good example of how an analogical model too can be built to represent both empirical
and theoretical arrangements at the same time, just like Ricardo’s model farm in Chapter 2. See
also Morrison and Morgan (1999) and the discussion in Chapter 1.
18 See Swade (1995), who, as curator of the computation gallery at the London Science Museum, was
responsible for the move of the LSE Machine to the Museum. On the Machine as a computer, see
also Swade (2000) and Bissell (2007).
19 Air Trainers Ltd. of Aylesbury, U.K. (who, according to Newlyn’s notes, produced the
Machine commercially), produced a training manual entitled “National Income Monetary
Flow Demonstrator”, explaining how to set up the Machine, maintain it, and gave exercises
Choosing the World of the Model 181
two national economies, such policy coordination was even more dicult and such
lessons usually resulted in water all over the oor!
Over the years since the rst prototype was built, it has periodically reap-
peared in press articles, invariably accompanied either by the kind of joking we
see in the reports above, or by a cartoon of the Machine, and oen by both. e
most famous of these cartoons is that drawn for the satirical magazine Punch
by Rowland Emett on April 15, 1953, the day aer the Budget speech by the
Chancellor of the Exchequer.20 Emett, who had seen the Machine in action, gives
a wonderful feeling for the Heath-Robinson aspect of the Machine (its home-
made qualities and its quirkiness), which is indeed part of the Machine’s charm,
whilst simultaneously for us now, depicting the tribulations of economic life
and policy in the threadbare postwar days of early 1950s Britain (Figure 5.3).
Emett’s cartoon itself created a genre of depictions of the economic system as
the ad hoc machine of an eccentric scientist, the most recent being a similar one
of the global nancial system for the front cover of e Economist (of November
15, 2008).
e Machine is an exceedingly dicult object to describe and to convey in
words. e accompanying article in Punch in 1953 referred to the Machine as a
“creature”, a “nancephalograph”, “an automechonomist, an economechanical
brain, an engine of startling ingenuity”, “a creature capable of clarifying the whole
situation before the man in the street could say John Maynard Keynes” (Boothroyd,
Punch, p. 456). e Daily Mail of March 8, 1965 headlined it as “the monster money
machine that gurgles”. e Financial Times of April 1/2, 1995 (an apt date indeed)
depicted it as half sci- creature and half industrial-chemical plant alongside a seri-
ous article on the Machine by economist Robert Chote: “e miracle of the liquid
for its use in teaching. For example, it suggested “. . . . detail one student to try to maintain
internal balance by continuous adjustment of credit and annual adjustments of the budget,
and another to try to maintain external balance by, say, annual adjustments of the rate of
exchange. A change made by either will upset the attempts of the other unless their efforts
are co-ordinated, and the dynamic lags of the multiplier and the accelerator will further
increase their difficulties.” (p. 16) (Note the multiplier and accelerator elements of the mech-
anism, parallelling Samuelson’s equations model in Chapter 6.) The manual was probably
written by, or with the help of, Phillips (neither Phillips nor Newlyn’s name are mentioned
in it). I thank Robert Dixon of the University of Melbourne for supplying me with a copy
of this manual, probably shipped with their Machine in 1953. Vines (2000) reproduces the
“operational notes” of this manual (not the set up, nor maintenance notes) in an Appendix to
his paper.
20 ere a number of unclear dates in this history in the sense that the dates from memoirs do not
always agree, nor with those of Newlyn’s diary. is is a case in point, though nothing much hangs
upon the exact record. e story is that the cartoonist Emett and the Chancellor of the Exchequer
both came to see the Machine in action. Newlyn’s later notes say it was in late 1949 in those early
days of the prototype’s demonstrations at LSE (before it moved to Leeds in early 1950), and that the
Chancellor was Hugh Dalton (although by then he was ex-Chancellor). Elsewhere he remembers
it as Rab Butler, who was indeed Chancellor in 1953, and this ts with the cartoon date but not
with a demonstration in 1949: a mystery! Whatever the date, accounts agree that Emett did see a
demonstration and the cartoon was the result.
Choosing the World of the Model 183
economy”.21 In its early years, the Machine even had nicknames. Press reports of
the Leeds Machine refer to it as the “Weasel” – possibly named by Newlyn aer the
nursery rhyme about money that has one verse domiciled in the City of London.22
In America, by contrast, it was named the “Moniac” by the economist Abba Lerner
“to suggest money, the contemporary rst generation computer known as ENIAC,
and something maniacal” (Fortune, March 1952, p. 101).23 ese nicknames, labels,
cartoons, and joking descriptions capture some essential dualities of the Newlyn-
Phillips Machine, an invention that appears to those who see it in action to be both
a machine and a living thing at the same time. ey succeed – far better than the
serious descriptions, static photos, or analytical diagrams – in capturing the truly
analogical nature of the model in use as both a busy, alive, economy and a working
hydraulic machine.
e startling character of the Machine has always brought a smile to economists’
faces, yet during the 1970s, it came to be seen as a faintly embarrassing reminder
of a pre-mathematical age, an historical artefact t only to languish in dark corners
waiting to be scrapped. With the further passage of time, it has gained the status
of an icon, a symbol both of economists’ attempts to graduate from their predomi-
nantly verbal and political culture of the nineteenth century into the more scientic
and technocratic practices of their current expertise and of a more “heroic age”
when it seemed that a national economy – with great care and attention – could be
made not just to run like a machine but be set up to run better.24 Now, more than
half a century aer its commissioning, this iconic Machine is treated with more
aection. e institutions that own one have, over the last years, sought to restore
them and to display them proudly in prominent positions. Four are worth special
mention because of their connections with the Machine’s inventors. e rst proto-
type is on display at Leeds University (Newlyn’s home university), and the Reserve
Bank of New Zealand (the home country of Phillips) displays the rst production
model of the Machine (which has also featured in the 50th Venice Bienniale of
21 See Chote (1995), in which the Machine was described as “may be the only truly tangible achieve-
ment in the history of economics”; following an earlier Machine cartoon that accompanied his
article for e Independent on Sunday, June 5, 1994. For the Daily Mail article, see MacArthur,
1965. e Times Higher Education Supplement of May 5, 1978 depicted it as a large gaming
machine labelled “Economics Without Tears” (see McKie’s “Old Economic Pipe-Dream Flows
Again”, 1965). Another recent discussion came in an article on large-scale economic models (e
Economist, July 13, 2006, pp. 75–7).
22 “Up and down the City Road, In and out of the Eagle, at’s the way the money goes, Pop goes
the weasel.” e Eagle is the name of a pub on City Road, a road that comes down into the City of
London from the north. On the next two lines, there is no agreed interpretation. On one account,
to ‘pop’ means to pawn, and ‘weasel’ might come from the Cockney rhyming slang for coat –
weasel and stoat, so that the whole verse could refer to the weekly circulation of money.
23 ENIAC was the rst large-scale digital computer: the Electronic Numerical Integrator and
Calculator, then recently built at the University of Pennsylvania.
24 See Morgan (2003) on this engineering view of economics in the twentieth century. e term
“heroic age” was used in a letter from Arthur Brown the chair of the Leeds department (who
funded the construction of the prototype Machine) in a letter to Nicholas Barr on the occasion of
LSE’s restoration of its Machine (STICERD archive, Box 2, File 7).
e World in the Model
184
Contemporary Art).25 e most publicly accessible of these restorations is the LSE
Mark II Machine, which was built with certain additional features by Phillips with
James Meade at LSE. Since 1995, it has been displayed in the computation gal-
lery of the London Science Museum, directly opposite their specially built Babbage
Machine (see Swade, 1995). It is perhaps the only artefact of economic science in
the Museum, yet is displayed there as an analogue computer rather than an object
of economic science. Meade moved from LSE to Cambridge, which has recently
restored its Machine to working order and where it can occasionally be seen in
action.
3. e Machine’s Inventors: Walter Newlyn and Bill Phillips
e Machine’s inventors, Walter Newlyn and Bill Phillips, came from very dier-
ent backgrounds but experienced the mid-twentieth century in parallel ways and
shared more talents in common than at rst appears.
Walter Tessier Newlyn was born in Wimbledon in 1915. He le school at six-
teen without qualications.26 He joined the London oce of Darlings, a rm of
Australian grain merchants, as junior clerk, and got his rst promotion to senior
clerk when the latter failed to keep the stamp book in balance. He grew into a young
“city gent”, enjoying London’s social life and enrolling in evening classes in various
aspects of shipping and in economics in 1936 (in University of London Extension
courses). He continued his studies in economics as an ‘external’ student during the
following two years (and even into the war years, winning the University’s Gilchrist
Medal in 1943).27 At the same time, he also rose to become Darlings’ chartering clerk
and representative on the Baltic Exchange, not only a major grain exchange, but
also the main shipping and freighting exchange in the world in the 1930s. Newlyn’s
experience there is important to the story, for while money was not literally going
through his ngers, as the representative of a grain rm on the Baltic Exchange, he
worked at the heart of a large wholesale market, trading and chartering space for
millions of pounds worth of cargoes on a daily basis. is was the central point of
the market economy: such activities as his kept the ow of money and trade going
around the world. Just listen to him explaining later on how a rm nances large
25 Other restoration projects have been apparent in universities at Cambridge (where Meade, Phillips’
second collaborator, was based), Melbourne, and Erasmus (Rotterdam). Currently, the Cambridge
Machine restored by Allan McRobie is the only one in working order.
26 I thank Doreen Newlyn for the information provided about Walter Newlyn’s early life history in
this section, some of which comes from his personal notes “Growing Up” (in which he suggests
that he was good at mental arithmetic and not much else), and his CVs of various dates.
27 Newlyn’s studies gained him a scholarship to study full time when war intervened, but he contin-
ued his “external” studies during the war. He had won the Cobden Prize in his rst year of study
and the Gilchrist was awarded every three years for the best performance for economics in a
Diploma course. is success no doubt eased his way into LSE in January 1946, particularly as he
had arrived a semester late.
Choosing the World of the Model 185
commodity trades while maintaining zero bank balances, an account that surely
draws on his working life in the 1930s:
Take, for example, the case of a large-scale merchanting rm disposing
of a bulk cargo of grain purchased abroad. Having received the cheque
at 2.45 p.m. a messenger will have deposited it at the merchant’s bank at
2.50. e messenger then proceeds round the corner and at 2.55 depos-
its a cheque for the same amount drawn on his rm’s bank account to
one of the London discount houses. Moreover, he probably passes in his
walk a messenger of the buying rm who has collected a cheque of similar
amount from another discount house and deposited it in the buyer’s bank
at 2.45 p.m. (Newlyn, 1971, p. 60)28
Walter Newlyn’s work as a charter clerk on the Exchange set these large cheques in
motion (to be cleared within the City of London), and simultaneously sent cargoes
of grain around the world.
Alban William (Bill) Housego Phillips was born in Te Rehunga, on New Zealand’s
North Island, in 1914. As his sister’s account of their early life tells, their parents,
both mother and father, were ingenious in developing the stream that ran through
their dairy farm, both to generate electricity via a water wheel for milking their Jersey
cows, and to create a ush toilet: unusual luxuries in their rural neighbourhood of
New Zealand in the interwar years.29 Such systems of electric power dependent upon
the stream were then brought inside the house, and governed their daily life:
Of course, it was wasteful to run a generator when not required.
Consequently, Dad built a neat winch into the ceiling in their bedroom and
when they decided it was “lights-out” time, the sound of the winch being
wound alerted us to the imminent “blackout”. … As the winch wound in
the cable, the trap-door was raised the water was then diverted to the side
of the water-wheel to rejoin the stream.… the wheel stopped turning, gen-
eration stopped and LIGHTS-OUT. (Carol Ibbotson-Somervell, p. 5)30
Bill Phillips, along with his brother, developed additional ingenious strings and
pulleys to make life easier still – bringing light switches within reach of their beds.
So Phillips knew about hydraulic systems from the inside, for his family home was
run as just such a machine. At een, he le school, becoming an apprentice elec-
trician and, aer various wandering employments (including, apparently, crocodile
hunting in Australia) made his way via China and Russia (and the Trans-Siberian
28 Newlyn may well have accompanied the rm’s messenger on some occasions. is description did
not appear in the rst edition of his eory of Money of 1962, but came into the 2nd edition (1971),
along with the Emett cartoon (as a frontispiece) and two diagrams of the Machine to explore mon-
etary circulation. On the Baltic Exchange during this period, see Barty-King (1994).
29 ese details come from a memoire written by Phillips’ sister, Carol Ibbotson-Somervell, about
their early life (from the LSE STICERD archive).
30 I thank Carol Ibbotson-Somervell for permission to quote from her memoire held at the LSE
STICERD archive.
e World in the Model
186
Railway) to London, where he joined the London Electric Supply Company.31 He
enrolled in evening classes in social sciences at LSE and completed the Part I exams
of a BSc in 1940.32
Both our inventors were active in World War II service. In 1938, Newlyn joined
the Territorial Army, which was draed into active service a few weeks before the
outbreak of war in 1939. His technical training in the Royal Corp of Signals ensured
he could run and mend communication systems, so he became procient in certain
areas of electrical engineering. He served as a signalman in Europe, being evacuated
with his brother on “a shing smack” from the beaches of Dunkirk. Of this dramatic
and harrowing event, his diary entry merely records: “31 May: Closed Signals Oce
Bray Dune 2000 hours and embarked at 2200 hours. 1 June: Landed in England 0800
hours.”33 He was subsequently commissioned and served in the Far East. Phillips’ war
service was equally active. He received an MBE, both for technical contributions (mak-
ing Bualo aircra function more eectively) and for bravery, and was taken prisoner
of war by the Japanese in Java.34 Amongst the severe deprivations of the camp, he
learnt Chinese, and improved his Russian, while using his electrical engineering skills
to help make life a little easier for his fellow prisoners (of which more later).
As returning ex-servicemen with some previous university studies in social
sciences, which no doubt made up for their lack of school years, both Newlyn and
Phillips found their way into LSE: Newlyn became a student in 1945 and Phillips
in 1946. is was a fortuitous moment and a shared experience, and they got to
know each other well. Newlyn helped Phillips with his economics, and they became
great friends, socialising together, both in weekend country walking and having
fun on evenings out at London shows (see Newlyn, 2000). Immediately on gradu-
ating in 1948 with honours, Newlyn became an Assistant Lecturer in Economics at
Leeds University. He was promoted to Lecturer in 1949, the year that Phillips grad-
uated with a bare pass degree in Sociology and Economics. eir idea of creating
a machine began even before Phillips had graduated. e two built the rst proto-
type Machine together and demonstrated it in 1949. A Mark II model, improved by
Phillips with the help of the already well established economist James Meade, was
built by specialist machine makers in 1950 (and this was the one that was subse-
quently marketed around the world). ereaer, the prototype was used by Newlyn
at Leeds and the improved Mark II version by Phillips in London.
On the strength of this Machine, and his academic papers and thesis on the
Machine, Phillips gained an academic position at LSE. e Machine experience
led to his subsequent work on dynamics and the use of control theory in economic
analysis and policy, for which he gained the Tooke Chair in 1958. He became best
31 See also Blyth (1975) on Phillips’ early life.
32 is is according to a STICERD Archive CV for Phillips of 1958; at that stage, the BSc (Econ) had
a general social science rst year of study.
33 I thank Doreen Newlyn for permission to quote from her husband’s diary (p. 100 in her personal
memoire).
34 See Leeson (2000a) and Blyth (1975).
Choosing the World of the Model 187
known for the consequent work that launched the “Phillips curve” into macroeco-
nomics (an empirical relation between unemployment and ination). In the 1960s,
his interests in these kinds of economics problems waned in favour of his longer-
standing interest in things Chinese, and in 1967 he went to the Australian National
University to work jointly on economics and Chinese studies. He retired due to ill
health in 1970 and returned to his native New Zealand, where he died in 1975.
Newlyn had meanwhile achieved a Personal Chair in Development Economics
at Leeds University by 1967. His interests, originally in monetary and macroeco-
nomics, turned to development issues, following his visits to Africa that began in
the early 1950s. His rst visit to that continent on a Houblon-Norman award from
the Bank of England enabled him to write about colonial banking, while a later
visit to Nigeria in 1953–4 found him measuring inputs and outputs of peasant agri-
culture. During the next two decades, he worked for periods rst as a government
advisor, and then a research institute director, in Uganda where he helped found
Uganda’s rst multiracial theatre group. Back at Leeds University, he established the
African Studies Unit, co-founded the national Development Studies Association,
and was active in the campaign to create a repertory theatre in Leeds. On retire-
ment from Leeds in 1978, he continued to work in development studies with the
Sussex Development Studies Institute and died in 2002.
Newlyn and Phillips were both early school leavers, with war experiences to
tell, yet enabled by those same circumstances to study at LSE in the late 1940s.
eir meeting there resulted in the creation of the most famous physical model in
economics. ey brought dierent but complementary resources to that project.
Bill Phillips was a highly competent electrical engineer, and had vast experiences in
making things work in many dierent situations, both during his 1930s wanderings
around the world and later inside the prisoner of war camp. In addition, he had
the kind of deep tacit understanding that comes from his earlier, daily, experience
living, literally, inside a domestic hydraulic system. Walter Newlyn had a similarly
deep kind of tacit knowledge from his daily work in the City of London before
the war, sending money circulating through the international economy. So Newlyn
did not just know the theory of money as an economist, but he knew about how
money behaved in the economy in ways that very few academic economists could
have matched. Newlyn too had a considerable competence in electrical engineering
matters, and, as we shall see later, they shared a love of fashioning bits and pieces of
equipment into new things.
4. Inventing the Newlyn-Phillips Machine
Newlyn and Phillips chose to model the economy as a hydraulic machine, but there
is a long way from using the metaphor that ‘money is liquid’ to conceiving and con-
structing such a machine. is returns us to the cognitive problem – how did these
two young economists come to this choice, and how did they move from thinking
e World in the Model
188
about the economy as a hydraulic system to making a model of the economy as a
hydraulic machine? e history of this Machine is usually told placing Phillips at
its centre, and concentrates on the LSE end of the story, and on the Machine’s later
development with Meade (see Barr, 1988 and 2000). Here I am concerned with its
invention and the creation of the original prototype Mark I Machine. is means
taking Newlyn’s participation seriously, for the evidence indicates he was not only a
genuine partner in that inventive process, but even the catalyst whose imagination
set the Machine project going.35 And, to understand how two young economists
came to model the economy as an hydraulic system, we need to pay attention to
the resources they brought to the project: not only their cognitive and imaginative
resources that enabled them to see how such a system might be (as I suggested in
the introduction), but also their creativity in designing the analogical features to t
together, and work together, in a model.
Let me outline the bare bones of the three steps in this inventive collaboration
before a more serious analysis. According to Newlyn’s spare historical notes, it began
properly with a paper that Bill Phillips wrote during his nal year studies and showed
to his good friend Newlyn in early 1949.36 e essay constituted Phillips’ attempts
to understand stock and ow relationships of economics by re-presenting them in
terms of hydraulic systems. Newlyn recognised something signicant here, and he
suggested to Phillips that a real machine version of the system might be made. During
the Easter vacation of 1949, in the second step of their collaboration, Newlyn brought
his economic knowledge to the design of such a machine. And he approached his
head of department, Arthur Brown, who provided £100 “to cover the cost of materi-
als” of building the Machine for Leeds.37 In the third step, Newlyn and Phillips built
the prototype hydraulic Machine together in the summer of 1949. It was demon-
strated at the LSE in late 1949 and arrived at its Leeds home in early 1950.
We gain here an initial picture of collaborative work in which Newlyn’s under-
standing of economics was combined with Phillips’ understanding of hydraulic engi-
neering. e impression in the existing literature is that each had something of a
cognitive decit that was made up by the other and this is certainly consistent with
the academic papers that each wrote on the launch of the Machine: Phillips’ 1950
“Mechanical Models in Economic Dynamics” paper is strong on the engineering, and
N ew l y n’s 1950 paper “e Phillips/Newlyn Hydraulic Model” concentrates on the
economics, and particularly the Machine’s monetary circulation aspects. It sounds as
if turning the metaphor into the model was just a question of getting two smart peo-
ple with complementary sets of knowledge together. But if we think of the Machine
as an invention, this suggests something new. And invention requires imagination.
35 Newlyn was a modest man, and at some stage his name became detached from the Machine’s
authorship, but Phillips always acknowledged the genuine collaboration.
36 Newlyn, in one of his memoirs (see note 46), also notes an earlier conversation on July 28, 1948 as
the point when they rst discussed the possibilities.
37 Only aer the prototype had been demonstrated at LSE under Meade’s patronage did the LSE eco-
nomics faculty under Robbins take the Machine seriously. ey then funded the manufacture of
the Mark II Machine and supported Phillips to a lectureship in the department.
Choosing the World of the Model 189
Where then did the imagination come in? And just what was new about the model of
the economy? Filling in the history of their collaboration in turning a metaphor into
a machine recovers the creative, imaginative, and new elements in this episode of
analogical model-making and reveals more specically how their complementary –
and similar – skills and knowledge came together in the inventive process.
Step 1: Phillips chooses the analogy for his supply/demand
model (early 1949)
Let me return to the beginning of the story of the Machine-building collaboration,
which began in early 1949 when, meeting by appointment in the LSE refectory,
Phillips (still an undergraduate student) showed a paper he had just written to his
great friend, and one-year-ahead economics mentor, Newlyn. e paper, entitled
“Savings and Investment. Rate of Interest and Level of Income,” caught Newlyn’s
attention so strongly that he saved the original (that Phillips gave to him), for more
than ve decades.38 He could recall its importance in his notes on the history, and
could lend it to the LSE in 1991 for the occasion of their launch of their restored
Mark II Machine in 1992. It was the diagrams in the paper that caught Newlyn’s eye,
for “they diered signicantly from previous stock/ow diagrams in texts”.39
In this student paper, Phillips turned some conventional economics diagram-
matic models into diagrams of hydraulic systems. He began with the supply/
demand diagrams usually drawn by economists, showing prices graphed against
quantities. ese diagrams represent an abstract conceptualization of the market-
place relations for such demand and supply curves cannot be seen in the market;
rather these curves are understood by economists as representing the intentions
that consumers and suppliers hold about their demand and their supply at dier-
ent prices. Phillips wanted to get at the process relations between stock and ows
of quantities of goods in a market, rather than – as such diagrams were habitually
used – to interpret the change in ‘equilibrium position’ (the points of intersection
of the curves) before and aer a change in the market relations (as I shall discuss
in Chapter 7). e main problem he saw was that such market analysis treats these
hypothesized demand and supply quantities without being clear whether these
quantities are stocks at a given point in time or rates of ow during a given period of
time. He began by showing how such diagrams could easily support either a stock
interpretation of quantity at a point in time (his gure 1, our Figure 5.4a) or a ow
38 Newlyn was shown this paper by his friend when he was visiting LSE in early 1949 (while on a trip
to visit R.S. Sayers, the Professor of Money and Banking, for whom he was writing an article, see
Newlyn, 2000, p. 31). e original manuscript was given by Phillips to Newlyn, and is now owned
by the Oxford economist Martin Slater (Newlyn’s son-in-law) and has been lodged with Newlyn’s
papers in the Brotherton Library, University of Leeds. A copy is in STICERD’s collection of papers
on the Machine at LSE. Philips’ paper is a six-page typed paper – the diagrams are drawn and
labelled by hand (the handwriting on the graphs is not like Phillips’ normal (terrible) hand, but
does match that of the handwritten labels on his thesis diagrams).
39 Newlyn, RES Newsletter no. 77, April 1992, p. 12.
e World in the Model
190
(a) (b)
(c) (d)
Figure 5.4. Bill Phillips’ Undergraduate Essay Diagrams and the Inspiration from Boulding.
(a), (b), and (d) Bill Phillips’ 1948/9 undergraduate essay gures 1, 2, and 3. Source: Original
essay now in University of Leeds, Brotherton Library Archive.
(c) Kenneth Boulding’s plumbing diagram. Source: gure 9, p. 117, from Economic Analysis
(New York, 1948). Reproduced with permission from e Archives, University of Colorado at
Boulder Libraries.
interpretation of quantities over a period of time (his gure 2, our Figure 5.4b)
on the horizontal axis. He pointed to the dierent implications of these two inter-
pretations once the model is used as can be seen from the comparison of the two
gures.40 And, if the quantities of stocks do not remain constant, then “e process
40 One shows the eect of an upward shi in the demand curve when quantity is stocks held and the
adjustment is an increase in price only (to p′). e other shows the eects of change in demand
when quantity is a rate of ow, where we see (with stocks assumed constant) an immediate
response in price to p′ but then adjusted to a new position at p′′. Dierent interpretations – stocks
and ows – provide dierent processes of change and outcomes.
Choosing the World of the Model 191
of change cannot then be shown on a graph, since stocks and rates of ow are
as incommensurable as, for example, distance and speed.” (Phillips, unpublished,
p. 1.) e resources of the conventional diagrammatic model proved too restrictive
for his purposes for he wanted to embed an analysis of both stocks and ows at
once onto the same diagram.
Prompted by a contemporary analogical drawing of the price system in terms
of a piece of domestic plumbing by Kenneth Boulding (1948, shown here too as
Figure 5.4c), Phillips oered instead “a hydraulic analogy” of how stocks and ows
and their inter-relationship might be integrated together into one model. Phillips’
diagram (his gure 3, our Figure 5.4d) turns the conventional economic demand
and supply curves (or equations) into a piece of plumbing in which quantities sup-
plied ow into, and those demanded ow out of, a tank containing a stock of the
good.41 In Phillips’ version of the diagram, these ows were controlled by a ful-
crum attached to a sensor in the tank whose reaction to changes in the stocks was
depicted as price changes. His analogical model considerably extends and lls out
the economic content of Boulding’s analogy, adding in the shiing demand and
supply curves from the conventional analysis (via the valves impacting the ow),
and representing and interpreting the fulcrum lengths and sides of the tank (see the
slight curve at the top of the tank) in terms of price ‘elasticities’ or responsiveness.
is critical rst step consisted in nding the analogy and making good the
rst analogical representations and interpretations. at is, Phillips takes the meta-
phor that quantities of economic goods could be conceived in terms of liquids, and,
following Boulding’s lead, he makes the starting point for the analogical account
that the economic system is like a domestic plumbing system (rather than, say, a
natural ecology or a bodily physiology). He then lls in that analogy: all the ele-
ments of the economic diagram were transformed into the analogous hydraulic
diagram in such a way that it is a fully reconceptualized description how the market
works, and how adjustments to changes occur, in terms of the three interconnected
elements: prices, ows, and stocks of the good. e economists’ original concep-
tual apparatus of supply and demand curves are no longer depicted, but the usually
hypothesized movements in them are written onto these new diagrams as causes
for valves to open and close. e distinctions between stocks and ow of goods in
an economic market that remained opaque in the economics diagrams (and oen
in the equivalent equations) are made completely clear in the new hydraulics anal-
ogy and their relationships laid out to see.
Already we can see something new happening here. As Phillips rethinks eco-
nomics into his own engineering domain to make sense of it, he depicts the rela-
tions in a new way. at new-world model focuses attention onto the stocks and
ows and relations between them, rather than onto the shape and position of the
hypothetical demand and supply curves. e drawing shows, in a new form, how
41 is is clearly a forerunner of his gure 2 in his 1950 paper on the Machine, but this initial analog-
ical diagram is more communicative.
e World in the Model
192
the ows of goods on and o the market and the stocks held in a market are aected
by the demand and supply curve positions, their elasticities, and the price changes,
interacting altogether, and consequently what it really means to say that there is an
equilibrium in the market.
We can also see here how the cognitive problems and the creative process of
model-making interact. Phillips, in trying to understand the stocks and ows of an
economics market, developed an alternative model by thinking analogically, start-
ing from the imaginative stimulus provided by Boulding. We can almost hear his
cognitive struggle in the text that accompanies his attempts to gra stocks and
ows onto the traditional models, and we can see the creative work to overcome
this impasse in his series of three little diagrams. is sequence of diagrams cap-
tures the process by which Phillips took the conventional economics model world
and transformed it into another one based on hydraulics.
Phillips’ own imaginative leap in his paper becomes evident in the next step
into the macroeconomic system. Unlike the well-known supply and demand dia-
grams of microeconomics, most conventional macroeconomic theories of the time
were expressed verbally, and Phillips seems to have been unaware of those that
were expressed in diagrams and mathematics (see Chapter 6). So, he drew on his
own resources and understanding of hydraulics to move that successful rst anal-
ogy to another domain. Here the analogy is not that goods can be thought of as liq-
uids, but that money is like water in a hydraulic system, and he presents a diagram
of monetary circulation in an aggregate economy (his gure 4, our Figure 5.5).
is represents a circular ow of income/expenditure, and ow of savings into, and
investment out of, a tank representing money and securities. It is not simply a water
ow system, but already a partly engineered system, where the oats and levers
oer the elements of control in the system, for example, on savings and investment
behaviour.42 But while some of the economic sectors are represented into hydrau-
lics, two important elements are hardly sketched in at all, namely trade and the
government sector. And while there is little economic content in some of the engi-
neering elements, others seem to have captured the economics in creative ways.
e new diagram shows at least one element that would appear in the built
Machine: the interesting shape needed to make the hydraulic elements t to
the economic presumptions about liquidity preference in the le-hand side of the
money tank. As stocks of money build up in the tank of money balances (M), the
interest rate falls and successive increases in the level have less and less impact
on investment, indicated by the curved side of the tank. Phillips continued his
undergraduate paper (p. 4) by using this segment of his diagram in a discussion
of the theory of loanable funds, a theory that he attempts to represent back into a
two-dimensional diagram that graphs such investment funds against interest. at
graph (not shown) provides a mess of lines (though not quite as bad as Leontief ’s
42 Although Phillips’ undergraduate paper has not been published, Newlyn (2000) reproduces
Phillips’ diagram and gives a fuller description of it there.
Choosing the World of the Model 193
Figure 5.5. Bill Phillips’ Undergraduate Monetary-Circulation Diagram.
Source: Bill Philips’ 1948/9 undergraduate essay, gure 4. Original essay now in University
of Leeds, Brotherton Library Archive.
e World in the Model
194
Box diagram that we saw in Chapter 3), and Phillips complains that “the use of the
graph makes considerable demand on the imagination”!43
While Phillips’ discussion relates to the contemporary controversy that, later
on, the working Machine most obviously ‘solved’: namely whether the interest rate
is determined by stocks or ows of funds, he had considerable diculties in mak-
ing his arguments work in the two-dimensional diagrams of his paper. Vines (2000)
argues from his later analysis of this monetary circulation diagram that Phillips
must have understood very little of the monetary macroeconomics of his time.44
Indeed, as Meade noted at the time, Phillips was pretty confused about economics,
but
He was lucky enough to rub shoulders with a fellow student, Mr. W. T.
Newlyn, now lecturing on money at the University of Leeds, who was less
of an engineer but more of a monetary theorist than himself. Together
they discussed how monetary theory could be represented by an hydraulic
model. (Meade, 1951, p. 10)
Newlyn had indeed a considerable knowledge of monetary economics, not just
from his stint working in the City of London, but from his LSE degree, as is evi-
dent in his undergraduate essays of 1946–7. ese show familiarity with the profes-
sional literature and considerable facility in its analysis, most notably – compared
to Phillips’ essay – in his comparison and ‘reconciliation’ of the dierent contempo-
rary theories of interest rate determination.45 More surprising perhaps is his sketch
of a physical arrangement of pipes to understand the relationships between nan-
cial and physical controls over the ow of funds. is analogy was less successful
than Phillips’ initial hydraulic designs, but does show a certain congruence in their
way of thinking about these matters.
Step 2: Newlyn designs the blueprint for a monetary
circulation machine (Easter 1949)
Problematic though it now seems, it was the diagram of the whole monetary circu-
lation around an economy (Phillips’ gure 4, our Figure 5.5) that especially grabbed
43 His paper goes on to a comparison of various theories of the day: the classical system the Keynesian
system, Robertson’s theory of loanable funds, and the possibilities for scal and monetary policy.
His two-dimensional graph has some similarities to the famous Hicks IS/LM diagrammatic model
of 1937 (see Chapter 6) which Phillips seems not to have known, another sign of his need for
Newlyn’s superior expertise (see Newlyn’s remarks on this section of Phillips’ paper, 2000, p. 35).
44 See Vines (2000), p. 66, fn 12.
45 Some of his essays and class presentations in courses on “Banking and Currency” and Professor
Sayers’s “Advanced Banking Seminar” survive. e one mentioned here was called “A reconciliation
between the “loanable funds” and the “Keynsian (sic) theories of the rate of interest” (July, 1947)
and covered some of the professional literature of the day, including Hicks’ and Keynes’ analyses.
Others covered sterling balances, the American nancial system, the exit from the gold standard,
and cheap money policy of 1931–2. Again, I thank Doreen Newlyn for access to these essays.
Choosing the World of the Model 195
Newlyn’s attention when Phillips showed him the paper in early 1949, and he later
claimed that he never read beyond this diagram to the rest of the paper, he was so
taken by it (see Newlyn, 2000, p. 34). Newlyn saw Phillips’ drawing as full of new
possibilities to rethink monetary macroeconomics by the “introduction of a third
dimension”, namely time, through creating a mechanical version to simulate the
economic system:46
. . . the innovation in the paper was that it included drawings which showed
in detail the mechanical means of eecting the inter-related changes in the
levels of stocks and ows of water representing money, thus simulating the
economic behaviour of the economy in this sector. (Newlyn, “Historical
Summary”, dated 8.7.92)
and so “I said to Bill that it should be possible to construct a machine to reect the
articulation of the diagram as a teaching aid” (Newlyn, 2000, p. 34). In particular,
Newlyn was struck by the importance that such a machine would have for under-
standing the timing of monetary relations. From his point of view, the diagram
contained a very important insight:
Implicit in Bill’s illustration of an income ow through a tank is a time lag
from which it follows that changes in the inow impart changes in the rate
of outow over time. (Newlyn, “Historical Summary”, dated 2003)47
Making explicit the importance of time lags between inows and outows intrigued
Newlyn because he saw that these lags were critical to the circulation of money and
thus to the process of how all the monetary macroeconomic elements interacted
and evolved through time. ese issues informed the way he came to the design of
the Machine, and in turn continued into his treatment of money in his subsequent
eory of Money. Of course, these issues must also have also resonated with his ear-
lier experiences that we found in his description of a trading community that circu-
lates large ows of money within ve or ten minutes while holding no stocks.48
e suggestion that such a diagram could be turned into a real machine took
root. So, during the Easter vacation of 1949, these two friends, Bill Phillips (who
was in his last year of study and should have been working on his sociology) and
Walter Newlyn (in a junior academic position at Leeds, but staying at the fam-
ily home in Wimbledon for the vacation), worked on the specications for the
46 ere are various historical summaries of the Machine’s history written by Newlyn at dierent
dates. It is in a handwritten version held by Doreen Newlyn that Newlyn referred to “the introduc-
tion of a third dimension”, the quote below comes from a typed 1992 version that has a copy in LSE
STICERD Archive.
47 From Newlyn’s memoire account of the model (2003, p. 1), provided by Doreen Newlyn (some of
which appears in Newlyn, 2000, or in his 1992). Other details and quotes from the same sources
appear in this section.
48 As Arthur Brown wrote at Newlyn’s retirement: “His initial career – on the Baltic Exchange – was
not altogether irrelevant to his later activities; he has always shown a clearer sense than most
economists of how a market really works” (Brown, 1978 pp. 206–7).
e World in the Model
196
Machine. Newlyn tells us that “I drew the full economy version”, while Phillips
worked on the problem of “converting a diagram into a physical form” (Newlyn,
2000, p. 34). Newlyn’s contribution was surely critical here as the full design involved
all the major monetary ows in a complete economy with foreign trade, a public
sector, a central bank and dierent kinds of stocks of money.49 A few elements of
the saving-investment sector design were taken over from Phillips’ original dia-
gram, but the basic shape is very noticeably dierent from that. We can see all this
in the May 5, 1949 large scale “blueprint” (reproduced here as Figure 5.6) drawn
by Newlyn, probably to show Arthur Brown, his head of department at Leeds, to
secure funding for the Machine building to come.50 ough there are some dif-
ferences between this blueprint and the rst published schematic diagrams of the
Machine (in his 1950 paper for example, or Phillips’ diagram in 1950), it is sub-
stantially how the Machine came to be. We can see that the basic components and
structure of the Machine are xed at this stage in Newlyn’s diagram, though some
rearrangement of the parts occurs, and some elements of the Machine are ipped
over right to le relative to the blueprint.51
Newlyn’s “blueprint” design of May 1949 is a full one in the sense that the eco-
nomics has been thoroughly represented. Compared to Phillips’ rst attempt (his
gure 4, our Figure 5.5), we see that Newlyn’s collaboration has produced a design
for a real analogical economic model by instantiating the following economic fea-
tures into the Machine:
(a) e circular ow of income/expenditure has been divided into savings,
investments, consumption, taxes, imports, exports, etc., all in monetary
form.
(b) e other main economic sectors (the overseas and government sectors)
have been drawn and integrated into the circular ow model.
(c) e ows have been separated from the stocks of money, and those in turn
separated into stocks held in four tanks: by the government, in the asset
market, in the foreign exchange market, and as working balances for cur-
rent activity.
49 And, as we shall see during the Machine building period later that year, Newlyn continued to be
responsible for explaining much of the detail of macro-economics to Phillips.
50 Newlyn refers to it as a “blueprint” in his letter of January 24, 1991, to Nicholas Stern, then head of
STICERD at LSE STICERD Archive (where it exists only as a photocopy in two pieces indicating
an original A2 size). Possibly, the existence of this May 5 diagram is the source of the confusion
over dates about when Brown was approached. Newlyn (2000, p. 34) tells us that he drew the full
economy version (but refers to his later 1950 diagram 1 (equivalent to his 2000, gure 8.2) before
approaching Brown for funds to build the Machine and that this was before the Easter vacation in
which they worked on the specications. Yet from his diaries, it seems that they began work on the
designs on April 14, 1949. A few days later, Newlyn went back to Leeds, perhaps with Phillips, and
less than a month later, his blueprint of May 5 was nished.
51 In their separate 1950 publications, Phillips’ more descriptive diagram shows the right–le orien-
tation as in the blueprint, and as in the Mark II Machine which he was then developing, whereas
Newlyn’s diagram (which is more schematic than descriptive) has the same orientation as the built
Mark I.
Choosing the World of the Model 197
Figure 5.6. Walter Newlyn’s Blueprint Design for the Machine, May 1949.
Source: STICERD Phillips Machine Archive. Reproduced by permission from Doreen Newlyn.
e World in the Model
198
(d) e inows and outows are given sensible economics meanings.
(e) e functional equations of economic behaviour in Phillips’ diagram have
been replaced by “slides” which incorporate (as linear or nonlinear func-
tions) those macroeconomic relationships (e.g., the propensity to save
slide: Y′ related to S) to control the valves.
(f) e monetary tanks are directly linked to calibrated scales to report changes
in national income (£m), the exchange rate ($/£), the price of bonds, and
the rate of interest. (In this particular respect, the reporting charts in the
design are more ambitious than those developed in the Machine, where, for
example, exchange rates are not registered.) 52
e main hydraulics and controls have also been indicated on this diagram, the
sensors for registering changes are in place, and the motive power of the Machine is
shown in the pump, so that we can see where Phillips must have also been involved
in the hydraulic engineering elements. e functional relations scribbled in a dif-
ferent hand are also probably by Phillips. We can also see that the design might be
transformed into a working machine, but still it hardly constitutes an engineering
drawing giving sucient detail for others to build the Machine: it is not an engi-
neering blueprint.53 Newlyn’s drawing privileges the economics of the model, and
around the sides of his blueprint, we see some doodled ‘mountains’, perhaps drawn
in Phillips’ hand, but that appear in Newlyn’s 1950 publication on the Machine as
his way of depicting the “time shape of money balances held by an individual” (with
time on the horizontal axis; 1950, p. 117) and thus the passage of money in and out
of the “active money” balances tank, M1. He goes on to explain how this pattern
determines the level in the “idle money” M2 tank, within which money changes
hands (nance house to nance house as in his commodity trading) yet has no
52 Possibly this was because this aspect of the Machine did not work very well. e Training Manual
notes (p. 10) that “e readings on the various scales may be found not consistent with one
another, and this is due in part, to basic errors in the Machine. No attempt has been made a
achieve a high degree of accuracy” and gave some hints about how to keep inconsistencies to
a minimum. It is not clear what accuracy might mean here, though see Morgan and Boumans
(2004) for some further discussion. Allan McRobie has restored the Cambridge Machine to be
accurate when measured against the solutions to the equations that are taken to represent the
Machine.
53 Newlyn reports that during the vacation Phillips “solved some hydraulic problems such as having
constant base outows from the tanks. e nal drawings were made” (both quotes: Newlyn, in
RES Newsletter, no. 77, April 1992). is might suggest that there were separate engineering draw-
ings, but Newlyn’s 2000 reference to Phillips’ technical specications refers us only to his 1950
account (p. 284 to top of p. 287), which is a technical verbal description of the Machine’s setup.
In addition, there is nothing in the STICERD Archive like the full set of engineering diagrams
that Phillips produced aer the building of the Mark II Machine in his LSE PhD thesis of 1954 to
cement his LSE career. is evidence suggests that the prototype Machine was built from a version
of Newlyn’s blueprint diagram and from piecemeal sketches made on the job. (is is compati-
ble with the sketches that were used in Phillips’ later work with Meade redesigning parts of the
Machine; see Meade’s papers at LSE, les 16/2 and 3.)
Choosing the World of the Model 199
eect on the level of monetary circulation or income and expenditure through the
M1 tank at the foot of the drawing.
ough their new design was set up using the terms, elements, and rela-
tions of contemporary macroeconomics, we learn from the discussion of the
prototype model in Newlyn’s 1950 paper that the way the Machine’s elements
were dened was not entirely the same as other denitions of the day.54 For
example, as seen above, money is divided in the model according to its activ-
ity in the economy, not according to the motivations of individuals who hold it
as in Keynes’ analysis. ere was, at this point, no general agreement amongst
economists about these denitions, and, in any case, certain things were dened
dierently in the Machine just because the medium of expression was dierent
from the verbal or mathematical accounts. And, because of its hydraulic form,
the Machine’s design particularly required stocks and ows to be accurately and
carefully dierentiated, as they had not been in verbal versions of macroeco-
nomics at the time.
Newlyn also discusses how a variety of theoretical positions can be under-
stood and demonstrated: the “Keynesian special case”, “the Wicksellian process”,
“Kalecki’s accelerator”, and so forth (ideal for the teaching purposes that he had
in mind for the Machine). Similarly, Phillips, in his 1950 paper, discusses dierent
kinds of “lags” and “multipliers”, and so forth, for he understood each theory of the
day as being a particular physical setup of the Machine. Newlyn was adamant that
the system was designed not only to express a range of dierent macroeconomics
ideas available at that time, but also to describe dierent institutional arrangements
or policy questions in dierent kinds of economy. For example, the diagram Newlyn
drew showed a tank labelled “sterling balances”, a category of U.K.-based, but over-
seas owned, sterling money that provided a worrying problem for the British post-
war economy (see on the le in Figure 5.6).
In this second step, it was Newlyn, whose knowledge of macroeconomics was
far more advanced than Phillips’, and whose special knowledge and interest was
in monetary economics, who was important in this basic change of shape and the
additions and extensions of the Machine’s economy compared to Phillips’ original
diagram. Whereas in the rst step, Phillips had transformed the microeconomics
of markets into hydraulics to make sense of it, Newlyn’s contribution in the sec-
ond step was apparently to recognise the macroeconomic possibilities in Phillips’
hydraulics and then to show how and where the monetary and macroeconomics
could be transposed into hydraulics and thus where the hydraulics could be made
to speak to the problems of understanding the aggregate economy. is was a pro-
cess of comparison and mutual translation between the two worlds that involved
both scientists.
54 For example, he explains how the denitions used in the Machine dier from those of the Central
Statistical Oce’s accounts as well as from those of Keynes and of Robertson; see Newlyn (1950),
pp. 115–9.
e World in the Model
200
Step 3: Phillips and Newlyn build the prototype
Machine (Summer 1949)
When he found out how badly Phillips had done in his exams, Newlyn felt guilty
about the amount of time they had spent working together lling in the specica-
tions that were needed in designing the analogical model during the Easter break
(see Newlyn, 2000, p. 34). Nevertheless, aer Phillips’ nal exams, and in the sum-
mer break between university terms of 1949 while Newlyn was again in London,
the pair set out to make the prototype Machine. Here is Newlyn’s description:
e actual construction was carried out in the garage of Bill’s friends in
Croydon [South London] during the summer vacation of 1949. My inter-
mittent role was that of crasman’s mate – sanding and glueing pieces of
perspex. But one rather long pause in the work was devoted to elucidating
the complexities of the reciprocal eects of the external sector, with which
Bill was not familiar, but he wanted to understand how the simplied rela-
tionships of the model tted into the theory. (Newlyn, 1992, p. 12)55
It was a genuinely collaborative eort, in which Newlyn’s expertise in economics
complemented Phillips’ in engineering. In his 2000 historical account, Newlyn
records their working together on the public sector:
One case in which an economic input from me was needed was the intro-
duction of the Public Sector Borrowing Requirement; it was incorporated
by linking the government’s working balances to the money market. A
hinged barrier in the centre opened and closed to reect changes in the
government decit/surplus. e other case was that of the external bal-
ance. is was a closed book to Bill and, as one would expect, he wanted a
full brieng on what lay behind the functions we proposed using to reect
the response of imports and exports to changes in the exchange rate which
is determined by dierences in the rates of change of imports and exports.
I checked my le and found that I drew een graphs to illustrate the
multiplicity of the elasticities of domestic and foreign supply and demand
which our values should have reected. (Newlyn, 2000, p. 35)
ey each had their own cognitive comparative advantage – and surely each had to
be creative and patient in explaining their knowledge to the other. But the resource-
fulness of these two inventors was in fact much more balanced than these quotes
from Newlyn suggest, for they shared a love of making machines that worked, and
to make this Machine work required a labour of love.
Bill Phillips had grown up inventing things to make his life easier, playing around
with crystal radio sets and so forth. His habits of mending all things mechanical
and electrical – when he visited friends, or in his colleagues’ oces – became the
55 Perspex is actually a trade name for acrylic glass that came into use during World War II for safety
reasons.
Choosing the World of the Model 201
subject of fond anecdote. His exploits in the prisoner of war camps are legendary,
especially his ability to make and maintain radios out of the smallest and least
prepossessing bits of equipment, as Laurens van der Post was to recount later. His
invention that allowed prisoners to brew their own tea last thing at night caused the
Japanese guards to wonder why the lights dimmed.56 As Brown remarked of him
“Primarily, he was a problem solver. . . . He wanted to know how systems worked
and how they could be made to work better” (Brown, 2000, p. xiv), a remark that
serves equally well to characterize Phillips’ work in economics.
In many respects, Walter Newlyn had a similar character. His wartime training
in communications equipment built upon an earlier aptitude and even necessity
for his father, who had been a civil engineer (building bridges and roads in South
America) had died in the Battle of the Somme before his young son’s rst birthday
and Newlyn and his brother had grown into his role, using his tools and workshop
to keep their mother’s home going. Newlyn’s wife (Doreen Newlyn) recalls his skills
in such diverse but technical tasks as stage management and lighting as they sup-
ported travelling theatre expeditions around Africa, and keeping a “great tank of
a car alive over 12,000 miles of corrugated murram roads in Nigeria” by nightly
maintenance shis.57
Both Walter Newlyn and Bill Phillips were creative in fashioning bits and pieces
of equipment into something else, and this is just what they did in building their
prototype hydraulic Machine of the economy. ey used pieces of Perspex (then
a very expensive material) from the windows of bombers, while the engine that
pumped the water through the system came from the wind-screen wipers on a
Lancaster bomber – perhaps from the aireld near Croydon where they built the
Machine. e electric motor for the graphs came from an old clock, while certain
of the smaller parts were made by “a friend who owned a factory for making dolls’
eyes – known to the small group of friends involved as Mr. Dolls-Eyes”.58 Each and
every hydraulic element had to be carefully designed to t the purposes of the eco-
nomic meanings, and the Machine built in such a way that each of these bits tted
together in both engineering and economic senses59. eir Machine-building is a
perfect example of Boumans’ (1999) idea of how model-making involves putting
together disparate bits and pieces, in this case literally! ey celebrated the com-
pletion of “the rst item, the large tank” by being photographed together holding
56 See Leeson (1994, 2000b) for his detective work that pieced Phillips’ war experiences together, in
which he manages to identify Phillips as the New Zealand magician who kept the radio alive in van
der Post’s 1985 autobiographical account.
57 I am indebted once again to Doreen Newlyn for lling in these important details, this in a personal
communication of August 19, 2006.
58 Newlyn, 2001/3, p. 3 “e Phillips/Newlyn Hydraulic Model: e Leeds Prototype”. Unpublished
memoire, see notes 46 and 47.
59 In Morgan and Boumans (2004, p. 283) we list the elements that all have to be engineered to make
the Machine work eectively. Vines (2000) pays very particular attention to these analogical points
and is most admiring of how these two senses of t – the economics to the hydraulics and the
hydraulics to the economics – are achieved.
e World in the Model
202
it (Figure 5.7); as Newlyn wrote remembering this event: “It was rather like laying
a foundation stone”.60
Once the Machine was nished, their engineering skills were still required. It
was not always easy to get it to work – it oen had to be coaxed and sometimes bul-
lied – and it was certainly not easy to maintain.61 It is a signicant sign of Newlyn’s
engineering abilities that he kept the Leeds prototype Machine going until his
retirement in 1978, with only occasional help from his colleagues in mechanical
engineering and odd visits from Phillips. Phillips himself regularly had to attend
to keep the LSE Machine in working order, and it languished aer his departure in
the mid-1960s.
Bill Phillips was surely the senior engineer, but Walter Newlyn was certainly
qualied as a junior engineer. Senior and junior, these two engineers attempted
to calibrate the time for the Machine to get to a position of stable levels of water
in the main tank (and thus stable levels of national income on the chart) aer a
‘policy intervention’ experiment using the Machine. Such calibration was not sur-
prisingly quite dicult to achieve and then to interpret in economics terms, and it
was a worry that Newlyn expressed in the last part of his article on the Machine in
60 I thank Doreen Newlyn, owner of the photograph, for giving permission to reproduce it; the quote
comes from Newlyn’s handwritten notes for his history of the Machine that she also holds.
61 Even at the point when Nobel Prize Laureate James Meade arrived at LSE in the early 1990s to
make a video record of how to use the Machine, it refused to work without considerable attention
from its restorers!
Figure 5.7. Bill Phillips (le) and Walter Newlyn (right) celebrate completing the rst
tank during the Machine building in Croydon, Summer 1949.
Reproduced with permission from Doreen Newlyn.
Choosing the World of the Model 203
1950. Fiy years aer these events, in his short article about Phillips, Newlyn wrote
about this as a problem, of getting the analogy between economic time lags and
machine time lags correct, as if it were fresh in his mind.
In the model, perforce, the time-lag is a function of the capacity of the ‘active
money balances’ tank … which is adjustable within the structural limits . . . .
in the case of the time-lag, the model is not correct, being imposed by the
hydraulic analogy as the frequency of the circulation of active balances. But,
as in FM radio, it is the modulation of the frequency of carrier wavelengths,
not the frequency of it, which generates the signal. It is the decisions to
change the determinations of the rate of ow of money, with the capacity of
the active balances tank [M1] xed, which should determine the time-lag
which will apply to any impulse. (Newlyn, 2000, p. 38, his italics)
No doubt his wartime experiences as signalman made these kinds of analogical
comparisons and explanations of second nature.
is three-step sequence of analogical model-making for the Machine really
began with verbal economics. Using the stepping stone of the market hydraulics,
Phillips rst sketched an analogical hydraulic diagram of monetary circulation,
then Newlyn developed a full macro-model design and together they built the sub-
sequent prototype Machine. In his 1950 paper explaining the Machine, Phillips
then proceeded to expound the mathematics of the economic model that the
hydraulic model represented. at is, he used the Machine to get the stocks and
ows of money rightly understood, and then undertook to make a mathematical
description of the macroeconomic system that the hydraulics represented. ough
Newlyn was procient in electrical engineering, he was not so in mathematics (in
his 1950 paper, he footnoted the help of the econometrician Sargan), and as we see
from his subsequent use of the Machine in his work on money, he too understood
the Machine in hydraulic rather than mathematical terms. us, in inventing their
Machine, both Phillips and Newlyn reasoned analogically, translating directly back
and forth between ideas and knowledge about monetary circulation in the mone-
tary economy and water in hydraulic systems. is was a real substantive analogy
between economics and hydraulics and they reaped the real benets of the analogy
in subject matter, as we shall see later.62
62 Nagel (1961, p. 110) makes the distinction between substantive analogies and formal ones (i.e.,
mathematical descriptions of substantive systems), It is clear that this was a substantive anal-
ogy: the analogical translation did not come via mathematics. And when I have talked about the
Machine to engineers, they have usually responded that they would nd it very dicult, and prob-
ably impossible, to translate back, that is, to write down the mathematics to capture entirely the
full workings of the hydraulic ows in the Machine. An additional distinction here is between
real analogical systems and paper designs for analogical systems. For example, others during the
early 1950s were working with substantive electric analogies, but not with realised systems: see
Morehouse et al., 1950; Enke, 1951; and Copeland, 1952 for other paper designs or mathematical
descriptions of engineering systems; and for an earlier design, see Barker (1906). For an insightful
review and comparison of dierent electrical circuit designs, see Allen (1955).
e World in the Model
204
eir Machine was invented in a process of analogical modelling – of
refashioning economics into another kind of substantive system. is required cog-
nitive, imaginative, and technical creativity of particular kinds. In retrospect, we
can see how dependent it was upon a remarkably fortuitous combination of people:
Newlyn and Phillips and of their respective experiences, skills, and knowledge.63
5. Analogical Models and New ings
e Newlyn-Phillips Machine has oen been understood as a merely heuristic
device, something to teach with: a wonderful object, an inspired piece of economic
model building, but ultimately not really the place to develop new ideas. In contrast
the standard account amongst philosophers of science of how analogical models
are chosen and used suggest that they are particularly associated with the devel-
opment of new insights into the nature of the world being modelled.64 Analogical
models have thus been associated with strong claims to act as agents of ‘discovery’,
particularly in Mary Hesse’s 1966 classic account. e analogical world is chosen by
a scientist because of perceived “positive features”: the qualities shared in common
between the home eld and the analogical case, for example, the way economists
perceive money as having the quality of behaving as a liquid. But, as Hesse argues,
it is then by systematically investigating the characteristics of the “neutral features”,
those that are neither recognisably the same (positive features) nor obviously dif-
ferent (the “negative features”), that scientists nd potential for new insights. Such
neutral features provide likely growing points for theorizing or experimental work,
and these may reveal new aspects of the world of interest. Of course, this kind of
analysis of positive and neutral features is not one that the scientist self-consciously
carries out, but is rather one for the historian or philosopher who wants to under-
stand how, and pinpoint where, analogical models have been fruitful in the scien-
tic work of the past.
63 It was lucky for Phillips to nd not just Newlyn to work with, but later Meade, who also loved to
make artefacts. Brown remarks on the similar complementary and shared t by noting that Meade
“had started his textbook twenty years before with an exposition of the circular ow of money. . . .
to which the Phillips Machine provided a perfect concrete illustration. Meade had himself dealt in
a famous article with the stability conditions of a Keynesian system [see Chapter 6 this volume],
and was himself no mean amateur producer of precision artefacts – from kites to cabinets” (Brown,
2000, p. xv). In Meade’s archive at LSE, les 16/3 and 16/4, there is an example of this in his design
for a rope and pulley machine for teaching macroeconomics, and a correspondence about it with
Guy Orcutt (see Chapter 8), who had made his own regression analyser around this same time.
64 ese kinds of claims come from an important older tradition in the philosophy of models, par-
ticularly the work of Mary Hesse (1966). Her treatment, discussed here, combines a sense of the
imaginative and cognitive issues in her philosophy, as does Max Black (1962) (see particularly his
pp. 242–3) and, in a broader sense, Steven Toulmin (1953). (See also Achinstein (1964) on models
and Ortony (ed, 1994) on metaphors). For more recent work that extends the treatment of anal-
ogies in creative ways, see Gentner and Gentner (1983) on cognitive aspects and Schlimm (2008)
on analogies in mathematical domains.
Choosing the World of the Model 205
Irving Fisher’s mechanical balance model of 1911 forms an ideal case where we
can see the relevance of Hesse’s analysis, and it will provide a good comparative basis
for going back to the Newlyn-Phillips Machine to think about this question. It is also
a particularly apt comparison, for Fisher, not unlike Newlyn and Phillips, had a pas-
sion for making devices. Indeed, he had turned inventor as a teenager when his Father
died and he needed income to support his remaining family, and himself through
college. Like many professional inventors, most of his inventions were unsuccessful
in the marketplace, but his visible card le index system that he invented in 1913 radi-
cally cut the time for telephone operators to look up telephone numbers and was sold
out to Remington Rand for several million dollars in 1925. Well before this success,
he had entered Yale to study physics and ended up with a thesis in economics, his
work supervised by the most famous American physicist of the day, Willard Gibbs,
and the most famous American economist of the day, William Sumner.
Fisher became a professor of economics at Yale University and a monetary
economist of great note, and this is the eld of his mechanical analogical model.65
In his 1911 book on money, he produced these three “illustrations” of his equation
of exchange, in arithmetic, diagrammatic, and accounting form (see Figure 5.8).
e second diagrammatic form – the picture of the mechanical balance – is an ana-
logical model for the rst arithmetic model, a simplied economy with only three
goods (where the prices and amounts of coal in the scuttle and cloth in the bale
have been changed to t the balance’s scale). e aggregate accounting relation is
Figure 5.8. Irving Fisher’s Arithmetical, Mechanical, and Accounting Versions of His
Monetary Balance.
Source: Irving Fisher, e Purchasing Power of Money. New York: Macmillan, 1911,
arithmetic balance, p. 18; mechanical balance, p. 21; accounting equation, p. 26. Reproduced
with permission from George Fisher.
65 As part of his 1892 thesis he built an operating hydraulic system to demonstrate general equilib-
rium theory in a three-good, three-consumer economy (shown in Chapter 1). He also designed
(on paper) a hydraulic model to demonstrate the various arrangements of the money system –
gold standard, silver standard or bimetallic standard. I shall be concerned here only with another
paper-based analogical model, however, that of the mechanical balance. See Morgan (1999) and
(1997) for more materials on both these episodes of Fisher’s model building.
e World in the Model
206
the third model: MV = ΣpQ (or later MV = PT), and relates aggregate exchanges
of goods (all the Qs, or T, times their prices) for money (the stock of M times its
velocity of circulation V) in the exchange process.66 An analysis along the lines
suggested by Hesse points us to the positive features that justied Fisher’s choice of
analogical model, namely that the mechanical balance balances money (M, in the
purse) with the goods exchanged (the Qs or transactions T) on each side of the bal-
ance in the same way that the arithmetic equation of exchange does.
On the basis of these positive shared analogical features, we can also see how
Fisher mapped the velocity of circulation of money (V) as the distance to hang the
money purse along one arm, and the prices of the goods (p) along the other arm
of the balance in such a way that the arms stay in balance just as the equation does
provided, of course, that when any one of its terms are altered, one of the other
elements alters to maintain the balance. We might judge these as the neutral fea-
tures, and since this is a paper model, not a real machine like the Newlyn-Phillips
Machine, this analogical work does not have to be accurately calibrated: it only has
to work conceptually.67 Yet even to get the analogical model to work conceptually
needs the economic materials to t well onto the mechanical analogy, requiring
creativity and imagination to overcome any initial cognitive dissonance about the
relevance of the analogy.
Fisher gained a particularly important new insight from using the neutral fea-
tures to t the economics onto the balance. e problem in adopting the analogy
came with the move from this arithmetical three-good world to the aggregate level
needed to investigate certain theoretical claims, and for this, the aggregate prices
and quantities must somehow be mapped along the right arm of the balance. is
led Fisher to develop the concept of the “weighted average” for the aggregate ver-
sion of his equation of exchange (see how the goods formed the “weights” that had
to be averaged along the balance arm).68 From this inspired prompt, Fisher made
seminal contributions to the development of index number theory – a fundamental
theory of aggregate measurement in economics – in a project that ultimately grew
into a massive book of 1922 that still forms the classic text on the subject.
is successful mapping of the economics onto the mechanical diagram also
led to Fisher’s subsequent use of the analogical model for other measuring purposes
66 For many, MV = PT might seem either an obvious relation or a tautology, whereas in fact it is an
accounting identity. It was by no means uncontentious: other economists favoured other equa-
tions; and it was by no means useless: such equations of exchange form the building blocks of mac-
roeconomic reasoning (see Bordo, 1987).
67 In contrast, the Newlyn-Phillips Machine has to work properly otherwise it demonstrates nothing.
Further discussion on the diculties to be overcome to make the Machine work is contained in
Morgan and Boumans (2004).
68 See Boumans (2001) for a discussion of how Fisher’s index number theory also grew out of his
invention of a measuring instrument to arrive at a balanced nutritional diet (a problem with a
somewhat similar structure) that he developed during his recovery from TB in the early years
of the twentieth century. is device combined Fisher’s fad for healthy eating with his inventive
capacities.
Choosing the World of the Model 207
and for reasoning about various debates in monetary economics, particularly
about the nature of the quantity theory of money, and about directions of causality
between changes in the elements depicted on the balance.69 ese points could have
been made using the general algebraic version of the equation of exchange, but they
were demonstrated much more eectively on the mechanical balance diagram.
Analogies grow out of metaphors and, rather like the two-way street of meta-
phors, they enable the user to reect both ways across the comparison.70 Analogies
prompt scientists to rethink their understanding in two ways: rst in translating
the economy into the analogous system and then in seeing what new insights that
analogous system might suggest to them about their own eld.
So, in the rst move: making the economics t onto the mechanical balance,
the neutral features of the analogy were extremely fruitful for Fisher, and proved
particularly creative in his measurement theory (see Morgan, 1999). But consider-
ing the second aspect of his analogical modelling, we should not ignore the neg-
ative features – those features which at rst sight seemed dissimilar between the
economics world and the mechanical one (see Morgan, 1997). Negative features
can oen be turned to advantage and provide further points of insight because they
stem from this second aspect of reection: the point when scientists reect back
those negative features from the analogous world, to see how they too might t,
onto their own world.71
Fisher’s work with his mechanical balance illustrates how this second part of
two-way comparison works in scientic modelling. In reecting back from the anal-
ogy, he noticed two apparently negative features in the dierent concepts of balance.
Fisher understood his economic equation of exchange to be an accounting identity.
And it is the nature of an accounting identity that whenever anything happens in
the economy represented in that accounting relation, a balancing change necessarily
takes place elsewhere to keep the identity in balance. Of course this is not so with
a mechanical balance: the money purse could be increased without any necessary
69 He used the analogical model as a means to check his measurements of the velocity of money, the
element of the equation that was most dicult to measure (see Morgan, 2007). He used the his-
torical series of statistical data mapped onto the mechanical balance over a period of more than
een years to show the impossibility of reading o any empirical or logical proof of the quantity
theory of money: the theory, much in dispute at the time, that any increase in money supply auto-
matically increased the price level (see his 1911, gure 12.2, reproduced in Morgan, 1999, and the
discussion therein).
70 e claim about metaphor is that we gain insight into both ends of the metaphor: in saying “man is
a wolf”, we gain potential insight into the wolf-like elements of man’s nature and into the man-like
elements of the wolf ’s nature. Here the claim with analogical models is somewhat dierent – the
comparison involves a two-way process of comparison and so potential insight, but both are con-
cerned with learning about only one system of interest, in this case, the economic system, not the
machine system.
71 In my earlier account of these negative features, I suggested that Fisher was just unusually creative
in turning these negative features to his advantage; here I suggest that the potential of working
both ways across the analogy is a more general feature of the double reective aspect of working
with analogical models.
e World in the Model
208
change elsewhere that would maintain the balance at a point of equality – one arm
can fall if extra weight is added to it. e two concepts of balance: the economic
accounting and the mechanical are apparently incompatible. Another negative fea-
ture of the balance comparison lay in the fact that when a mechanical balance is
disturbed, it comes to a point of rest with an oscillation, rather than directly to that
point, once again, unlike his accounting relation. Fisher, from reecting on both
these physical features of the mechanical balance, changed his economics. His expe-
rience of working with the balance model (and the economic statistics he mapped
on to it) led him to a reinterpretation of his balance equation: while he still thought
that the accounting identity held as an overall constraint on the economic system,
he came to see it as only a tendency to equilibrium, rather than a continuous equi-
librium outcome at every moment in the economy. And he was inspired by the oscil-
lation problem to see how the theory of cycles in economic life might be integrated
with monetary theory as parts of the same system, the cycles being an adjustment
to the changes in the monetary elements as depicted on the balance.72 So he used
the behavioural features of a real mechanical balance – the initial non-matching fea-
tures – to throw light onto and rethink his economic theories about the relationship
of money and the economic system in some quite fundamental respects.
Fisher’s success with his analogical balance model arose from his working, in
quite a systematic way, through both sides of the analogical comparison, as a meta-
phor invites us to do. First he gained new insights from tting his economics ideas
onto the balance, and second he took features of how a real balance works and t-
ted those ideas back into his economics to refurnish his economic theories in some
fundamental ways.73 Perhaps, by the time he had nished working with it, Fisher no
longer regarded the world in his model as an analogical model for by then he had
made his economics into a mechanical model and some mechanical features had
been incorporated into his economics.
How does this account of the way that analogical models give scientists new
insight enable us to appreciate the Newlyn-Phillips Machine as a research machine?
We have seen already how Phillips rst translated some economics into hydraulics,
how Newlyn was instrumental in making the monetary system and hydraulics t
together in a Machine design, and how they then together built the Machine. What
insight did this process of making the economics t the hydraulics provoke? Let
me go back to the rst demonstration of the prototype Mark I Machine – to the
72 See Morgan (1999) for further details of this example. One of the dierences between the Mark I
Newlyn-Phillips and the Mark II Phillips-Newlyn Machines is that the latter has an ‘accelerator’
relationship built into it (as may be seen labelled in Figure 5.2); this is the same relation that fea-
tures in Samuelson’s equations model (see Chapter 6). Newlyn suggested that this be le out of
the Mark I Machine for ease of use and explanation. Vines (2000) suggests that it is this additional
connection that creates cycles and thus integrates cycles into the Machine economy in parallel to
Fisher’s use of his analogical balance to integrate cycles into his monetary economics.
73 is is a very concise account of the matter: a fuller discussion of how the negative features play an
important role is provided in Morgan (1997), and a fuller analysis of the analogical modelling in
Fisher is given in Morgan (1999).
Choosing the World of the Model 209
LSE faculty assembled under the eye of the sceptical Lionel Robbins in November
1949. When the red water owed around the Newlyn-Phillips Machine on that
day, it resolved for that audience a strongly fought controversy in macroeconom-
ics. In simplied form, Keynesians argued that the interest rate is determined by
liquidity preference: people’s preferences for holding stocks of money versus bonds.
Robertson argued that the interest rate is determined by the supply and demand
for loanable funds: primarily the ow of savings versus that of investment. When
stocks and ows really work together – as they did that day in the Machine dem-
onstration – it became clear that the theories of Robertson and Keynes were nei-
ther inconsistent nor alternative theories but rather were complementary, but more
important – they had been integrated in the Machine’s economic world.74
ey all sat around gazing in some wonder at this thing [the Machine] in
the middle of the room . . . . en he [Phillips] switched it on. And it worked!
“ere was income dividing itself into saving and consumption . . . . ” He really
had created a machine which simplied the problems and arguments econ-
omists had been having for years. “Keynes and Robertson need never have
quarrelled if they had the Phillips Machine before them”. (Robbins in 197275)
is controversy over the determination of the interest rate that Robbins sug-
gested the Machine settled is usually portrayed as one arising from the confusion
that resulted from relying on purely verbal treatments of the interaction of stocks
and ows. is insistence on the problems of verbal economics is somewhat mis-
placed. ere were already a few small diagrammatic and mathematical models
(even numerical simulations) and these had been used to explore the workings of
the Keynesian system in the late 1930s (as we shall see in Chapter 6). Yet, as we have
also seen from Phillips’ undergraduate paper, economists’ diagrammatic models
failed to elucidate certain problems because they could not show both stocks and
74 In a short correspondence prompted by Robertson’s reading of Phillips’ 1950 paper about the
Machine, Robertson wrote: “I have just been reading the account of the God (with frontispiece –
he is certainly handsomer than most human economics). . .” (Letter, 27.8.50 Robertson to Meade),
it seems that Robertson, who had not seen the demonstration, could not see this point. In reply,
Phillips suggested of the Machine “that by distinguishing between stock and ow schedules
(which, incidentally, can only be done in a continuous analysis), and by putting income eects
into the model instead of having to allow for them by making shis in the curves, the process is at
any rate shown more clearly, and the dierent parts of the theories integrated into a wider formal
system.” (Reply from Phillips to Robertson, September 19, 1950. Both letters, Meade Papers, File
4/1, LSE Library Archives.)
75 Notes by Chapman from a 1972 conversation with Lionel Robbins, at whose seminar at LSE
the prototype Machine was rst demonstrated in 1949 (LSE STICERD Archive). Being an LSE
account, Newlyn had already been written out, but by all accounts, Phillips always insisted on the
important role played by Newlyn in developing the rst Mark I Machine, and Meade, in his early
remarks made the same points. us when Meade wrote to Arthur Brown at Leeds (on December
12, 1949) asking to keep the Mark I prototype for a few more months he was most hesitant: “When
I mentioned the matter to Phillips he was shocked by it and stressed very heavily the moral obliga-
tion which he was under to you [Brown had funded the Mark I] and to Newlyn who is, of course,
co-inventor. . . .” see Meade Papers. le 16/2, LSE Library Archives.
e World in the Model
210
ows at once. In the analogical Machine, both stocks and ows work separately
and combine together to determine the interest rate, and they do so in a way that
makes use of the necessary time gap, or lag, in the interactions between investment
and income. In Newlyn and Phillips’ model world, such time lags played an impor-
tant role in the circulation of liquid around the Machine and the levels of national
income.
So, Phillips and Newlyn did not just create a machine to solve the stock-ow
problem. Rather they invented an economic model world in which the dynamics
and time relations of these circular ows and stocks of money in the economic sys-
tem could be more fully represented and integrated than in other media. eir new
way of representing the economy as a hydraulic one in which money is red water
enabled them to combine the many macroeconomic elements and allow for their
interaction, and gave users a new way of exploring the complex system experimen-
tally by dierent runs of the model. is was the rst part of the two-way analogical
comparison: namely to see and gain understanding from making an economic sys-
tem behave as a hydraulic system. e Machine enabled a new understanding about
these matters because in this new model world, the elements were liquid stocks and
ows and fully obeyed the laws of stocks and ows; and the system was genuinely
dynamic – the liquid did take time to circulate. It was this newfound compatibil-
ity between the materials and the theories that economists had been struggling to
express in words and diagrams that not only provoked satisfaction and enjoyment
at the sight of it happening in the circulation of water in the Machine, but also
deepened their understanding of the economic system that had been represented
in the analogical model.
ese claims about the Newlyn-Phillips Machine are dicult to make convin-
cingly just because they depend on the real Machine in action, and so commenta-
tors have struggled to see what was so special about the Machine for professional
economists. More recently, as part of a volume of essays in honour of Phillips, the
economist David Vines studied a Mark II Machine in Cambridge to nd out what
it really could tell him (see his 2000). Vines, with a background in maths and phys-
ics, carried out, through visual study of the passive Machine, the set of actions
suggested by the original training manual that told the user how to set up and run
particular experiments: conjunctions of initial settings and interventions on the
Machine.76 And, at the end of each suggested ‘experiment’, he reected on what
he had learnt from the Machine as opposed to what was known (then and now)
from conventional theoretical mathematical modelling and verbal discussions. He
found that there is always some additional insight that comes from the four aspects
of the analogical model that we have already noted: the fact that stocks and ows
are really working together; that time matters; that the continuous and sequential
76 Vines (2000) reads as if he actually carried out the experiments on a working Machine, but it turns
out that these were close study of a passive Machine during the 1990s (in a personal communi-
cation August 28, 2006). At that stage, the Cambridge Machine had not been restored to working
order. See note 19 for information on the training manual.
Choosing the World of the Model 211
pattern of changes gives a real dynamics (as apposed to a sequence of statics); and
that the interactions of the various elements are really working, as opposed to us
thinking about them working (although of course, in this case Vines was visualiz-
ing them working).77
Vines came to have an appreciation not just for the engineering, but for the
tness between the economic and the hydraulics in the Machine, which in eect,
gives credit to the imaginative, cognitive, and creative work undertaken by both
the original inventors, Newlyn and Phillips. He came to see the Machine as “truly
progressive” as well as being an incredible heuristic device:
It is not true that ‘everything is in the machine’ .… But there is in fact much
more in the machine on these subjects than is allowed in macroeconomic
conventional wisdom. And it is immensely visible. It easily stimulates fur-
ther thoughts and conjectures .… (Vines, 2000, p. 49)
Such further thoughts and conjectures are evident in the work of our two
inventors: we can nd insights from their interaction with the Machine’s hydrau-
lics reected in their subsequent economics. Just as Fisher had used insights from
his analogical balance model to question and rethink his account of the monetary
economy, so too did Newlyn and Phillips. Vines (2000) makes a strong case that
the ways in which the Machine problematizes issues of time lags, dynamics, and
control provided the prompts for Phillips widely recognised and inuential later
contributions in econometrics, control theory, and stabilization theory. In Newlyn’s
case, the pattern of reection from the Machine is more dicult to trace because he
soon turned to development economics. But we can see how he develops his ideas
about monetary circulation from his work with the Machine, rst in the charts
and diagrams in his 1950 paper on the Machine, and then through his book on
monetary theory (1962 and several editions). We can see these machine insights
in his questions about, and the attention he gives, to the circulation patterns of the
“active money” (depicted in the Machine), which in turn depended on the behav-
iour and speed of reaction times of dierent individuals in the economy: “It is not
the frequency of payments in which we are interested but the speed of reaction to
amplitude” (Newlyn, 1962, p. 85).78
Just as Fisher took his insights from the behaviour of his mechanical balance
into his ideas about economic balance, so too did Newlyn and Fisher use their expe-
riences of how their hydraulics model worked to rethink some of their economics.
77 e sequence of moves, or ‘comparative statics’, on a diagrammatic model was the usual way econ-
omists investigated dynamics, at that time, as we shall see later in Samuelson’s simulated model of
the macroeconomy in Chapter 6.
78 In these, he interpreted the multiplier time not as the time lag between income reappearing as
expenditure (or v.v.) but the response time for individuals to react to a change in volume of pay-
ments. While this relates to earlier ideas about the velocity of circulation that indeed go back to
Irving Fisher’s work on velocity with his equation of exchange (see Morgan, 2007), the details of
the trails le by Newlyn’s writings suggest that they are the development of his own studies with
the Machine.
e World in the Model
212
So creativity, imagination, and cognition came not just in the process of develop-
ing an analogical model, but in bringing insights back from that analogy into their
economics. As with Flatland, the three-dimensional reader who succeeds in using
his imagination to understand a two-dimensional worldview not only gains insight
into the nature of the two-dimensional world, but learns something new about his
own three-dimensional world too.
Reecting both ways across the analogy – rst in tting the economics onto
the hydraulics in building the Machine, and then in later work, developing insights
from the hydraulics and engineering in their economics – appears to have been a
source of fruitful ideas in the work of both these economists. But, just as no econo-
mists nowadays will think of Fisher’s mechanical balance when they use the term
“weighted average”, the faint traces of the Newlyn-Phillips hydraulic Machine have
become lost over time as the insights they drew from their engineering became
taken for granted in those parts of economics where they have been used.
Despite this memory loss, the Newlyn-Phillips Machine might be regarded as
one of the most inventive models in economics. Indeed, it was so inventive – almost
a piece of science ction – that people did not know how to take it. At the rst pub-
lic outings of the prototype, the reactions of the economists were ones of amaze-
ment that it worked, of enjoyment at the spectacle, and of enlightenment about
the dynamics of the macroeconomic system. Such a mixture of delight and insight
were remarked whenever the Machine’s workings were displayed. e newspaper
reports aer the Leeds demonstration argued that it was a purveyor of both facts
and a machine to sort theories, a knowledge maker with a personality, yet a techno-
cratic object. Cartoons ever since have xed on similar features: as a personality: a
somewhat makeshi character; as an economy: a vibrantly alive and eccentric sys-
tem; yet as a purveyor of ideas: something of an economics ‘fruit-machine’ spewing
out new sets of results with each experiment conducted by its scientist-attendants.
Economists loved the Machine for its sheer boldness and eccentricity, but it proved
a dicult thing to work with, dependant upon the care of its inventors Newlyn,
Phillips, and later Meade, to keep it alive. And despite the fact that few people have
seen the Machine at work, it remains perhaps the only economic model to have
seeped into the public imagination. From the original Emett cartoon, to a recent
cover of e Economist, the Newlyn-Phillips Machine exists as a folk object for
people who have never seen or even heard of the original economic model.
Acknowledgement
e main case study for this chapter grew out of a paper written jointly with Marcel
Boumans (2004) on three-dimensional models and the Phillips Machine, but the question
here is a dierent one, and oers an analysis based on some new historical materials: drawn
both from the LSE Archives (Meade’s papers) and the STICERD Phillips Machine Archive
(thanks to Sue Donnelly and Angela Swain respectively) and from information from cor-
respondence and conversations with Mrs. Doreen Newlyn, in turn based on her husband’s
Choosing the World of the Model 213
diaries, records and notes. My very sincere thanks go to Mrs. Newlyn for digging out the
answers to my questions and her willingness to share her records and photographs and give
me permission to use them in this chapter. anks also to Lesley Chadwick, Martin Slater,
Martin Carter, Greg Radick, Mike Flinn, in connection with Newlyn’s history and the Leeds
Machine; Robert Dixon in connection with the Melbourne Machine; Brian Silverstone and
Robert Leeson for their help with the New Zealand end of the story; David Vines for email
discussions of his “experiments”; and participants at seminars at LSE, Leeds, Amsterdam
and the History of Economics Society (especially Roy Weintraub). e chapter also uses
in very concise form and for comparative purposes, materials from my study of Fisher’s
mechanical balance model (the full stories are given in Morgan, 1997, 1999). Finally, I thank
Marcel Boumans for permission to draw on our earlier joint work on the Machine and for
his many helpful comments on this chapter.
References
Abbott, Edwin A. (1884/1952) Flatland. A Romance of Many Dimensions. New York:
Dover.
Achinstein, Peter (1964) “Models, Analogies, and eories”. Philosophy of Science, 31:4,
328–50.
Allen, Roy G. D. (1955) “e Engineer’s Approach to Economic Models”. Economica, 22,
158–68.
Bacon, Francis (1625/1985) In John Pitcher (ed), e Essays. London: Penguin Classics.
Barker, D. A. (1906) “An Hydraulic Model to Illustrate Currency Phenomena”. Economic
Journal, 16, 461–6.
Barr, Nicolas (1988) “e Phillips Machine”. LSE Quarterly, 2, 305–37.
(2000) “e History of the Phillips Machine”. In Robert Leeson (ed), A.W. H. Phillips:
Collected Works in Contemporary Perspective (pp. 89–114). Cambridge: Cambridge
University Press.
Barty-King, Hugh (1994) e Baltic Story: Baltic Coee House to Baltic Exchange. London:
Quiller Press.
Bissell, Chris (2007) “e Moniac: A Hydromechanical Analog Computer of the 1950s”.
IEEE Control Systems Magazine, 27(1), 59–64.
Black, Max (1962) Models and Metaphors. Studies in Language and Philosophy. Ithaca, NY:
Cornell University Press.
Blyth, C. A. (1975) “A.W. H. Phillips, M.B.E.: 1914–1975”. e Economic Record, 51, 135,
303–7.
Boothroyd (1953) “e Financephalograph Position: Serious Lag in Production.” Punch,
April 15, p. 456.
Bordo, Michael D. (1987) “Equations of Exchange”. In J. Eatwell, M. Milgate, and P. Newman
(eds), e New Palgrave: A Dictionary of Economics, Vol. 2 (pp. 175–77). London:
Macmillan.
Boulding, Kenneth J. (1948), Economic Analysis (revised edition). New York: Harper.
Boumans, Marcel (1999) “Built-In Justication”. In Mary S. Morgan and Margaret Morrison
(eds), Models as Mediators: Perspectives on Natural and Social Science (pp. 66–96).
Cambridge: Cambridge University Press.
(2001) “Fisher’s Instrumental Approach to Index Numbers”. In Judy L. Klein and Mary S.
Morgan (eds), e Age of Economic Measurement (pp. 313–44). Annual Supplement to
History of Political Economy, Vol. 33. Durham, NC: Duke University Press.
e World in the Model
214
Brown, Arthur J. (1978) “Appreciation at Retirement”. University of Leeds Review, 21.
(2000) In Robert Leeson (ed), A.W. H. Phillips: Collected Works in Contemporary
Perspective (pp. xii–xv). Cambridge: Cambridge University Press.
Chapman, Shirley (1972) Some notes on Bill Phillips and his machine … from a conversa-
tion with Lord Robbins. 1 Dec. 72 (Box 3, LSE STICERD Archive).
Chote, Robert (1994) “e Dangers of Stirring up Chaos”. e Independent on Sunday,
June 5.
(1995) “Miracle of the Liquid Economy”. Financial Times, Weekend Section, April 1/2,
p. I–II.
Copeland, Morris A. (1952) A Study of Money Flows. New York: National Bureau of
Economic Research.
Daily Mail (1965) See MacArthur.
Daily Mirror (1950) “Water Keeps Running through His Hands Just Like Money”. January
26, 1950.
e Economist (2006) “Big Questions and Big Numbers”. July 15, pp. 75–7.
e Economist (2008) November 15–21, front cover.
Edgeworth, F. Y. (1881) Mathematical Psychics. London: Kegan Paul, London. (New anno-
tated edition. In Peter Newman (ed), F. Y. Edgeworth’s Mathematical Psychics and
Further Papers on Political Economy (pp. 1–174). Oxford: Oxford University Press for
the Royal Economic Society, 2003.
Emett, Rowland (1953) “Machine Designed to Show the Working of the Economic System.
Cartoon, Punch, April 15, p. 457.
Enke, Stephen (1951) “Equilibrium among Spatially Separated Markets: Solution by
Electronic Analogue”. Econometrica, 19, 40–7.
Financial Times (1995) See Chote.
Fisher, Irving (1911) e Purchasing Power of Money. New York: Macmillan.
(1922) e Making of Index Numbers. New York: Pollak Foundation for Economic
Research.
Fortune (1952) “e Moniac: Economics in irty Fascinating Minutes”. March, p. 101.
Gentner, D. and D. R. Gentner (1983) “Flowing Waters or Teeming Crowds: Mental Models
of Electricity”. In D. Gentner and A. L. Stevens (eds), Mental Models (pp. 99–129).
Hillsdale, NJ: Lawrence Erlbaum.
Gordon, Con (1950) “New Machine Shows How the Money Goes”. Yorkshire Evening Post,
January 20, p. 7.
Hesse, Mary (1966) Models and Analogies in Science. Notre Dame, IN: University of Notre
Dame Press.
Hume, David (1955) “Of the Balance of Trade”. In E. Rotwein (ed), David Hume: Writings
on Economics (pp. 60–78). Madison: University of Wisconsin Press.
Ibbotson-Somervell, Carol (1994) “A.W.H. Phillips, MBE: 1914–1975, A.M.I.E.E.,
A.I.L., Ph.D.Econ., Professor Emeritus; Sibling Memories, Press Cuttings, Selected
Biographical Notes”. Unpublished memoire, LSE STICERD archive, Box 7, File 6.
e Independent on Sunday (1994) See Chote.
Klamer, Arjo and omas C. Leonard (1994) “So What’s an Economic Metaphor?” In
Philip Mirowski (ed), Natural Images in Economic ought (pp. 20–51). New York:
Cambridge University Press.
Langman, Michiel (1985) “Geld als Water; De Droom van Elke Econoom. Economisch
Bulletin, Oktober: 8–11, p. 9.
Law, J. and Michael Lynch (1990) “Lists, Field Guides, and the Descriptive Organisation
of Seeing: Birdwatching as an Exemplary Observational Activity”. In M. Lynch and
Choosing the World of the Model 215
S. Woolgar (eds), Representation in Scientic Practice (pp. 269–99). Cambridge, MA:
MIT Press.
Leeson, Robert (1994) “A.W. H. Phillips M.B.E. (Military Division)”. e Economic Journal,
104, 605–18.
(2000a) [ed] A.W.H. Phillips: Collected Works in Contemporary Perspective. Cambridge:
Cambridge University Press.
(2000b) “A.W. H. Phillips: An Extraordinary Life”. In Robert Leeson (ed), A.W. H. Phillips:
Collected Works in Contemporary Perspective (pp. 3–17). Cambridge: Cambridge
University Press.
MacArthur, Brian (1965) “All Done by Water …”. Daily Mail, March 8, p. 10.
McCloskey, D. N. (1990) “Storytelling in Economics”. In Don Lavoie (ed), Economics and
Hermeneutics (pp. 61–75). London: Routledge.
McKie, Robin (1978) “Old Economic Pipe-Dream Flows Again”. Times Higher Education
Supplement, May 5, 1978.
Meade, James (1951) “at’s the Way the Money Goes”. LSE Society Magazine, January,
10–11.
Mirowski, Philip (1989) More Heat than Light: Economics as Social Physics, Physics as
Nature’s Economics. Cambridge: Cambridge University Press.
Moghadam, Reza and Carter, Colin (1989) “e Restoration of the Phillips Machine:
Pumping up the Economy”. Economic Aairs, October/November, 21–27.
Morehouse, N. F., R. H. Strotz, and S. J. Horwitz (1950) “An Electro-Analog Method for
Investigating Problems in Economic Dynamics: Inventory Oscillations”. Econometrica,
18, 313–28.
Morgan, Mary S. (1997) “e Technology of Analogical Models: Irving Fisher’s Monetary
Worlds”. Philosophy of Science, 64, S304–14.
(1999) “Learning from Models”. In Morgan and Morrison (eds), Models as Mediators, pp.
347–88.
(2001) “Models, Stories and the Economic World”. Journal of Economic Methodology,
8:3, 361–84. Reprinted in U. Maki (ed), Fact and Fiction in Economics (pp. 178–201).
Cambridge: Cambridge University Press.
(2003) “Economics”. In T. Porter and D. Ross (eds), e Cambridge History of Science, Vol.
7: e Modern Social Sciences (pp. 275–305). Cambridge: Cambridge University Press.
(2007) “An Analytical History of Measuring Practices: e Case of Velocities of Money”. In
M. Boumans (ed), Measurement in Economics: A Handbook (pp. 105–32). Philadelphia:
Elsevier.
Morgan Mary S. and Marcel Boumans (2004) “Secrets Hidden by Two-Dimensionality: e
Economy as an Hydraulic Machine”. In Soraya de Chadarevian and Nick Hopwood
(eds), Models: e ird Dimension of Science (pp. 369–401). Stanford, CA: Stanford
University Press.
Morgan, Mary S. and M. Morrison (1999) [eds] Models as Mediators. Cambridge: Cambridge
University Press.
Morrison, M. and M. S. Morgan (1999) “Models as Mediating Instruments”. In Mary S.
Morgan and Margaret Morrison (eds), Models as Mediators: Perspectives on Natural
and Social Science (pp. 10–37). Cambridge: Cambridge University Press.
Nagel, Ernest (1961) e Structure of Science. London: Routledge & Kegan Paul.
Newlyn, Walter T. (1950) “e Phillips/Newlyn Hydraulic Model”. Yorkshire Bulletin of
Economic and Social Research, 2, 111–27.
(1962/1971) eory of Money. Oxford: Clarendon Press.
(1992) “A Back of the Garage Job”. RES Newsletter, no. 77, April, 12–13.
e World in the Model
216
(2000) “e Origins of the Machine in a Personal Context”. In Leeson, 2000 (ed), pp. 31–8.
Ortony, Andrew (1994) Metaphor and ought, 2nd ed. Cambridge: Cambridge University
Press.
Phillips, A. W. (Bill) H. (1950), “Mechanical Models in Economic Dynamics”. Economica,
17, 282–305.
Schlimm, Dirk (2008) “Two Ways of Analogy: Extending the Study of Analogies to
Mathematical Domains”. Philosophy of Science, 75, 178–200.
Swade, Doron (1995) “e Phillips Economics Computer”. Resurrection no. 12, 11–18.
(2000) “e Phillips Machine and the History of Computing”. In Robert Leeson (ed),
A.W. H. Phillips: Collected Works in Contemporary Perspective (pp. 120–6). Cambridge:
Cambridge University Press.
Times Higher Education Supplement (1978). See McKie.
Toulmin, Stephen (1953) e Philosophy of Science. London, Hutchinson University
Library.
van der Post, Laurens (1985) e Night of the New Moon. London: Hogarth Press.
Veblen, orstein (1904) eory of Business Enterprise. New York: Scribner.
Vines, David (2000) “e Phillips Machine as a ‘Progressive’ Model”. In Robert Leeson (ed),
A.W. H. Phillips: Collected Works in Contemporary Perspective (pp. 39–67). Cambridge:
Cambridge University Press.
Walras, Leon (1874) Elements d’Economie Pure. English translation by William Jaé (1954).
London: Allen and Unwin.
Yorkshire Evening Post (1950) See Gordon.
217
6
Questions and Stories: Capturing the Heart
of Matters
1. Introduction 217
2. Stories to Shape Model Resources: Frisch’s Macro-Dynamic Scheme 218
3. Questions and Stories Capturing Keynes’ General eory 221
3.i Modelling Keynes’ General eory: Meade 222
3.ii Reasoning with Models: e External and Internal Dynamics 225
3.iii Modelling Keynes’ General eory: Samuelson 228
4. Finding New Dimensions and Telling New Stories 232
4.i Modelling Keynes’ General eory: Hicks 232
4.ii Demonstrations, Variety, and Fruitfulness 236
5. Capturing the Heart of the Matter with Narratives 239
5.i Narratives and Identity in the World of the Model 239
5.ii Model Narratives and Making Sense of the Economic World 242
5.iii Narrative as a Testing Bed for Models 246
6. Where Next? 251
1. Introduction
Scientic models are not passive objects but form sophisticated instruments
of enquiry.1 Models are objects to enquire into and to enquire with: economists
enquire into the world of the economic model, and use them to enquire with into
the economic world that the model represents. What kind of reasoning turns these
pieces of mathematics or little diagrams into a means of enquiry? And how is it
that these enquiries lead economists to feel that they have captured something of
the heart of the matter, either of their theories or of the economic world, in their
models?
e question: ‘How do economists use models?’ is, in one sense, easy to answer:
they ask questions with them and tell stories! Or more exactly: they ask questions,
1 See Morrison and Morgan (1999) and Morgan (1999).
e World in the Model
218
use the resources of the model to demonstrate something, and tell stories in the
process. At rst sight, it is dicult to see exactly why questions are needed, or what
the stories do.2 How does asking questions of models and telling stories with them
enable them to function as epistemic instruments that economists might learn from
using and that might capture the heart of anything? Let me begin with an example
that shows how stories can shape the reasoning resources of models before going
on to show how and why economists working with models typically ask questions
and tell similar kinds of stories when they reason with them.
2. Stories to Shape Model Resources: Frisch’s
Macro-Dynamic Scheme
One of the greatest challenges for economists in the 1920s and early 1930s was to
get to the heart of the matter of business cycles. is was a theoretically complex
puzzle, namely to work out what particular combinations of economic elements,
and their relationships, might be responsible for creating business cycles. It was
also a real economy problem, evidenced in the deep depression of 1921–2 and the
Great Depression of 1929 onwards.
Against these backgrounds, the Norwegian economist Ragnar Frisch (1933)
set himself to solve one important aspect of this puzzle: to gure out what kind of
mathematical model of the economy could produce a cyclical pattern in general eco-
nomic activity in the world of the model.3 He began his modelling of the economic
system from his visual sketch of the economic system, a Tabl e au Économique, depict-
ing the elements and circulating ows of the economy from which he fashioned a
simpler, mathematical, model, both shown in Chapter 1 (Figure 1.6).4 is latter
2 Several commentators have discussed stories: McCloskey (1990a, 1990b and 1994) and Mäki
(1992), or questions and stories: Gibbard and Varian (1978), in the context of economic models.
My own account, of 2001 and here, begins with the last named work for they raise and note some
important aspects of modelling – including that both questions and stories are involved; but they
do not really explain how, and so why, stories are critical to the identity of a model. (More recent
work has discussed models as ctions; see, e.g., Suárez [2009] and Frigg [2009]; or Le Gall [2008]
for economic models, but my focus here is on the role of narratives in model usage, not on the
status of models; of course not all stories are ctional.)
3 Frisch (1895–1973), the Norwegian equivalent to Keynes in terms of his position and profes-
sional stature, was, along with Tinbergen, one of the leaders of the econometric movement and
together, they were responsible for developing the ideas and practices of modelling in the interwar
period. Mathematical modelling was pretty unusual at this time, and the term ‘model’ was not yet
introduced, so Frisch talked of his “macro-dynamic system”. See Chapter 1 here for the history of
modelling in general, and Boumans (2005) for the early history of business cycle mathematical
modelling.
4 e story of Frisch’s model has been told several times in the history of economics. Boumans (1999)
tells how and why he picked out elements to make a model at “the extreme limit of simplication”
(1933, p. 174), and how he moulded them together with a mathematical formalism to make a “new
recipe” for business cycles; Morgan (1990) concentrates on its place in the history of econometrics;
and Louça (2007) on its analogical aspects.
Questions and Stories 219
“ macro-dynamic system” had the resources – of both mathematical and economic
content – for Frisch to think of it as a kind of machine. It was a machine that could
produce cycles in economic activity in the world of the model in a seamless pro-
cess of change, and these cycles gradually died down over time of their own accord.
ese two qualities of the world created in his model were vitally important in ful-
lling Frisch’s requirements for the model, for while cycles were a feature of the real
economy, it was a widely held theory amongst economists of the time that, if the
economic system were le to itself and without disturbances, the cycles would die
out and the economy would tend towards a position of rest or ‘equilibrium’.5 Frisch
went on to show, by adding some reasonable guesses about the numbers in his sim-
ple model system, that it could produce cycles that matched the lengths of economic
cycles in the real economic system. So, his little model was consistent with theoret-
ical assumptions, and he took comfort from its ability to mimic the length of real
economic cycles.
But this neat cyclical activity produced in the world of the model was just too
neat to t the more unruly pattern of activity found in the real world, and, as he
said, “in reality the cycles we have occasion to observe are generally not damped”
(Frisch, 1933, p. 197). ese observations led Frisch to ask:
. . . in what respect do the dynamic laws need to be completed in order to
explain the real happenings? . . . . what would become of the solution of a
determinate dynamic system [such as his little model] if it were exposed to
a stream of erratic shocks that constantly upsets the continuous evolution,
and by so doing introduces into the system the energy necessary to main-
tain the swings. (Frisch, 1933, p. 197)
is is where the nal, third, step of his model-making occurred, and where stories
with extended analogies began to play a serious role in shaping his model.6
In this third step of his model-making, Frisch followed the lead of the preem-
inent Swedish economist Knut Wicksell, who had distinguished between the prop-
agation problem (the economic machine that created the cycles) and the impulse
problem (what kept the cycles going) with a memorable story-cum-analogy: “If
you hit a wooden rocking-horse with a club, the movement of the horse will be very
dierent to that of the club” (Frisch quoting Wicksell, p. 198). e motion of the
horse is a rocking one (the propagating element), but the horse will gradually come
5 On the history of this assumption, see Ingrao and Israel (1990); and for discussion of its impor-
tance in mathematical economics and the econometric models of the mid-twentieth century, see
Weintraub (1991) and Morgan (1991).
6 Stories were critical to his model design here but not all analogies involve good stories. us Frisch
rejected an alternative analogy, which conceived of the long, several-year, period of the business
cycles as waves on a stream’s surface with the yearly seasonal variations in economic activity as
ripples caused by stones on a river bed. ere was no narrative to connect the elements. A contrast-
ing example of where an analogy worked well without narratives is found in creating the Newlyn-
Phillips hydraulic Machine of Chapter 5. For a case of stories guring in model construction in
physics, see Hartmann (1999).
e World in the Model
220
to a position of rest unless there is some reason for it to continue to rock by the boy
hitting it with a club (the impulse). For Frisch, the propagating part of his model
and the impulse part were dierent motions and there was no reason for them to
be concurrent or for the impulses to be regular: imagine a small, angry boy hitting
his toy horse with a stick at random intervals and with random amounts of force,
and you have the right idea.
How then did Frisch turn this story about impulses into an element that could
be joined to his economic mathematical (propagation) model? He found inspira-
tion in the statistical experiments reported in 1927 by G. Udny Yule and Eugen
Slutsky.7 Yule in England had used a story of small boys shooting peas at a moving
pendulum to explain his statistical experiments in which an harmonic process was
disturbed by random elements, a story rather similar to Wicksell’s. Slutsky, across
the other side of Europe in Russia, had picked out and summed a series of succes-
sive lottery numbers to create a second series of numbers that showed a maintained
cyclical pattern but with jagged shapes that were very similar to those of business
cycle data (see Chapter 8, Figure 8.5). ese stories were attached to demonstra-
tions: graphs that showed Frisch how random shocks or erratic elements could pro-
vide data patterns that looked much more like business cycle data than the smooth
waves created by his economic mechanism model.
Using these stories and their statistical demonstrations to motivate his own model
design, Frisch added a set of random shocks into his economic mechanism, intro-
ducing them in such a way that the mathematical model of economic activity car-
ried along the random shocks (or propagated them) through following time periods.
Using these stories of small, mischievous boys to shape his model so that it contained
both mathematical and statistical resources, Frisch was able to produce simulations
that demonstrated not only how his world in the model could produce the kinds of
damped cycles required of contemporary business cycles theorizing, but could at the
same time imitate the kind of jagged and maintained cycles of data produced by the
real world (that we see in the nancial reports of newspapers and television).
Emulating the data pattern was a useful attribute of the model, but the small
boy story of impulses had no obvious equivalent back in the economic world. Frisch
sought an economic interpretation in another story using an analogy, a pendulum
mechanism fed by a stream of water through a valve, that he designed and drew to
understand Joseph Schumpeter’s theory of cycles (see Louça, 2007). According to
this account, cycles were maintained in the economy because of the role of inno-
vations in the economic system: innovations in technology, in the organisation of
work, in nding new supplies and markets, and in new products. Frisch argued
that such innovations “accumulate in a more or less continuous fashion, but are put
into practical application on a larger scale only during certain phases of the cycle”
7 See Yule (1927) and Slutsky (1927); Slutsky’s work was published in Russian but immediately
abstracted and known by European and American economics (see Morgan, 1990; Judy Klein, 1997;
and Barnett, 2006).
Questions and Stories 221
(Frisch 1933, p. 203), so that, as he put it, it is not the innovations themselves, but
their pattern of utilization in the economy that “constitutes the new energy which
maintains the oscillations” (Frisch, 1933, p. 204). Frisch adopted Schumpeter’s
account to provide an economic explanation for the maintenance of cycles that
occurred in using his model. So here we see a story being used in a dierent way,
not to shape the creation of the model as the rocking horse story did, but now as
a means of relating the modelling result back to the world to oer an economic
explanation of why the economic world behaves as it does.
In this now classic paper of 1933, written in the depths of the Great Depression,
Frisch had set about modelling why the economy experienced business cycles. He
began with a visual schema of economic activity, developed a smaller mathemat-
ical model of the economy as a mechanism that would produce damped cycles,
and combined it with a random shock element so that it would produce patterns
that matched business cycle data. In other words, he succeeded in capturing some
important elements of the theory and of the world behaviour in his model world.
Stories, or story analogies, were critical in building up or creating the model and
joining the elements together. But his last story analogy was also critical for point-
ing to the way the model could be used to provide explanations. It is this latter role
of stories that features regularly in the way that economists use their models.
3. Questions and Stories Capturing Keynes’ General eory
e appearance of Frisch’s model in 1933 was a rare event, for this was a period
when the majority of the economics profession did not indulge in mathematical
modelling about the economic system as a whole. But the extended length and
depth of the Great Depression into the 1930s meant that many economists became
obsessed by the question of why the cycle had got stuck in a depression and why
the economy did not right itself and recovery begin. e most important theoret-
ical contribution to this problem was the publication of John Maynard Keynes’
General eory in 1936 – a book generally taken to epitomise the development of
macroeconomic theory, a theory that replaced business cycle theories (at least, for
half a century). ose who approach this famous book now will nd its argument
mode opaque, for it is a curious mixture of mathematics and words.8 Its opacity
was equally true then, for the immediate reaction of a number of young economists
of the day was to create various algebraic and geometric models in their attempts
to understand and capture the heart of Keynes’ theory. In some cases, they tried to
provide a representation of his ideas that would allow comparison with other sys-
tems, particularly the classical system.9 e most inuential of these attempts was
8 See Andvig (1991), Solow (1997), and Lucas (2004, p. 13), who noted that “you had to have an
intermediary to get close to the General eory. Somebody had to help you get at it.”
9 ough not all these attempts were self-described as ‘models’, Darity and Young (1995) have
rightly referred to these attempts in the two or three years following publication of Keynes’ book as
e World in the Model
222
the one by John Hicks, which morphed into one of the most ubiquitous models of
macroeconomics, namely the IS/LM diagram. I concentrate initially on two others,
one by the young British economist James Meade, and one by the young American
economist Paul Samuelson, to introduce my discussion of the typical questions and
storytelling characteristics of model usage in economics.10
3.i Modelling Keynes’ General eory: Meade
James Meade’s paper began:
e object of this article is to construct a simple model of the economic sys-
tem discussed in Mr. Keynes’ e General eory of Employment, Interest
and Money, in order to illustrate:
(i) the conditions necessary for equilibrium;
(ii) the conditions necessary for stability of equilibrium; and
(iii) the eect on employment of changes in certain variables. (Meade, 1937,
p. 98)
Meade began with seven assumptions about specic elements in the economy (e.g.,
that the prime cost in every industry is wages); these were followed by a list of the
eight conditions (e.g., that prices of goods are equal to marginal costs; and that
total income equals wages plus prots) under which an economy based on the
seven initial assumptions will be in short-period equilibrium. From these, Meade
constructed eight relationships, mirrored in a mathematical model. (Just as Alfred
Marshall [1890] kept his diagrams in the footnote, Meade kept his mathematical
model in his Appendix, clear evidence that such models were still not the accepted
and acceptable way of doing economics.) It is these eight relationships – the model –
that Meade reasoned with in the rest of the paper, telling us that:
By means of these eight relationships we can show that the volume of
employment is determined for every given supply of money, for every
given money wage-rate, and for every given proportion of income saved.
(Meade, 1937, p. 99)
We might ask where this requirement to determine the volume of employment
came from? It did not come from the model itself, which is Meade’s interpreta-
tion of the main contribution of Keynes’ book: namely the development of a
“models purporting to represent Keynes’s message” (p. 1). eir survey of these models (translated
into common format, and with modern modelling terminology) discusses eight papers, reviews,
or responses that appeared in print in the period 1936–8.
10 is is the same Meade who helped Phillips design the second, or Mark II hydraulic machine at
LSE (see Chapter 5). Meade’s (1907–95) training and career were associated with Oxford, London
School of Economics (LSE), and Cambridge; Samuelson (1915–2009) was associated with
University of Chicago, Harvard, and MIT; and Hicks (1904–1989) was associated with Oxford,
LSE, and Manchester. All three economists became Nobel Prize winners.
Questions and Stories 223
macroeconomic aggregate account that integrated the real and monetary side of
the economic system. It came rather from an understanding of the main economic
problem and policy question of the day that Keynes’ book addressed: solving the
unemployment problem of the Great Depression.
But before he could get to grips with that question about employment, Meade
had to satisfy himself about the nature of the world in his model. Just as Frisch had
checked that his model world could generate cycles in economic activity and that
these would dampen down to make sure it fullled the necessary requirements
to be a business cycle model, Meade rst checked that his mathematical model
world would return to an equilibrium situation following a change in one element
of the system, and that this equilibrium point would be a stable one (his points (i)
and (ii) in his introduction). is habit of checking if certain general mathematical
qualities that t broader economic assumptions hold in the world of the model is a
general feature of modelling in economics, and so oen features as the rst usage of
a model. And, as we have seen with Frisch, it was the general assumption of his gen-
eration of economists that the economic system is one that tends to return to posi-
tions of rest following a disturbance.11 Somewhat disarmingly, Meade concludes
his model checking with: “It is of course possible that in the real world the system
is unstable” (p. 102) but he continues with his model on the basis that it would be
dicult to carry out his analysis of employment unless the system were stable (a
point illuminated by Samuelson’s work; see below). And while this comment might
have struck a reader living in the earlier 1930s as ironic (given that so many econ-
omies did seem to be stuck at the bottom of the cycle), by 1937, the economy was
beginning to recover, which seemed to support economists’ beliefs about the nature
of the economic system.
We have already noticed that, in this domain of model questions, the demand
for labour – the most pressing problem of the Great Depression in the U.K. con-
text – is the critical criterion for Meade. He works through four cases to answer the
questions: What is
. . . the eect on employment of (1) a reduction in interest rates, (2) an
increase in the total supply of money, (3) a reduction in money rate-wages
[sic], and (4) a reduction in the proportion of income saved? (Meade, 1937,
p. 102)
In addressing these questions, he works through the model, tracing the eects of
changing one thing in the model (while holding certain others constant) to see the
outcomes of such changes on all the intervening elements (whether it raises or low-
ers other things in the model) as well as on the “short-period demand for labour”.
11 ese checks – to see what happened to the short-period equilibrium of the model when some
element in it was changed – were discussed verbally in the text and demonstrated formally in the
appendix with the mathematical model. On the history of mathematical analysis of dynamics
and stability analysis, see Weintraub (1991), who gives considerable attention to Hicks and to
Samuelson (he does not discuss Meade’s work).
e World in the Model
224
For each question put to the model, the answer involves an implicit set of causal
links, signalled by the order in which the tracing process is followed. is tracing
allows consideration of whether each of the linked changes that occur are plausible
ones in the context of the economic world portrayed in the model, but perhaps also
in the context of the economic world that Meade lived in. ese are the narratives of
model usage: each answering argument to each question oers a narrative sequence
of connected events as each change alters the value of some other element in the
model; this requires tracing all these changes through the various relationships in
the model.
At one point Meade traces through the eect of two of these critical factors
changing at once, and unusually the changes are specied in size. is provides an
eective illustration of model narratives, so I report the narrative reasoning verba-
tim here:
Suppose that there were a 10 per cent reduction in all money wage-rates
combined with a 10 per cent reduction in the supply of money. en if out-
put and employment remained unchanged, the marginal prime cost and so
the price of all commodities would fall by 10 per cent in view of the 10 per
cent fall in the money wage-rate; and in consequence all money incomes
would fall by 10 per cent. Ten per cent less money would be required to
nance current transactions, and, as the total supply of money is also
reduced by 10 per cent, the supply of “idle” money would also have fallen
by 10 per cent because of the 10 per cent fall in money incomes. Money
investment would also have fallen by 10 per cent if expected prots had
fallen by 10 per cent; for the rate of interest being unchanged, and supply
price of capital goods and the expected money yield on them having fallen
by 10 per cent, there would be no incentive to change the value of real
investment, so that . . . (Meade, 1937, p. 103, his italics)
Meade’s text shows how this tracing process produces the narrative that accom-
panies his use of the resources of the model: each narrative begins with a starting
point given by the question asked, and follows the order that the model is solved to
reach outcomes.12
We can see the general features of model usage here: in using his model to answer
economically interesting problems, Meade began with questions (about employ-
ment in relation to other things in the economy). He used his model resources
(the eight equations) to answer them, and in doing so told a series of stories with
the model – for these questions required attention not only to nal outcomes but
also to the multiple intervening elements, processes, and side eects, on the path to
them. e stories were shaped by the mathematics of the content and constrained
by it, but not fully determined by it. e decision what to change depended on
12 Readers may recognise that this is fundamentally the same method used by Ricardo in arguing
with his accounting model farm, discussed in Chapter 2.
Questions and Stories 225
the economic question, and the description of what happened depended on the
economic content of the model, so that the narratives were economic stories about
the world depicted in the model. In the process, the eect of whatever happened on
the demand for labour (the 1930s problem) was assessed in its own terms but also
for various other impacts on other elements in the model. So, the way the question
was asked, the objects of interest, what else was held constant and what allowed to
vary, and the order of solution: all these aected the way any particular story was
told. As Barthes wrote in a very dierent context: “meaning is not ‘at the end’ of the
narrative, it runs across it” (1982, p. 259).
3.ii Reasoning with Models: e External and Internal Dynamics
Reasoning with models involves four closely related elements. Scientists create a
model to answer a set of questions they nd of interest. ey manipulate the model
to demonstrate the answers to those questions. In the process they tell narratives
about the world in the model, narratives that might also be useful for understand-
ing the world that the model is made to represent. We can write these down as four
steps, but of course as we have already seen with Meade, they are not completely
separate, or indeed separable, activities:
Step 1: Create or Construct a model relevant for a topic or problem of interest.
Step 2: Question that model world: the ‘external dynamic’.
Step 3: Demonstrate the answer to the questions using the model’s resources:
the ‘internal dynamic’.
Step 4: Narrative accompanies the demonstration to link the answers back to
the questions and to their domains: both to the world in the model and the
world that the model represents.
Model-making: the activity of representing or denoting some aspect of the
world into a model was discussed in the earlier chapters of this book.13 e fea-
tures that are unusual in the account here are my insistence on questions as a sep-
arate element in the way models are used and the claim that demonstrations with
models are inextricably bound up with narratives or stories (at least in the way
that economists use models). ese narratives not only provide the form in which
questions are answered but also help economists to learn and understand things
about the world in the model, and/or provide interpretations and insight into the
world that the model represents. So these narratives provide the correspondence
13 Steps 1, 3, and 4 here are parallelled in R. I. G. Hughes’ (1997) DDI account of the way models are
used in physics: Denote, Demonstrate and Interpret. Denotation, is his word for the model-making
practices analysed in my previous chapters. His terminology follows Nelson Goodman (1968,
p. 5), who points out that denotation entails representation, but is independent of resemblance
and I am happy to follow Goodman’s sense of the matter (see Chapter 1 for a further discussion). I
add in as Step 2: Questions, for they are essential to the way that a model is used. For his nal Step
3: Interpretation, I use the term Narrative.
e World in the Model
226
links between the demonstration made with the model and the events, situations
and processes of change in the real world. I discuss questions and the model
resources that enable demonstrations next; stories or narratives are discussed later
in the chapter.
Models have to be ‘questioned’ to make use of their resources. I call such ques-
tions the ‘external dynamic’ because they are the prompt for the economist to begin
manipulating their model. Economists typically begin their model usage with a
question about something in the model or in the world. For example, a query may
be raised by a casual observation about something in the world that needs account-
ing for. Or the prompting question might occur by considering a change to some
term in the model implied by a policy option. Equally it may be a question about
the world in the model, for example, about the modication of an assumption that
seems interesting from a theoretical point of view such as whether the model has a
tendency to equilibrium. Such questions as “How does it happen that . . . . .?”, “What
happens if . . .?” or a “Let us assume that . . .” prompt some term or element in the
model to be set at a new value or a modication is made to the model to represent
the question or arrangement, just as in Meade’s account, which we can take as fairly
typical. So, the external dynamic is not ‘external’ in the sense that it is motivated by
the events of the world rather than the contents of the model but in the simple sense
that it comes from the scientist-user.
en, it is in using models to answer questions that we nd demonstrations
going on; and these depend on the ‘internal dynamic’. is term comes from
Hughes work on physics:
Its [the model’s] function is epistemological. To be predictive, a science
must provide representations that have a dynamic of this kind [provided
by mathematics] built into them. at is one reason why mathematical
models are the norm in physics. eir internal dynamic is supplied – at
least in part – by the deductive resources of the mathematics they employ.
(Hughes, 1997, p. 332)
It is indeed tempting to think that the deductive work of models is determined
only by their mathematics. But deductive resources of models in economics are not
restricted to any particular form: the model could be mathematical (geometric, or
algebraic, or arithmetic) but need not be, for there are deductive resources in many
diagrammatic or material object models (think of the hydraulic machine of Chapter
5). But it is an essential characteristic of models that they have resources that can
be manipulated to produce outcomes; otherwise no demonstrations are possible.14
14 It is a good place to note here if it is not already obvious that the ‘internal dynamic’ of a model does
not require a model to have dynamic properties, nor to have conventionally understood deductive
resources, in the mathematical sense. Similarly, not all models appear as mechanisms that have to
be ‘cranked’ to make demonstrations. e claim is merely that to be useful in economics, models
must have some manipulable resources that can be put to work to answer questions, whether this
is by arithmetical simulation, algebraic solving, or setting a machine to work, or whatever.
Questions and Stories 227
And, as I have already suggested in Chapter 1, the workable content of a model
hangs not just on its manipulable resources, but on a broader combination of those
resources as well as their rules for manipulation. In my account, these together form
the internal dynamic used in model demonstrations. We can see both illustrated in
Meade’s case.
e rules of reasoning that are applied to any model can be understood as lan-
guage rules, and content-based rules (as also discussed in Chapter 1). If a model is
created as a set of equations as Meade’s model, the rules for manipulating it or for
reasoning with it come from algebra, so he could use the deductive reasoning mode
of that particular mathematical language to demonstrate certain outcomes of the
model. But the particular economic content of a model also determines some of
the rules for manipulation or reasoning. For Meade, the assumptions in Keynesian
macroeconomics determine the allowable starting points and forbid other starting
points, and they dictate the causal ordering of the variables in the order of model
manipulation. But these two sources of rules may not be easily separable into lan-
guage and subject matter for, of course, the economics has been expressed into that
language in making the model. Nevertheless, economic content does supply some
of the rules of model manipulation and thus the possibilities for reasoning with the
model. We saw how Ricardo’s model farm (Chapter 2) used an accounting logic,
and the rules for manipulating his farm accounts were set by that language; but the
economic content in his model – his classical laws and assumptions – also dictated
some of the rules, and constrained the ways in which he manipulated his model
farm accounts.
It is evident, of course, from the examples in this chapter, that these rules of
reasoning must have content to work upon, namely the model resources. Meade’s
model of eight equations contained many such resources. In contrast, Frisch’s
Tabl e au Économique, a visual sketch, provided some resources to reason with, but
little that could be used deductively until he turned it into a mathematical model,
which contained fewer subject matter resources, but more manipulable qualities.
So, the resources of any model provide the materials on which the rules of reason-
ing appropriate to it can be used and it is this ‘internal dynamic’ that scientists use
to demonstrate answers to their questions.
One of our earlier cases in which the rules and resources are very clearly
demarcated is the material object model of the Newlyn-Phillips Machine discussed
in Chapter 5. ere the language of the model is not a mathematical one, but the
language of real hydraulics, and the economic content has been denoted into ows,
stocks, and tanks of water too. e circulation and manipulation of the ows of
water representing the ows of money are governed by the hydraulics. But the ows
are, in turn, controlled by valves and “slides” in which the economic relations are
expressed. Evidently the reasoning rules – the subject matter rules and the language
rules – come from dierent sources, but they work simultaneously together on a
machine with many resources for demonstration. Together, they create the internal
dynamic of that model in making demonstrations.
e World in the Model
228
3.iii Modelling Keynes’ General eory: Samuelson
We can see how the questions or external dynamic and the internal dynamic
together create and enable demonstrations in another of the contemporary attempts
to make sense of Keynes’ ideas by the use of modelling. Alvin Hansen is generally
regarded as the American interpreter of Keynes, and the young Paul Samuelson,
in one of his earliest papers in 1939, adopted Hansen’s model of Keynes’ ideas to
explore the joint roles of the “multiplier” and “accelerator”, the two relations that
came to be understood as important for total eective demand in the Keynesian
system. Samuelson’s model was:
(1) Yt = gt + Ct + It
(2) Ct = αYt – 1
(3) It = β(Ct – Ct – 1)
where Y is aggregate national income, g is government expenditure, C is con-
sumption expenditure, I is induced private investment, and t is the time indi-
cator. In this model, equation (1) is the normal Keynesian aggregate (national)
income identity; relation (2), the Keynesian aggregate consumption function is
interpreted as the multiplier relation, and (3) is interpreted as the accelerator
relation. In this model, when government spending increases, income rises, but
in successive time periods the initial increase in national income that this creates
is ‘multiplied’ by an increase in consumption and ‘accelerated’ as the increase
in consumption induces increases in private investment. ese interpretations
rely on the time dependencies in the relations (noted in the subscripts) and the
format of the model, which links decisions by dierent groups of people in the
economy through time, based on the modelling practices of the Dutch econo-
mist Jan Tinbergen and the younger economists of Wicksell’s Stockholm school.
As Samuelson argued, this combination of the multiplier and accelerator rela-
tions was responsible for the novelty of his results, but also their complexity.
Rather than checking that his model exhibited “well-behaved” stable equilibria
in advance of his more specic questions, as had Frisch and Meade, Samuelson
chose rst to use simulations to examine how this model world worked and to
show that it was not always well behaved.
Samuelson’s question, the external dynamic, was: “What happens if government
expenditure increases?” and was primarily an enquiry into the world of the model,
the world of Keynesian economic theory. He rst carried out some arithmetical
simulations of the model to show how the two relations (2 and 3) in the model
interact. Each simulation is based on injecting into the model world a continu-
ous stream of single units of government spending in each period, setting o, via
the model equations, a sequence of changes in aggregate income over succeeding
time periods. He traces out several such sequences for aggregate income in tabular
form (his table 2, our Figure 6.1), according to the values chosen for the param-
eters in the two relations (seen in the top row of the table). ese dierent starting
points and settings are what Samuelson calls his “hypotheses” about the world in
Questions and Stories 229
the model. e rst of these columns represents the model with only the multiplier
relation at work (β is set at zero), and shows an increase in aggregate income up to
a certain point, but no cycles. Of these other three simulated sequences where both
relations are active, one produces cycles that are regular but undamped, one explo-
sive cycles in aggregate output, and the last one exponential increases in output.
at is, the question and model do not alter, but with dierent parameter values for
the same model, the internal dynamic of the model – its resources and reasoning
rules – enable Samuelson to demonstrate dierent sequences in the arithmetical
simulations and so tell a set of dierent narratives. And these dierent narratives
suggest that, for many values of the parameters, unlike Meade’s model, the system
is not stable nor does it have a well-behaved tendency towards equilibrium.
As Samuelson noted of these demonstrations with the model:
By this time the investigator is inclined to feel somewhat disorganized.
A variety of qualitatively dierent results emerge in a seemingly capri-
cious manner from minor changes in hypotheses [settings of the model].
Worse than this, how can we be sure that for still dierent selected values
of our coecients new and stronger types of behaviour will not emerge? Is
it not even possible that if Table 2 [the arithmetic simulation results in our
Figure 6.1] were extended to cover more periods, new types of behaviour
might result for these selected coecients?
Fortunately, these questions can be given a denite negative answer.
Arithmetical methods cannot do so since we cannot try all possible val-
ues of the coecients nor compute the endless terms in each sequence.
Nevertheless, comparatively simple algebraic analysis can be applied which
Figure 6.1. Samuelson’s Arithmetic Simulation.
Source: Paul Samuelson (May, 1939) “Interactions between the Multiplier Analysis and the
Principle of Acceleration”, e Review of Economics and Statistics, 21:2, 75–78; table 2 on
p. 77. Reproduced with permission from MIT Press Journals.
e World in the Model
230
will yield all possible qualitative types of behaviour and enable us to unify
our results. (Samuelson, 1939, p. 76)
Using his model (above), Samuelson then solves for the dierent roots of the equa-
tion system as a whole.15 He maps these solutions onto a graph (Figure 6.2) where
the axes denotes the values of the parameters (α and β) in the multiplier and accel-
erator relations, so that
It can be easily shown that the whole eld of possible values of α and β can
be divided into four regions, each of which gives qualitatively dierent types
of behaviour. . . . . . Each point in this diagram represents a selection of val-
ues of the marginal propensity to consume and the relation [the accelerator
relation]. Corresponding to each point there will be a model sequence of
national income through time. e qualitative properties of this sequence
depend upon whether the point is in region A, B, C, or D. (Samuelson, 1939,
p. 77, his italics)
Each region (on Figure 6.2) marks out an area with a dierent qualitative story as to
what happens to the behaviour of aggregate income as the quantitative values of the
two parameters in the model vary together. e government action is also allowed
to vary: that is, the external dynamic changes to ask what happens if government
spending is a single impulse, or a continuous impulse (as in his rst arithmetic
simulations), or follows a cyclical pattern. So, for example, a single period of gov-
ernment spending creates a gradual return back to the original level of aggregate
income in region A, damped oscillations around that level in region B, explosive
oscillations in C, and explosive growth in D. e eects of alternative government
actions within the world of the model are also explained in the qualitative stories
for each region of the map. e behaviour of aggregate income is thus characterized
in terms of periodicity, damping factors, and eectiveness of government expendi-
tures used to pump-prime national income.
So, by the use of analytical solution methods, Samuelson is able to take account
of joint variation in both multiplier and accelerator parameters and to demonstrate
how these varied together over the full range of values, rather than just for those
values chosen in his earlier arithmetic simulations. He is also able to demonstrate,
using the model’s resources of the multiplier and accelerator relations, how some
rather bizarre narrative results come from what seemed to be simple assumptions
about parameter values in those behavioural relations and about policy actions. For
example, as he explains, in region D, with large values of the two parameters (as in
his fourth column of his table 2), either single or constant increases in government
expenditure will send national income increasing dramatically; but there is a down-
side too, for a small disinvestment by the government will “send the system ever
downward at an increasing rate. is is a highly unstable situation, but corresponds
most closely to the pure case of pump-priming” (Samuelson, 1939, p. 78).
15 For example, where gt (government expenditure in time t) equals 1 unit, the system to be solved
becomes: Yt = 1 + α[1 + β]Yt – 1 – αβYt – 2
Questions and Stories 231
e chart and its regions enable Samuelson to demarcate, and type, the full
range of possible stories about what will happen to aggregate income in the world
of his Keynesian model from using the model resources (the internal dynamic) to
answer questions about changes in government spending (the external dynamic).
Samuelson claims that the generality – meaning both the full range and their
classication – of these new stories compared to previous analyses is useful. But
note that it is not the equation solutions themselves that are interesting here.
Rather it is the range of government actions assumed in the questions (the exter-
nal dynamic), the range of parameter values in his hypotheses, and the patterns
of economic behaviour reported in the narrative answers attached to the map.
ese narratives succinctly summarise the relations between questions, hypothe-
ses, and outcomes: it is these that are demonstrated by using the internal dynamic
of the model.
With Meade and Samuelson we have a range of examples of questions (the external
dynamic) and answers in which we see how the internal dynamic of their models are
used to demonstrate dierent outcomes, or even kinds of outcomes, as each question
Figure 6.2. Samuelson’s Model Solution Graph.
Source: Paul A. Samuelson (May, 1939) “Interactions between the Multiplier Analysis and the
Principle of Acceleration”, e Review of Economics and Statistics, 21:2, 75–78; chart 2 from p. 78.
Reproduced with permission from MIT Press Journals.
e World in the Model
232
changes the set-up or details in the model. ey both used small algebraic Keynesian
models, Samuelson’s a much simpler model than Meade’s. Meade kept the same model
throughout and asked dierent questions, telling dierent stories as he manipulated
the model resources to trace through answers to those questions. Samuelson asked
variations on the same general question of his one model, but with dierent param-
eter values creating dierent stories in conjunction rst with arithmetic simulation
methods and then with analytical solution methods. While Meade had checked the
‘good behaviour’ of his model (that it fullled certain requirements of stability) before
using it to investigate the possibilities of government policy, Samuelson showed how
certain government actions could destabilize the behaviour of the economic world
in the model. As we see from this brief comparison with Meade, there are dierent
ways to manipulate the same kinds of model resources, even while these manipula-
tions are still determined by the same language of the model and its similar economic
content. Dierent questions and dierent modes of demonstration create dierent
stories, showing the importance of understanding the nature of the internal dynamic
to the possibilities of demonstrations made with the model.
ese examples also point to the important role of the scientist both in ask-
ing the questions and in carrying out the manipulations necessary for the dem-
onstrations. e model itself does not pose the question and the internal dynamic
does not work without an external dynamic. Scientists pose the question or the
‘external dynamic’, and put the model to work to make use of its ‘internal dynamic’
to demonstrate some answer with the model. e model cannot demonstrate these
answers by sheer deductive logic or unadulterated mathematics without the prompt
given by the subject matter question, which both determines and constrains, how
those deductive resources are used. en, using the appropriate rules of reason-
ing, elements in the model have to be mentally or physically shied around on the
diagram, or the algebra has to be manipulated and solved through, for the econo-
mist to demonstrate answers. Even with models in which the system can be pro-
grammed to solve itself (so to speak), as in computer simulations with certain kinds
of mathematical models or the hydraulic Newlyn-Phillips machine (see Morgan
and Boumans, 2004), each time the scientist asks a question, the model has to be
calibrated properly and set going to answer the relevant question. Models may
require more or less human manipulation to provide demonstrations, but they do
not manipulate (or solve) themselves, nor will they do so in the absence of an exter-
nal dynamic provided by the scientists’ questions.
4. Finding New Dimensions and Telling New Stories
4.i Modelling Keynes’ General eory: Hicks
In 1937, John Hicks, another British economist, introduced a ‘little apparatus’,
a model in two diagrams (derived from three equations) that grew into the cel-
ebrated IS/LM model of the Keynesian system. Hicks rst gave his account at a
Questions and Stories 233
meeting of the Econometric Society in Oxford in 1936, a meeting where those
interested in developing statistical and mathematical modes of reasoning into eco-
nomics had gathered. ese included the two economists most closely associated
with the development of macro-modelling, the Norwegian economist, Ragnar
Frisch (whose 1933 model was discussed above) and Jan Tinbergen, the young
Dutch economist who introduced the term “model” into economics, and had by
this time produced the rst macroeconometric model and tted it to data for the
Dutch economy.16 ough these two later (in 1969) won the rst Nobel Prize in
economics for these developments, it was Hicks’ diagram that gained longevity as a
working object in economics. His model, rst developed to represent Keynes’ ideas,
“became the organizing theoretical apparatus of the emerging discipline of macro-
economics” in the postwar years, and remained a generic tool for macroeconomic
analysis.17
Hicks’ agenda was to nd a way to compare Keynes’ account of the macro-
economy with the older classical account to pinpoint what was truly innovatory in
Keynes’ work. To do this he created a model within which he could represent both
accounts. He began by denoting with symbols the elements in the Keynesian theory
and, with these, constructed a small system of three functional relationships. He
produced four sets of these three relations, of which two sets are given here (from
his pp. 152 and 153).18
Classical theory: M = kI, Ix = C(i), Ix = S(i,I)
Keynes’ General eory: M = L(I, i) Ix = C(i), Ix = S(I)
where M is the given quantity of money, I total income and Ix investment, and i
the interest rate. Hicks’ use of such symbols hardly went further than labelling the
terms in the equations and using them to outline verbally his understanding of the
existing theories. From this kind of analysis, he claimed that there was nothing
particularly new in this second set of these equations – those he took to repre-
sent Keynes’ General eory – compared to the theory around in Cambridge of the
time.
In this kind of Keynesian macroeconomics, it is very dicult to follow the ver-
bal arguments and see what is determining what in any given discussion.19 It was
just such kinds of convoluted verbal reasoning that, continuing in macroeconomics
16 is model too had been questioned for historical explanations and simulated for policy options
(see chapter 4, Morgan, 1990).
17 For more general accounts of the history of the IS/LM model, see De Vroey and Hoover (2004),
particularly their introduction (p. 3 quoted here); and on what was lost as IS/LM became the
dominant model, see Backhouse and Laidler (2004) in that volume.
18 e other two sets denote Hicks’ version of “Mr Keynes’ special theory” and the “Treasury View”
(Hicks, 1937, p. 152).
19 Indeed, students nowadays nd Hicks’ original paper as impenetrable as Keynes’ book, for the
model, and what it might show, are both opaque to them. In contrast, Samuelson’s paper holds
no horrors for them. is demonstrates rather nicely how both Samuelson (and Meade’s) papers
can be considered ‘modern’ in modelling terms, while Hicks’ IS-LL diagram became claried and
understood only through much usage and further development by others.
e World in the Model
234
into the 1950s, prompted Newlyn and Phillips to turn macroeconomics into an
hydraulic machine (as we saw in Chapter 5). Hicks’ reasoning possibilities also
proved limited by the deductive resources of his equations and he, like Frisch,
Meade, and Samuelson, found the need for a more workable model to make pro-
gress in representing the complicated project of Keynes’ work and to understand
the dierence between the two sets of equations – of Keynes and of the classicals.
As he said, “Is there really any dierence between them, or is the whole thing a
sham ght? Let us have recourse to a diagram” (Hicks, 1937, p. 153).
Hicks’ diagrammatic model, his gure 1 (le side on Figure 6.3) was not sim-
ply a transposition from one form (equations) to another (diagrams), but involved
a second move of abstraction in which he moved from the labels and terms (as in
the equations) to derive relations from these that revealed more clearly the implica-
tions of their connections. e LL curve represents, for a given quantity of money,
the relation between aggregate income (on the horizontal axis) and the rate of
interest (on the vertical axis), drawn from the rst equation in the Keynesian sys-
tem. e IS curve came from the two other equations and was drawn to show the
relations between income and interest “which must be maintained in order to make
saving equal to investment” (p. 153). is derivation of the curves for his diagram-
matic model appears an eective conceptual innovation, one that prompted Hicks
towards a new analysis.20 ough he had found nothing new in the equations, this
diagrammatic modelling changed the dimension of the representation in a way that
enabled him to recognise and dene what he took to be the real novelty in Keynes’
account:
Income and the rate of interest are now determined together at P, the point
of intersection of the curves LL and IS. ey are determined together;
just as price and output are determined together in the modern theory of
demand and supply. Indeed, Mr. Keynes’ innovation is closely parallel, in
this respect, to the innovation of the marginalists. e quantity theory tries
to determine income without interest, just as the labour theory of value
tried to determine price without output; each has to give place to a theory
recognising a higher degree of interdependence. (Hicks, 1937, pp. 153–4)
e point here is not whether Hicks had ‘the correct interpretation’ of Keynes’
theory, but that in making the conceptual leap into this new model diagram and
answering questions with it, he created a form of Keynesian economics not just for
himself but for a generation of economists.
Hicks’ attempts to gure out further aspects of Keynes’ work prompted him to
think about the shape of the LL curve and to create his gure 2 (right-hand side of
Figure 6.3), where he argued that there was some minimum level of interest rate
in practice (a topical issue for the 1930s), and some maximum level of income
20 is situation is similar to the way Edgeworth’s development of indierence curves in the Box
diagram created new conceptual resources (see Chapter 3).
Questions and Stories 235
that could be nanced with the given quantity of money. Using this second gure
enabled him to compare theories in a way that illuminated their dierences. He
characterized the classical theory (in its recent Cambridge version) as the situation
when the IS curve cut the LL curve on the rising section to the right: where
An increase in the inducement to invest will raise the rate of interest, as
in the classical theory, but will also have the subsidiary eect in raising
income, and therefore employment as well (Mr. Keynes in 1936 is not the
rst Cambridge economist to have a temperate faith in Public Works).
But if the point P lies to the le of the LL curve, then the special form of
Mr. Keynes’ theory becomes valid. A rise in the schedule of the marginal
eciency of capital only increases employment, and does not raise the rate
of interest at all. We are completely out of touch with the classical world.
(Hicks, 1937, p. 154, his italics)
e shape of the LL curve represented dierent states of the economic world; the
dierence in theories came down to where the IS curve cut this LL curve. If the
money supply increases, the LL curve moves to the right (see the dotted line on
Figure 6.3). But if P remains on the le-hand section, then such a monetary policy
will fail to change the rate of interest and so fail to restart the economy.
Demonstrations with these curves enabled him to explain why the classical
policy response of increasing money in the system would not get the economy out
of the Great Depression. But they also showed him why his diagrammatic model
and reasoning mode was helpful, for they revealed that the problem was more com-
plex than his initial version of the Keynesian equations suggested. Hicks regarded
his diagram almost as a physical piece of apparatus:
Figure 6.3. Hicks’ IS-LL “Little Apparatus”.
Source: J. R. Hicks (April, 1937) “Mr. Keynes and the ‘Classics’; A Suggested Interpretation”
Econometrica, 5:2, 147–159; gures. 1 and 2, p. 153. Reproduced with permission from e
Econometric Society.
e World in the Model
236
In order to elucidate the relation between Mr. Keynes and the “Classics,” we
have invented a little apparatus. It does not appear that we have exhausted the
uses of that apparatus, so let us conclude by giving it a little run of its own.
With that apparatus at our disposal, we are no longer obliged to make
certain simplications which Mr. Keynes makes in his exposition. (Hicks,
1937, p. 156)
e diagram encouraged him to rethink some of the equations, so he made his
investment equation dependent not only on the interest rate but also on income. is
version of the equations had the eect of creating a more gradual rising LL curve on a
new version of the diagram so that the slopes of both curves became critical in deter-
mining the eects of changes in any elements in the diagrammatic model.
Hicks had made himself a model that he could work with: one that he could
ask questions of and demonstrate answers with, and that enabled him to go beyond
the “simplications” be found in Keynes’ book. It enabled him to explain and
“elucidate” the dierences between the two systems of theory, the classicals ver-
sus the Keynesian one. And, it enabled him to tell a story about what happened in
Keynes’ special case when there was no response of investment to lowering of inter-
est rates. In addition, he used it to work out and tell stories about other outcomes,
associating these, wherever possible, with the names of other economists whose
positions they represented. For example, he considered the interesting possibility
that the IS curve might be horizontal, another special case version of the model
that he labelled as Wicksell’s account. He was able to represent and discuss dierent
theories from dierent economists quite easily in the world of his little diagram.
Finally, he was also able to represent dierent states of the world using his model,
ones that might arguably be relevant for discussing and telling narratives about the
real world of the Great Depression.
Despite the many states of the economy he managed to represent, and the mul-
tiple economists whose ideas he managed to express as special cases within the
model, and the demonstrations that enabled him to show and explain things with
his model, Hicks ended by describing his invention as a “skeleton apparatus” for there
were all sorts of things that “you cannot get into a curve” (p. 158). Nevertheless, it
is because of its exibility to express lots of dierent theoretical identities and so
be used for dierent demonstrations that this new IS/LM diagram (it was renamed
by Hansen) had such a long life as a model. In some senses it never really died but
continued hidden inside policy models even though it fell out of fashion for theo-
rists. And, despite its multiple identities, and multiple users, it has remained rmly
attached to Hicks’ own name as inventor.
4.ii Demonstrations, Variety, and Fruitfulness
We have seen, with these three dierent reactions to Keynes’ work, how modelling
works as a method of enquiry, into both the nature and details of Keynesian theory
and into its portrait of the real economy. e answers to the questions that economists
Questions and Stories 237
raise depend on their model demonstrations, and this is where economists learn new
things from using their model that they did not know before, new things about the
world in the model that perhaps reect insight into the world that the model repre-
sents for, as Hughes (1997) suggested, “From the behavior of the model we can draw
hypothetical conclusions about the world over and above the data that we started
with” (p. 331). Of course, these “hypothetical conclusions” are conclusions only about
the world of the model and whether they transfer to the world that the model denotes
is a very tricky topic to which I return (later and in Chapter 7). It is evident from these
three cases that for models to be useful for enquiry, that is, for economists to learn
new things from their demonstrations, their models need certain qualities.
First, we have seen in these examples the importance of my argument that
models need sucient resources that can be manipulated to demonstrate or show
certain things with the model if they are to be useful as a means of enquiry. ey
must have sucient internal dynamic to answer some questions, that is, to make
some relevant demonstrations; models that have few resources have very limited
potential to produce demonstrations. As we saw, Hicks’ little sets of equations did
not provide him with the resources or rules of manipulations to do more than char-
acterize the dierences between the theories he was investigating. It was only when
he moved to a new form of representation, his “little apparatus”, that he had a model
with sucient internal dynamic to develop some new insight into questions about
Keynes’ theory. Samuelson’s model, a minimalist model, nevertheless provided
the resources, via two dierent ways of reasoning (simulation and analytical solu-
tions), to explore certain aspects of the Keynesian claims, with results that proved
quite surprising. Meade’s model – a causal model of the macroeconomy – had the
resources for him to develop quite complex accounts of how the macroeconomy
he portrayed might behave under a wide range of possible actions. In other words,
all these modellers produced dierent models of Keynes’ General eory that we
might call ‘workable’ – they could be put to work to demonstrate certain charac-
teristics, processes, independencies, outcomes, and so forth, oen ones that were
unexpected or new to the investigator.
Second, size in relation to content matters. Models must be suciently small
or simple to be manipulable, and yet suciently complex or sizeable to embody
the kind of resources that allow for fruitful investigation, and so demonstrations
that develop new or unexpected ndings. Yet models must not be too open-ended;
rather they must constrain in some degree, otherwise their demonstrations may
not be productive. Samuelson’s models produced almost too many outcomes: any
pattern in aggregate behaviour seemed consistent with his model.
ird, to generate interesting answers to questions in these demonstrations,
there must be some economic subject matter content in the workable resources. We
saw rst in Frisch’s case how the physical (non-economic) stories shaped the bits
of his model, but that he required an economic understanding of his model before
he could interpret the resulting demonstrations in a meaningful economic way.
For Meade, Samuelson, and Hicks, the internal dynamic already had economic
e World in the Model
238
content so that it could be immediately reected in the narratives told with the
model demonstrations. ese economics resources were based on time relations
(Samuelson), on causal orderings (Meade), or on possibilities of alternative inter-
pretations (Hicks). And critically perhaps, these resources might be at a dierent
conceptual level than those portrayed in the verbal language theorizing as we saw
in Hicks’ IS/LM diagram.
Fourth, models give rewarding demonstrations when they embody the kinds of
resources that create a certain amount of variety. Hicks’ model had the resources for
showing, and allowing him to compare, the dierent theories of many economists.
Samuelson’s model had the resources to demonstrate an extraordinary dierent
range of behavioural outcomes from the same stimulus of government expendi-
ture, with very dierent implications. e variety in Meade’s model was developed
in the range of behavioural or causal accounts and policy analyses he could make
with the same model. e possibility of variation allows explorations of dierent
theoretical positions, of the relative importance of dierent assumptions, and of
dierent world situations and behaviours.
Making demonstrations is the modelling activity that enables economists to
nd things in the world of the model that are new to them, that are not previously
recognised, or not fully understood. Clearly it is useful if a model demonstrates
things that accord what the economist already knows, but the payo from model-
ling lies in the unexpected outcomes, the demonstrations that surprise the econo-
mist (a topic to which I return in Chapter 7). And while these cases of Keynesian
modelling enable us to recognise the characteristics that made these particular
models useful for enquiry in terms of fruitfulness and variety of the demonstra-
tion possibilities, there is no metric that allows us to recognise or guarantee these
possibilities in advance. While it is probably self-evident that the possibilities
of the Newlyn-Phillips machine (of Chapter 5) are of an almost endless variety
because of the nature and mixture of the resources in both hydraulics and econom-
ics, it would probably not have been easy to predict that the Edgeworth Box (of
Chapter 3) would have been a fruitful model. In its initial version, it does not look
to have much workability or variety of applications as an instrument of enquiry, yet
it developed into a kind of nutshell model that has somehow come to represent the
neoclassical system of theory as a whole (see Chapter 10). Similarly, no one could
possibly have predicted the manifold usefulness, fruitfulness, and long working life
of Hicks’ IS-LL diagram at its birth, despite Hicks’ ability to use it to demonstrate
aspects of many dierent versions of macroeconomics.
While it is dicult to predict that a model will create new outcomes, or show
fruitfulness and variety – it is rather easier to recognise these qualities post hoc
from the narratives that go along with their usage. Narrative is the place where
these demonstrations are interpreted within the world of the model and in terms
of the things in the world that the model describes. e interpretations are not
where novelty lies; novelty and learning come in the things demonstrated with the
models, and narratives are the way to understand their importance and relevance
in answering the questions asked.
Questions and Stories 239
5. Capturing the Heart of the Matter with Narratives
Storytelling is not just a curious feature of Meade’s and Samuelson’s work, for it is a
matter of observation that economists commonly tell stories or narratives when they
carry out investigations with models. And though this practice is now mostly evi-
dent in their spoken rather than written arguments, it remains an essential element
of seminars and explanations using models. Commentators especially interested in
the practices of economists have discussed the prevalence of stories; for example,
McCloskey made the following observation on the rhetoric of economists:
Economists, especially theorists, are for ever spinning ‘parables’ or tell-
ing ‘stories’. e word ‘story’ has in fact come to have a technical mean-
ing in economics, though usually spoken in seminars rather than written
in papers. It means an extended example of the reasoning underlying the
mathematics, oen a simplied version of the situation in the real world
that the mathematics is meant to characterize. (McCloskey, 1983, p. 505)
e account of such model stories in this chapter suggests that they are not pri-
marily a rhetorical practice but an epistemic one, and perhaps this is why econo-
mists remain uneasy about recognising the role of stories in their modelling work.
Perhaps they think that economic models, particularly mathematical models – that
is, ‘scientic’ models, ought to be governed solely by deductive or mathematical
modes of arguing. Yet when economists use models, they typically also make use
of this other logic – the logic of narrative. e source of the tension may lie in a
confusion over the role of models in economics. Recognising – as I pointed out in
Chapter 1 – that economic modelling is not primarily a method of proof, but rather
a method of enquiry, in large part dissolves that tension.
To make these inquiries with models valuable, economists seek to capture the
heart of the matter in two senses, in two domains: the world of the model and the
world that the model represents or denotes. Model questions are designed to prompt
explorations of the relationships represented in the model. And since economic mod-
els are not only pieces of mathematics, but also pieces of economics, so their demon-
strations need to be interpreted, understood, and explained in economic terms. ese
model narratives provide not only the means to understand the economic world of
the model, but also to link the model with the economics of the world.
5.i Narratives and Identity in the World of the Model
How do narratives relate to enquiries into the world of the model? What do narra-
tives teach economists? Nancy Cartwright has suggested that models are “fables” in
their relationship to scientic laws and “parables” in relation to the world that they
purport to represent.21 Following the rst of these claims, she describes models as
21 See Cartwright (2010). A fable is usually dened as “a short story with a moral”, and a parable as
“a story used to illustrate a moral lesson” (OED denitions).
e World in the Model
240
tting out laws, just as a fable ts out an abstractly stated moral as a way for us to
explain or fully appreciate that moral.22 is seems an apt description of the way that
Frisch’s modelling went on, with two general theses that might together be taken as
the scientic equivalent of a moral: an abstract law that economists thought gov-
erned the economic cycle (a damped harmonic process) and an empirical law that
described their data (maintained, but disturbed harmonic movements). With the
help of story-analogies both these elements were tted out in the model’s construc-
tion – in the economic hypothesis about the rocking horse (the propagating mech-
anism) and in the description of stochastic processes inherent in the small boy with
the club (the impulses). Frisch’s tting out, and tting together, of these elements
in his model, and demonstrations with his model, showed why an adequate busi-
ness cycle model needs both kinds of ‘laws’: the ones from theory, and the ones that
describe empirical characteristics and how they could be made to work together.
In tting out these two laws in the shape of the model, he produced a “new recipe”
(see Boumans, 1999) with tremendous demonstrative power and so value for other
economists who came to understand and appreciate both the diculties of mod-
elling business cycles – and so the neatness of his solution. Or, to put the same
point in another way, other scientists learnt from the “mere existence” of Frisch’s
model (as Schlimm, 2009, suggests). He showed 1930s’ economists how to put these
abstract elements together and t them out to make their own meaningful models
that could be used to tell business cycle narratives, and enabled Tinbergen to fash-
ion the rst macroeconometric model.
We could equally well describe the way that Meade, Samuelson, and Hicks
developed their models as a process of ‘tting out’ Keynes’ General eory. His the-
ory (or laws), like the moral of a fable, were not hidden in one of their models to be
revealed by it, but were already given by him and written into their models by these
younger economists. But in these cases, we should ask not just what was learnt
from the tting out process of making their models, but what was understood from
using their models. And we might answer, recalling Samuelson’s demonstrations,
that “anything can happen”! But this judgement ignores the role and power of the
narratives that come from using such Keynesian models, which is where econo-
mists really came to understand and appreciate Keynes’ ideas. e problem was
well described by Solow, who learnt Keynesian economics from such “explanatory
articles” that turned Keynes book into models:
e General eory was and is a very dicult book to read. It contains
several distinct lines of thought that are never quite made mutually con-
sistent. . . . . . ese articles reduced one or two of those trains of thought to
an intelligible model, which for us became “Keynesian economics” . . . . [an]
22 See Cartwright’s 1991 paper, where she argues that “Fables transform the abstract into the con-
crete . . . . they function like models in physics” (p. 57). is is consistent with her simulacrum
account (1983) in which models make the link between a prepared description of the phenomena
and the laws that are thought to govern the phenomena.
Questions and Stories 241
illustration of the clarifying power of the model-building method. (Solow,
1997, p. 48, his italics)
ese models claried Keynes’ theory, and they did so by tting out the same gen-
eral theory in dierent ways (just as dierent fables can be created to t out the
same moral). But crucially those dierent models also produced dierent kinds
and pieces of information from the narratives associated with their usage. By work-
ing through the full range of more particular Keynesian stories that could be told by
using their models, each with specic details, they learnt things about the Keynesian
system that they did not know in advance. For example, even though Samuelson
knew the equations of his simple little Keynesian model, he still learnt lots of unex-
pected and complicated things about that Keynesian model world, including that it
was compatible with some implausible and bizarre stories as well as some meaning-
ful and plausible ones. e same kind of comments might be made with respect to
Meade and Hicks and their Keynesian models. No doubt, these economists made
their models in order to understand the Keynesian system, but they came to that
understanding not primarily from creating those models, but by using them to tell
a variety of stories.
is focus on particulars is just what we might expect from Cartwright’s
account of fables and their morals, for she agrees with Gotthold Lessing’s claim that
“the general only becomes graphic, or visualizable, in the particular” (Cartwright,
1991, p. 59).23 is is an epistemic claim: just as the fable provides the particulars to
understand the moral, so here, the scientists comes to grasp the general or abstract
in the model by working through the particular narratives that can be associated
with it.24 at these particulars are given and found in narrative form is agged in
the parallel eld of law, where Neil MacCormick argues that it is stories that enable
one to understand what more abstract legal statutes mean:
Undoubtedly, when one reads and tries to make sense of a complex statu-
tory text, or a legislative proposal, it can be dicult to see what it means,
unless you try to gure out how it might work in practice. You come to
understand it by guring hypothetical situations it would cover, that is by
guring stories that match the text. (MacCormick, 2005 p. 208)
Placing stories – not just particulars – as the vehicle for understanding a piece of
law resonates with the role of narratives in the practical usage of economic model-
ling. ink of Meade’s task of taking the reader through all the dierent eects of
23 In contrast, Hayden White claimed, for the narratives of history that “We understand the specic
story being told about the facts when we identify the generic story-type of which the particular
story is an instantiation” (1975, p. 58); see Morgan (2001) for further discussions of narratives in
science.
24 As Cartwright (1991, p. 61) points out, these particulars might still be abstract in relation to other
more concrete levels, just as Frisch’s model-based insight into business cycle data in general was more
abstract than Tinbergen’s statistical model of the Great Depression. See also Grüne-Yano (2009) and
my Chapters 7.2.iii, 9.4.iii and 10.3 on the importance of the levels at which models operate.
e World in the Model
242
a couple of small changes prompted by his question about the hypothetical world
in the model: communicating and understanding the outcomes from a compli-
cated eight-equation set of relationships works rather easily with a narrative mode.
ink of Samuelson, who was able to summarise the variety of output patterns
from a couple of relationships in a few succinct narratives. ese narratives report
the model demonstrations and their outcomes. ese model narratives were nei-
ther ‘merely heuristic’ nor ‘just rhetoric’ – important though heuristics and rhe-
toric are – but the way economists came to understand what lies at the heart of the
Keynesian system.
At the start of the chapter, I showed how economists sometimes use stories in
creating their models as Frisch with his rocking horse model. More usually, nar-
ratives appear with model usage and enable economists to gure out the charac-
teristics and nature of the economic world in their model, as we saw with Meade,
Samuelson, and Hicks. In carrying out model explorations and providing stories
in answers to their questions, these economist-scientists explored the behavioural
characteristics of the models they had made. From these they learnt the possible
processes and outcomes compatible with the mathematical and economic content
of their models. By identifying the specic stories that could be told with their
models (and the ones that they could not tell), these economists came to under-
stand the identity of the world that had been captured in their models.25
5.ii Model Narratives and Making Sense of the Economic World
What can models tell us about the world we live in? In creating the model, econo-
mists represent or denote the situation in the world in such a way as to incorporate
their theoretical claims or hypotheses about the world (e.g., Frisch’s beliefs about
cycles or the Keynesian account of the macroeconomy). But these denotations are
not very informative, for a diagram or an equation on its own can explain noth-
ing, or at least very little, about how the world works.26 If the activity of denoting
or model-making is the step of making connections from the world to the model,
it is the activity of using models to tell narratives that not only enables economists
25 e example of the Edgeworth Box diagram (Chapter 3) suggests that some models may carry
many dierent identities. is box has been used for the last 100 years to tell stories about con-
sumers in exchange situations, about rms and production decisions, about countries and trade
policy, about welfare questions, and so forth (see Humphrey, 1996). e basic form of the model
remains the same but the interpretation of the elements diers according to the domain, and the
stories that are told alter. Knowing that a piece of economics uses an Edgeworth Box diagram does
not even enable you to predict the domain of the economics, let alone the story it will be used
to tell.
26 For example, economists can denote aggregate consumption in the world with a C, and then
interpret C to refer back to aggregate consumption in the world; similarly with the consumption
function. is is basically the way that Gibbard and Varian (1978) understand stories: as an inter-
pretation of the assumptions, terms, and structure of the model, rather than of the demonstra-
tions made with the model, so there is no reason in their account why these interpretations need
a narrative form.
Questions and Stories 243
to understand their theories (e.g., the Keynesian system) but at the same time may
form the connections from the model back to the world. While the validity of such
back inference from models will feature in the discussions of later chapters, here in
this chapter, I want to focus on the way that these correspondence links are made.
In model usage, narratives provide the possible correspondence links between the
demonstrations made with the model and the events, processes and behaviour of
the world that the model represents. Narratives may show how to apply the model
to the world, and to oer potential insights, understandings, or even explanations
of how the world (that the model represents) works.27
At rst sight, the modelling eorts by Hicks, Samuelson, and Meade were solely
enquiries into the world of the model. But for any economist of the day, who had
just lived through the Great Depression, their model explorations spoke also to
the real economic problems of the period. Hicks’ enquiry can be understood to be
asking not only how dierent theories expressed in the model compared but also
whether the real economy behaves like the classical system or was better charac-
terized by the newer theory. Meade’s enquiry could be understood as an explora-
tion of policy options for the Great Depression. e patterns found by Samuelson’s
arithmetic simulations indicated, for example, that Keynesian policies based on the
two factors determining growth in the Keynesian model world might produce not
only growth in economic activity, but also cycles, or other more unexpected kinds
of economic behaviour. For economists, these model stories were not just stories
about the Keynesian theory, but models designed to tell Keynesian stories about
the real world.
ese model narratives function at a certain level: they construct a version of
events that is relatively simplied but yet also detailed in some respects. Elsewhere
in this book (Chapter 7) I have described this level as generic – for example, Hicks’
diagrams showed dierently sloped curves to describe the kinds of relationships
that might occur in the world. But the point I want to make here is somewhat dif-
ferent. Yes, the models discussed in this chapter were each one created to be more
specic and limited in certain respects than Keynes’ General eory, and Meade,
Samuelson, and Hicks consciously picked out dierent sections of that work to
form the central elements of their model as the most relevant for study. But in
usage, we saw that the stories that were told with these dierent models about the
world in those models were even more particular, more detailed, and more dif-
ferentiated. For example, Meade could tell stories about complex combinations of
events that could arise in his model usage, and describe those particular events
in numerical form. Samuelson too could tell a range of very dierent, but highly
particular, stories about the world in his model, qualitative stories that depended
on subtly dierent patterns of reaction as he varied the numbers to see what the
impact of government policies might be. With this range of patterns, he could tell
27 A parallel example is the way that chemical formulae were rst used with short narrative devices
to explain the details of how chemical reactions actually took place: see Ursula Klein (1999).
e World in the Model
244
stories about specic events that seemed likely, such as what happened when the
government withdrew its spending, as well as ones that seemed very unlikely, such
as the economy either collapsing to nothing or growing exponentially!
But the events of the world we live in are not only particular, they are also con-
crete, so that narratives must function not only to link the more general to the more
particular, but also to link the particular and the concrete. By linking the general
to the particular and the particular to the concrete, narratives provide explanatory
services for an economic science based on models.28
ere are two dierent ways to understand how narratives work in a scientic
context. On the rst account, we can characterize the role of model narratives as
stories about the world that the model represents by seeing them as a linking device,
a device that links demonstrations from the abstract, generic level, of the model to
the concrete particulars of the world. We can see how and why this is might be so by
looking at a parallel, once again in the case of law, where interpretations of events
made by lawyers have to bridge between abstract legal and everyday discourses.
ey typically depend on narratives or stories to make their interpretations com-
prehensible: stories operate or function as that bridge:
Stories thus function not as some kind of optional, aesthetically-pleasing
form, but as a response to the cognitive problems of abstraction and infor-
mation overload. (Jackson, 1988, p. 64)
Notice that there are two cognitive problems here that have to be overcome together
in making the narrative function eectively – the abstraction (of the law) and the
information overload of the concrete and specic details of the facts and events in
question.29 e modelling activity of the economist might be seen as like that of the
detective who rst puts together a case using various hypotheses and an array of
disjointed facts, or the lawyer who later must construct that same case so that it will
pass muster with a jury. Such stories necessarily have degrees of exibility and of
constraint in their construction. e economist, like the detective, has ideas, the-
ories, or hypotheses about how some set of events occurred, and an array of bits of
knowledge about the world, but is not sure which bits t together and how they do
so. Modelling might be seen as a way for economists to try out their hypotheses and
solve the tting together problem. So, in this account, narratives operate as a cog-
nitive bridge between the abstract and still relatively general economic model with
its demonstrations and the much more detailed accounts of the concrete events of
the real economic world. In making these correspondence links, narratives oer
potential explanations for those real-world events.30
28 e standard account of how explanation works in science is by guring out which scientic law
‘covers’ any particular phenomenon or event, and then arguing that the general law ‘explains’
that event. For a avour of more recent discussions, see, for example, the essays in de Regt et al.
(2009).
29 Jackson (1988) reports experiments that suggest that both overly simple stories and highly detailed
and complicated ones are equally problematic in making a case persuasive.
30 A fuller discussion of the explanations oered by models in economics is found in Chapter 9.
Questions and Stories 245
Alternatively, the explanatory function of narratives, and the level of account
of the world that narratives oer, can be understood as an epistemic claim, rather
than as a cognitive one. Louis Mink argues that narrative helps us to understand
the world not because it links the general and particular but rather because it oers
a distinctive form and level of understanding that sits in-between the general theory
and the fully detailed account of the world and does so by conguring the events of
world so that they can be understood.
On the one hand, there are all the occurrences of the world – at least all
that we may directly experience or inferentially know about – in their con-
crete particularity. On the other is an ideally theoretical understanding of
those occurrences that would treat each as nothing other than a replica-
ble instance of a systematically interconnected set of generalizations. But
between these extremes, narrative is the form in which we make compre-
hensible the many successful interrelationships that are comprised by a
career. (Mink, 1978, p. 132)
In this second account of narrative, there is no appeal to the abstract or general the-
oretical account in seeing how models might function to make sense of, or explain,
the events of the world (as in the standard account of scientic explanation).31 Nor
do narratives pretend to be a complete and exhaustive description of events in the
world. e focus here is on the understanding narratives oer, and the kind of com-
prehension that they provide. On this account, model narratives are not a special
kind of story, nor do they play a special role, nor are they a ground-level version of
something more general. Rather narratives, wherever they are found, are accounts
that congure – they make sense of or explain materials – at an intervening level
between complete and exhaustive detail and full systematic generalization.
Whether we think of narrative as a playing a cognitive bridging role or provid-
ing a conguring account, it is the qualities and the criteria that the narrative form
brings to explanations of the world that are used to judge them. MacCormick (2005)
suggests that good narratives need to show both ‘consistency’ and ‘coherence’, qual-
ities that are as important in the sciences as in the eld of law. Consistency refers to
the characteristic that the facts do not contradict each other just as, for economists,
the assumptions of a model must not contradict each other. Coherence refers to
a positive feature, namely that narrative makes a series of events hang together.
We expect coherence in a narrative whether in ctional stories or in the factual
accounts of law and history.32 Coherent stories both suppose a certain amount
of complexity and impose causal connections onto a set of disjointed elements:
a coherent narrative is one that ts apparently unconnected things together, puts
31 See footnote 28.
32 I thank Jon Adams here for several helpful discussions and his insights into the functions of nar-
rative. In addition, there are interesting questions about the nature of the causality involved with
narratives, and their inherent ambiguity over whether relations in them are ones of time, causal
necessity, or contingency (ambiguities that are consistent with the ways that economists think
about economic relations; see Morgan, 2001).
e World in the Model
246
things in order, lls in gaps, and makes sense of the relations of people and events.
is might be termed the logic of narrative explanation, not in terms of a literary
or linguistic analysis, but in terms of its epistemic role in science: narratives put
together materials in ways designed to make sense of events in the world. A coher-
ent model narrative about the world oers possible explanations of the world, not
explanations of possible worlds.33
Models in economics oer the same kind of explanatory services that planetary
motion models oered to early astronomers in showing them how the elements
of the universe that they observed t together into a systematic account. Models
show economists, for example, how all the elements of the Keynesian system work
together, or how both the multiplier and accelerator might together create eco-
nomic growth for the world. But, in using small abstract economic models to get a
grip on their concrete economic world, it is the coherence of these narrative-based
explanations that serve to pull disparate elements together, and to provide accounts
of the world. Economists don’t expect these narratives to be exactly true to every
last detail of any particular concrete events of the world. If they were, they would
probably not be good stories. But they trust that their models will capture some of
the heart of the matter, and that by telling such stories, they try to reconnect their
simple models with the facts of the messy economic world we all live in.
5.iii Narrative as a Testing Bed for Models
Economists use narratives as an informal test of the validity of the model, with
criteria that suggest in various ways why and how they nd their models useful.
As we have seen from the examples of Keynesian models and their usage in this
chapter, model narratives function both to take apart and explore the world in the
model, and to put together and make coherent accounts of the world that the model
represents. is double function may account for their endemic quality in econom-
ics, but it does make it more dicult to gure out what economists’ own criteria for
their model narratives might be. It seems that some models are considered better
than others because they can be used to tell better stories, so that the judgement
of models relies on judging the narratives. Hints about this are found in the kind
of reective, but nonanalytical, accounts that economists occasionally give of their
own practice that recognise the importance of storytelling. For example, Krugman,
in autobiographical mode, noted
e models I wrote down that winter and spring were incomplete, if one
demanded of them that they specify exactly who produced what. And yet
they told meaningful stories. (Krugman, 1993, p. 26)
33 is is an important distinction: other commentators prefer to think of models oering explana-
tions of possible worlds (e.g., Rappoport, 1989) as a way to get around the problem of “unrealistic
assumptions”, an issue that goes back to Milton Friedman (1953).
Questions and Stories 247
Or Franklin Fisher, commenting on the literature of industrial economics:
At present, oligopoly theory consists of a large number of stories, each one
an anecdote describing what might happen in some particular situation.
Such stories can be very interesting indeed. (Fisher, 1989, p. 118)
e notion that the quality of model narratives provide an informal test of a model
lurks in such comments. ey suggest that narratives attached to models have qual-
ities beyond those of consistency and coherence explored in the last section. Two
terms – ‘meaningful’ and ‘plausible’ – capture the sense of how economists think
about this matter.
‘Meaningful’ is a quality that refers to narratives told about the world of the
model. is has two aspects for economists. On the one hand, model stories need
to be theoretically meaningful. It is not just that a model has to have consistent
assumptions (the consistency check we saw paralleled in legal narratives), but that
a model must also have characteristics that are meaningful in terms of economists’
theories, which, of course, has implications for the narratives that can be told. For
example, business cycle models are meaningful only if they can generate cycles and,
in Frisch’s period, this meant damped cycles, just as later Meade needed to check
that his model had equilibrium tendencies.
On the other hand, the narratives need to be economically interesting in the
behaviour they reveal in the world in their model. Economists would even pre-
fer that these narrated behaviours and explanations are a little surprising, for
economists want to get more out of their modelling than they know to start with.
(Narratives that just repeat back what they already know are not very interesting.)
ose that reveal some strange elements, or surprising behaviour, or unusual con-
nections and eects, are more interesting to the economist, and so may be more
meaningful for them. Narratives of bizarre events might be problematic, but are
oen equally useful in revealing things about the model and thus re-enforce the
ways in which narratives provide a test-bed for the model.
‘Plausible’, in contrast, captures the idea that the stories map adequately to
certain characteristics of the phenomena in the real world that the models aim to
describe and that economists seek to explain. To get a useful narrative test of the
plausibility of a model, the model users rst have to make sensible choices about
what specic phenomena of the world their model might explain and then con-
sider how to connect their model with those specics. at is, they need to decide
where to start their tale and the order of solving the model and to carry through the
demonstrations that provide the narratives with care and attention – as we saw with
Meade, Samuelson, and Hicks. In other words, they rst need to ask plausible ques-
tions of their small mathematical models before they can tell stories that are plau-
sible about the events of world. But the term ‘plausible’ suggests not only that the
world of the economic model has been made to t (in some loose way) the world
the model represents, but also that it oers some insight into the economics of why
it is as it is. For example, Frisch’s model was not only meaningful in economic terms
e World in the Model
248
(with its damped cycles and equilibrium tendency), but also plausible in terms that
t the world (it could produce cycles that t the data pattern of the world), and that
could be explained by the way innovations came into the economy (rather than by
its mechanical pendulum analogy).
Economists do not take the plausibility of narratives as a proof, or even a sign,
of the truthfulness of a model. Yet, naturalistic accounts of economic modelling
(as mine here and others discussed in this section) have noticed how storytelling
about the world oen invokes shades of inference, as well as explanation, in the way
economists think about these stories. is is reected in Gibbard and Varian’s (1978)
account of “casual application”: the way economists apply mathematical models to
events in the world in contrast to the serious application of econometric models. In
that latter domain, the models are applied to data from the world, and are validated
with statistical testing. But in the domain of mathematical and diagrammatic mod-
els, as we have seen, the narrative forms the place where a looser ‘casual’ mode of
connection of the model to the world goes on and the criteria of validity are similarly
loose.34 But they are not absent. So, economists such as Hicks, Samuelson, and Meade
did not claim to learn from using a model whether Keynes’ General eory is gener-
ally true for the world. ey did learn – from enquiry into the world of the model –
how to use the elements of his theory to tell meaningful Keynesian narratives of
kinds of events (depressions), and to give plausible narrative explanations of particu-
lar concrete events that happened in their real world, such as the Great Depression.
Using such models narrative, they could also suggest how Keynesian policies might
work in the world that the model represents, though the looseness of the criteria of
plausibility always make it doubtful, dicult, and potentially dangerous, to use these
little mathematical models to intervene directly in the economic world.35
When storytelling with a model succeeds in oering accounts that are both
meaningful in their theoretical terms and plausible, and perhaps striking, in terms
of the explanations these narratives oer for real-world events, economists are
rather pleased with their eorts. Such a model may be understood by economists
as one that has already oered suggestions about the way that the economic world
might work, and might be used to generate additional insights. But what counts as
meaningful and plausible both change over time.
Consider rst what might counts as meaningful for economists. Whereas the
primary theoretical criteria for the macro-models that we saw economists using in
the interwar period was their equilibrium behaviour, by the second half of the twen-
tieth century, such an aggregate model also needed adequate ‘micro-foundations’
before it could count as meaningful. us, Gibbard and Varian in 1978 noted that
economists liked models that were meaningful in theory terms and that oered
an explanation of some easily noticed phenomena by some simple, but plausible,
behaviour of individuals:
34 Exactly how these narratives about the world are matched to the events of the world will become
much clearer in the discussion of game theory in Chapter 9.
35 See Cartwright (2009).
Questions and Stories 249
In some cases, an aspect of the world (such as price dispersal, housing
segregation, and the like) is noticed, and certain aspects of the micro-
situation are thought perhaps to explain it; a model is then constructed to
provide the explanation. If the model turns out to have striking features,
a casual search for economic situations with those features may then be
conducted. In either kind of case, no measurement that goes beyond casual
observation is involved. (Gibbard and Varian, 1978, p. 672)
MacCormick labels a narrative that oers such a kind of explanation “credible”,
meaning that it is not only coherent, but also provides a satisfactory “causal or moti-
vational account of the whole complex of events” (2005, pp. 226–7). Robert Sugden,
a microeconomist and reexive commentator of modelling practises in modern
economics, has the same sense, calling such model worlds that succeed in captur-
ing something of an observed pattern of a phenomenon by a simple behavioural
rule followed by individuals: “credible worlds”.36 Sugden’s paradigmatic example to
exemplify this notion is omas Schelling’s (1978) model of segregated housing: an
analogical model, wherein the ‘individuals’ are treated as pieces on a checkerboard,
each piece’s behaviour follows certain simple rules, and the outcome is a pattern of
pieces in which the colours are segregated. Sugden judges such a model world as
a “credible but counterfactual world(s), paralleling the real world” (Sugden, 2009,
p. 4), where the judgement of credibility hinges on the “sense that it [the model
world] is compatible with what we know, or think we know, about the general laws
governing events in the real world” (p.18). He oers, as an analogy for this sense of
credibility, the feeling we experience from reading “realistic novels” (2009, p. 18) –
which brings us back to both plausibility and narrative.37
But the licence for inferring that a model narrative parallels the real world,
that is that the model is credible, as with Gibbard and Varian, hangs on a pretty
loose sense of resemblance, or similarity, in the outcomes. In the Schelling case, the
similarity lies in the outcome checkerboard pattern that mimics, or ‘looks like’
the ones we observe in the world of segregated neighbourhoods. But for Sugden,
the economically striking thing that he notices about this parallel world is that the
checkerboard segregated outcome is not the result of an rule based on strong col-
our preferences but only on mild preferences in individual behaviour of the pieces.
36 See Sugden (2000, 2009). Sugden’s “credible worlds” account of modelling is in some ways quite
close to Gibbard and Varian’s account (1978) and in many ways compatible with my own here: all
three are practice-based accounts, and discuss the informal way that models are judged. But it is
not quite clear that “credible worlds” are a dierent kind of model, or that Sugden oers a dierent
philosophical account of how models are made and used. For example, Schelling’s model-making
may be understood in the tradition of analogical modelling (where the mimicking is both at the
level of the simple rules of games and of the phenomenonal outcome), a characterization that
oers a strong contrast with the idealization accounts of modelling (associated with Cartwright
and Mäki); see my Chapter 1. However, the possibility to explain phenomena with a credible
world model still needs an account of how models are used, and still relies on similarity claims to
sustain inference however loosely these claims are made.
37 See also Grüne-Yano (2009).
e World in the Model
250
is in turn reveals why the model is especially interesting for the economist: it is
not just that the model narrative satises economists’ current preferences for good,
theory-based, explanations in that it has micro-behaviour creating an aggregate
level phenomenon, but that the particular assumption about individual behaviour
needed to get the result (mild colour/racial preferences of the pieces) is appealingly
unexpected, but yet credible.
We have seen that the elements in a narrative that make a model count as
meaningful are contingent on local scientic knowledge: they depend on what
economists of a certain time take to be a good explanation of human behaviour or
of the behaviour of the whole economy; they depend on the theories and assump-
tions of the time and place and group of economists involved. But this is equally
so of the plausibility of models in relation to the world, for what counts as plausible
depends in part on the particular events to be explained. Where Depression-era
model narratives were plausible stories for the 1930s, and Keynesian stories told
with models were seen as plausible to many economists and policy makers and
the public during the 1950s and 1960s, they came to be seen as implausible dur-
ing the stagation of the 1970s, only to be resurrected, in certain respects, in the
economic crisis at the end of the rst decade of the twenty-rst century. So what
constitutes plausibility, like meaningfulness, is by no means a stable or universal
criterion.38 In part, this is of course because, as we know from the history of eco-
nomic science: economic theories, ideas, evidence, and methods change – just
as for any other science. But we also nd from historians of what happens in the
economy (economic historians) that their subject matter is not necessarily stable –
economies develop; there are crises, new phenomena to be explained, and old
ones to be reevaluated. Plausibility, like meaningfulness, depends on both content
and context.39
ese changing judgements of plausibility in modelling reect the in-between
level at which model narratives oer explanations, between general laws and every-
day particulars, between the abstract and concrete levels. Model accounts are
designed to be more specic in content than laws, so they are regularly adapted
to t new problems or new phenomena. At the same time, new theories and new
abstract concepts prompt changes in the character and content of models.
In addition, the notion of what even counts as plausible is moulded in a much
more general way by the epistemic genre – of modelling – within which econo-
mists operate. In Chapter 1 (Section 3), I explained how individual branches of
the sciences adopt particular modes of reasoning (modelling, laboratory experi-
ment, statistical reasoning, etc.) that form the context within which certain kinds
of arguments seem reasonable and right, and so plausible. As I also pointed out
there, this means that the knowledge obtained in each branch is relative to the
mode of doing science, but that each of these modes of doing science is considered
38 anks again to Jon Adams for helping me think this issue through.
39 See Hawthorn (1991) on the notion of “plausible worlds” for the social scientist.
Questions and Stories 251
valid. Modelling forms this broader context within which economic models are
judged plausible.
In other words, the eectiveness of model narratives in ‘explaining’ the world,
depends upon a lot of implicit and explicit, time and place dependent, science-
based knowledge that is both conceptual and empirical, both historical and theo-
retical as well as methodological. Models are ‘tested’ against this knowledge within
the accepted community norms of scientic argument with models, and found
meaningful, plausible, and credible, or found wanting. is situation seems to be
not incompatible with Cartwright’s (2010) idea that while models are “fables” in
relation to laws, they are “parables” in relation to the world. Unlike fables, the moral
of a parable is not written into the story but has to be drawn out of it. Conceived
as a parable, the meaning of a model for the ‘target system’ – the real world the sci-
entist is trying to understand – is a matter for interpretation and has to be drawn
out of it, with the help of other information, theory, concepts, and things econo-
mists already know about the world: the contingent scientic knowledge. But with
parables, as with fables earlier, the narrative form really matters. Narratives are not
just the vehicle for drawing out those interpretations, for narratives bring qualities
and criteria of their own. For economists, good model narratives have to be con-
sistent and meaningful with respect to the world in the model and they have to be
coherent, plausible, and even credible with respect to the world that the model rep-
resents. ese criteria for narratives are the means by which economists test out the
quality of their models: what counts as a good model depends on the good qualities
of the narratives that can be told with it.
6. Where Next?
It is a nice paradox of the way models are used that a humanistic notion – nar-
rative or storytelling – is critical to the way that models are used as a mode of
enquiry in economic science whether the model narrative is a story about the world
portrayed in the model or a correspondence story about the real world, past, pre-
sent, or future. Narratives are evident both in enquiries into the somewhat abstract
world of the model as much as in enquiries with the model into the more particular
and concrete world we live in. e discussion of narratives here has identied two
elements that need further investigation in the following chapters.
Following the rst track, I follow up my observation that narratives are used to
explore the world in the model by telling stories about more particular kinds of cases
and situations than are provided for in more general theories or laws. As we have
seen, with slightly dierent questions or slightly dierent arrangements or slightly
dierent values in the model – narratives provide dierent outcomes for that world in
the model. An unintended side eect of such model usage turns out to be the provi-
sion of classicatory services alongside the explanatory services. ese two outcomes
of model usage – of particularity in terms of the levels of explanation that models
e World in the Model
252
oer, and the way that leads to classication – are rst taken up in Chapter 7 and,
then, more strongly but in a dierent kind of way, in Chapter 9. In that latter chapter,
I also follow up my investigations into narratives in the context of game theory, where
narratives are found to play an even more critical role in model reasoning.
On a dierent track, I have suggested here that model narratives oer some
kind of inferential possibilities. is interpretation rests not only on the way that
economists place reliance on the credibility and plausibility of their model stories,
but even more so on the demonstrations that occur in model usage and that are
paralleled in model naratives. As we saw in this chapter, a model demonstration
is the result of a manipulation by the scientist, a manipulation that may equally
be redescribed as a mode of experiment but one with more limited possibilities
of inference. is interpretation of model reasoning is explored in Chapter 7 in
the context of supply and demand models. e mode of demonstration is even
more obviously an experimental mode when we come to the model simulations of
Chapter 8. is leads me to consider several ways in which judging the validity of
model results might be understood as questions of inference.
Acknowledgement
is chapter was originally written at Nueld College, Oxford, during my period in resi-
dence as the Norman Chester Senior Research Fellow, Autumn 1997, for presentation at
a conference at Erasmus University, Rotterdam, November, 1997. It circulated in revised
form as a University of Amsterdam Working Paper in 1999 and was published, more or
less in that form as Morgan (2001). Since then, this chapter has lost some of the literary
materials on narrative, but gained those on law, along with the discussion of the steps of
model usage (from Morgan, 2002) – and so it gained Sections 2, 3iii, 4, and 5.iii. I thank
the Warden, Fellows, and Students at Nueld for their hospitality and many discussions
of the role of models and my NAKE students (classes of 1997 and 1999) for pertinent
questions when I taught the topic. I thank participants at the Rotterdam conference, as
well as at subsequent seminars at Nueld College, Oxford, at Groningen, at the WRR
(Dutch Scientic Council for Government Policy) in the Hague, and at the HES meeting
in Montreal; and Ben Gales, Roger Backhouse, Deirdre McCloskey, Margaret Morrison,
Harro Maas, and Nancy Cartwright for their comments. I thank Till Grüne for research
assistance for the revised version of the chapter and Jon Adams for helpful discussions on
the nature of narrative.
References
Andvig, Jens Christopher (1991) “Verbalism and Denitions in Interwar eoretical
Macroeconomics”. History of Political Economy, 23, 431–55.
Backhouse, Roger E. And David Laidler (2004) “What Was Lost with IS-LM”. In Michel
De Vroey and Kevin D. Hoover (eds), e IS-LM Model: Its Rise, Fall and Strange
Persistence (pp. 25–56). Annual Supplement to History of Political Economy, Vol. 36.
Durham, NC: Duke University Press.
Questions and Stories 253
Barnett, Vincent (2006) “Chancing an Interpretation: Slutsky’s Random Cycles Revisited”.
European Journal for the History of Economic ought, 13:3, 411–32.
Barthes, Roland (1982) “Introduction to the Structural Analysis of Narratives”. In S. Sontag
(ed), A Roland Barthes Reader (pp. 251–95). London: Vintage.
Boumans, Marcel (1999) “Built-in Justication”. In Mary S. Morgan and Margaret Morrison
(eds), Models as Mediators: Perspectives on Natural and Social Science (pp. 66–96).
Cambridge: Cambridge University Press.
(2005) How Economists Model the World to Numbers. London: Routledge.
Cartwright, Nancy (1983) How the Laws of Physics Lie. Oxford: Clarendon.
(1991) “Fables and Morals”. e Aristotelian Society, Supplementary Volume 65, 55–68.
(2009) “If No Capacities en No Credible Worlds. But Can Models Reveal Capacities?”
Erkenntnis, 70:1, 45–58.
(2010) “Models: Parables v Fables”. In R. Frigg and M. Hunter (eds), Beyond Mimesis and
Convention: Representation in Art and Science (pp. 19–31). New York: Springer.
Darity, William and Warrren Young (1995) “IS-LM: An Inquest”. History of Political
Economy, 27, 1–41.
de Regt, H., Leonelli, S., and Eigner, K. (2009) [eds] Scientic Understanding: A Philosophical
Perspective. Pittsburgh: Pittsburgh University Press.
De Vroey, Michel, and Kevin D. Hoover (2004) [eds] e IS-LM Model: Its Rise, Fall and
Strange Persistence. Annual Supplement to History of Political Economy, Vol. 36.
Durham, NC: Duke University Press.
Fisher, Franklin M. (1989) “Games Economists Play: A Noncooperative View”. RAND
Journal of Economics, 20:1, 113–24.
Friedman, Milton (1953) “e Methodology of Positive Economics”. In Essays in Positive
Economics (pp. 3–46). Chicago: University of Chicago Press.
Frigg, Roman (2009) “Models and Fiction”. Synthese, 172:2, 251–68.
Frisch, Ragnar (1933) “Propagation Problems and Impulse Problems in Dynamic Economics”.
In Economic Essays in Honour of Gustav Cassel (pp. 171–205). London: Allen & Unwin.
Gibbard, Allan and Hal R. Varian (1978) “Economic Models”. e Journal of Philosophy,
75:11, 664–77.
Goodman, Nelson (1968) Languages of Art, 2nd ed, 1976. Cambridge: Hackett.
Grüne-Yano, Till (2009) “Learning from Minimal Economic Models”. Erkenntnis, 70:1,
81–99.
Hartmann, Stephan (1999) “Models and Stories in Hadron Physics”. In Mary S. Morgan
and Margaret Morrison (eds), Models as Mediators: Perspectives on Natural and Social
Science (pp. 326–46). Cambridge: Cambridge University Press.
Hawthorn Georey (1991) Plausible Worlds: Possibility and Understanding in History and
the Social Sciences. Cambridge: Cambridge University Press.
Hicks, John R. (1937) “Mr. Keynes and the “Classics”: a Suggested Interpretation”.
Econometrica, 5, 147–59.
Hughes, R. I. G. (1997) “Models and Representation”. Philosophy of Science, 64, S325–36.
Humphrey, omas M. (1996) “e Early History of the Box Diagram”. Federal Reserve
Board of Richmond. Economic Review, 82:1, 37–75.
Ingrao, Bruna and Giorgio Israel (1990) e Invisible Hand. Cambridge, MA: MIT Press.
Jackson, Bernard S. (1988) Law, Fact and Narrative Coherence. Liverpool: Deborah Charles
Publications.
Keynes, John M. (1936) e General eory of Employment, Interest and Money. London:
Macmillan.
Klein, Judy L. (1997) Statistical Visions in Time: A History of Time Series Analysis, 1662–
1938. Cambridge: Cambridge University Press.
e World in the Model
254
Klein, Ursula (1999) “Paper Tools and Techniques of Modelling in Classical Chemistry”. In
Mary S. Morgan and Margaret Morrison (eds), Models as Mediators: Perspectives on
Natural and Social Science (pp. 146–67). Cambridge: Cambridge University Press.
Krugman, Paul (1993) “How I Work”. e American Economist, 37:2, 25–31.
Le Gall, Philippe (2008) “L’Économie est elle une Science Fiction? Récit et Fiction en
Modélisation Economique et en Art”. Unpublished paper, University of Angers.
Louça, Francisco (2007) e Years of High Econometrics. London: Routledge.
Lucas, Robert E. Jr. (2004) “Keynote Address to the 2003 HOPE Conference: My Keynesian
Education”. In Michel De Vroey and Kevin D. Hoover (eds), e IS-LM Model: Its Rise,
Fall and Strange Persistence (pp. 12–24). Annual Supplement to History of Political
Economy, Vol. 36. Durham, NC: Duke University Press.
MacCormick, Neil (2005) Rhetoric and the Rule of Law: A eory of Legal Reasoning. Oxford:
Oxford University Press.
Mäki, Uskali (1992) “On the Method of Isolation in Economics”. In G. Dilworth (ed),
Intelligibility in Science (pp. 319–54). Studies in the Philosophy of the Sciences and
Humanities, Vol. 26. Amsterdam: Rodopi.
Marshall, Alfred (1890) Principles of Economics, 8th ed, 1930. London: Macmillan.
McCloskey, Deirdre N. (1983) “e Rhetoric of Economics”. Journal of Economic Literature,
21, 481–517.
(1990a) “Storytelling in Economics”. In D. Lavoie (ed), Economics and Hermeneutics
(pp. 61–75). London: Routledge.
(1990b) If You’re So Smart. Chicago: University of Chicago Press.
(1994) Knowledge and Persuasion in Economics. New York: Cambridge University Press.
Meade, James E. (1937) “A Simplied Model of Mr. Keynes’ System”. Review of Economic
Studies, 4:2, 98–107.
Mink, Louis O. (1978) “Narrative Form as a Cognitive Instrument”. In R. H. Canary and H.
Kozicki (eds), e Writing of History (pp. 129–49). Madison: University of Wisconsin
Press.
Morgan, Mary S. (1990) e History of Econometric Ideas. Cambridge: Cambridge University
Press.
(1991) “e Stamping Out of Process Analysis in Econometrics”. In Neil De Marchi and
Mark Blaug (eds), Appraising Economic eories (pp. 237–63 and 270–2). Cheltenham:
Edward Elgar.
(1999) “Learning from Models”. In Mary S. Morgan and Margaret Morrison (eds),
pp. 347–88.
(2001) “Models, Stories, and the Economic World”. Journal of Economic Methodology,
8:3, 361–84; reprinted in U. Mäki (ed), Fact and Fiction in Economics: Models, Realism
and Social Construction (pp. 178–201). Cambridge: Cambridge University Press.
(2002) “Model Experiments and Models in Experiments”. In Lorenzo Magnani and Nancy
J. Nersessian (eds), Model-Based Reasoning: Science, Technology, Values (pp. 41–58).
New York: Kluwer Academic/Plenum Press.
Morgan Mary S. and Marcel Boumans (2004) “Secrets Hidden by Two-Dimensionality:
e Economy as a Hydraulic Machine”. In S. de Chadarevian and N. Hopwood (eds),
Models: e ird Dimension of Science (pp. 369–401). Stanford: Stanford University
Press.
Morgan, Mary S. and Margaret Morrison (1999) [eds] Models as Mediators: Perspectives on
Natural and Social Science. Cambridge: Cambridge University Press.
Morrison Margaret and Mary S. Morgan (1999) “Models as Mediating Instruments”. In
Mary S. Morgan and Margaret Morrison (eds), Models as Mediators: Perspectives on
Natural and Social Science (pp. 10–37). Cambridge: Cambridge University Press.
Questions and Stories 255
Rappaport, Steven (1989) “Abstraction and Unrealistic Assumptions in Economics”. Journal
of Economic Methodology, 3:2, 215–36.
Samuelson, Paul A. (1939) “Interactions Between the Multiplier Analysis and the Principle
of Acceleration”. Review of Economics and Statistics, 21, 75–8.
Schelling, omas C. (1978) Micromotives and Macrobehaviour. New York: Norton.
Schlimm, Dirk (2009) “Learning from the Existence of Models. On Psychic Machines,
Tortoises, and Computer Simulations”. Synthese, 169(3), 521–38.
Slutsky, E. E. (1927) “e Summation of Random Causes as the Source of Cyclic Processes”.
e Problems of Economics Conditions. e Conjuncture Institute, Moscow, 3:1, 34–64
(English Summary, 156–61).
Solow, Robert M. (1997) “How Did Economics Get at Way and What Way Did It Get?”
Daedalus, Winter, 39–58.
Suárez, Mauricio (2009) [ed] Fictions in Science. London: Routledge.
Sugden, Robert (2000) “Credible Worlds: e Status of eoretical Models in Economics”.
Journal of Economic Methodology, 7, 1–31. Reprinted in U. Mäki (ed), Fact and Fiction
in Economics: Models, Realism and Social Construction (pp. 107–36) [2001]. Cambridge:
Cambridge University Press.
(2009) “Credible Worlds, Capacities and Mechanisms”. Erkenntnis, 70:1, 3–27.
Weintraub, E. Roy (1991) Stabilizing Dynamics: Constructing Economic Knowledge. New
York: Cambridge University Press.
White, Hayden (1975) “Historicism, History and the Figurative Imagination”. History and
eory, 14:4, 48–67.
Yule, George Udny (1927) “On a Method of Investigating Periodicities in Disturbed Series
with Special Reference to Wolfer’s Sunspot Numbers”. Philosophical Transactions of the
Royal Society of London, Series A, 226, 267–98.
256
7
Model Experiments?
1. Introduction 256
2. Experiments in the World of the Model 258
2.i Mangoldt and Jenkin 259
2.ii Marshall 267
2.iii Conceptual Work: Dening Generic Categories 270
3. Models in ‘Laboratory’ Experiments 272
4. Comparison: Model Experiments and Laboratory Experiments 277
4.i Controls and Demonstration 277
4.ii Experimental Validity and e Inference Gap 282
5. Hybrids 288
5.i Virtually Experiments 288
5.ii e Status of Hybrids 292
6. Materials Matter: Surprise versus Confoundment 293
1. Introduction
How can we characterize the way scientic modelling works? In Chapter 1, I sug-
gested economists use models as a means of investigation or enquiry: they both
enquire into the small worlds in their models, and use those enquiries as a way
to interrogate the nature of the world. In this chapter I explore how these kinds
of enquiries work by treating model-based reasoning as akin to experimental
investigations.
Treating model reasoning as a form of experiment inevitably raises questions
about the nature of such experiments. In Chapter 6, I portrayed model usage as
a process of asking questions about the circumscribed and limited world in the
model and using the model to derive answers about that small world. is is a
process in which scientist and model are jointly active participants: neither is
passive – the scientist experiments by manipulating the model, that is, he or she
uses the model’s resources (both its subject specic and deductive resources) to
Model Experiments? 257
demonstrate answers to questions of interest to the scientist. In this chapter I show
how the heart of the experimental action lies rst in the ways a model’s resources
are used to demonstrate answers to questions about that model world, and second
in using these experimental demonstrations to make inferences from that model
world to the real one.
First then, in making demonstrations, we will see that models feature in a vari-
ety of dierent experimental modes of enquiry. On the one hand, economists cre-
ate mathematical models and experiment on them, that is, they experiment within
the small model world. On the other hand, economists undertake laboratory or
classroom experiments, in which, as we shall see, models generally play a rather
more passive but still essential role. But in between, there is a whole range of hybrid
forms of experiments in which models feature in the experimental design, undergo
controlled variation in the experiment, and so forth. In other words, models fea-
ture either as the object of manipulation or set the constraints within which exper-
imentation takes place: there are both experiments in or on models and models in
experiments.
Second, the notion of model reasoning as oering a kind of experiment enables
me to take up the challenging problem, agged in Chapter 6, of how economists make
inferences from their model work, and what range of inferences such model demon-
strations support. In this context, I end with a discussion of the contrast in epistemic
power of model and laboratory experiments. On the way, however, I explore how
these model-based experiments prompt the development of more generic catego-
ries for analysis, conceptual work that is an important but unexpected side eect of
the historical shi to model-based reasoning in economics. ese generic categories
both dene and limit the relevant domains for model-based inferences.
I take as my exemplar model for this chapter one of the most common and well-
used models in economics, namely the supply and demand model, which appears
in textbooks now either as a diagram with supply and demand curves (each relat-
ing prices and quantities in the marketplace) or as a set of three equations (the two
functions and an equilibrium condition). Economists became so used to working
with this model that it seems always to have been there. But while arguments about
the laws of demand and supply may long have been at the centre of discussions
about markets, that does not mean the model itself did not have to be developed.
As I pointed out in Chapter 1, the transition from a verbal to a model-based sci-
ence took place between the late-nineteenth and the mid-twentieth centuries and
the earliest examples of supply and demand models shown in this chapter come
from the beginning of that period. Not surprisingly, this change in what counted
as scientic ways of doing economics required a shi in both cognition and per-
ception: economists had to learn to think in models and to perceive the world
in terms of models, and each depended upon the other. So the manner in which
these earliest experiments on models were conducted and explained was all rather
clunky. As such model-based reasoning became more commonplace, economists
became more adept at it, and the model-experimental process became smoother.
e World in the Model
258
e benet of choosing this supply and demand model as the exemplar for this
new mode of doing science is that it enables me to show how the means of model-
ling became standardized and even ‘black boxed’; it provides a site for study that is
more revealing than later examples. But it was also one of the rst models to feature
in classroom experiments with real subjects, enabling me to compare model and
laboratory experiments as well as to show how models also feature in this latter
kind of experiment. As new forms of using models and doing experiments ooded
into economics in the later twentieth century, we nd a variety of hybrid forms of
supply and demand experiments to ll in our comparison. Models lie at the heart
of these hybrids too, so that the historical trajectory of this model provides rich
materials for analysis.
2. Experiments in the World of the Model
We can start out by thinking of model experiments as a kind of gloried think-
ing or mental experiment.1 I call them ‘gloried’ only because such pen-and-paper
experiments are too complicated to be done in the head. Writing down a model and
manipulating it allows economists to think through in a consistent and logical way
how a number of variables might interrelate, and to nd the solutions to questions
about such systems. is habit of making and using models extends the powers of
the mind to ask questions and explore the answers in complicated cases. Sometimes
such questions are about theories, sometimes about possible interventions (policies),
sometimes about phenomena in the world. In this way, model experiments have
come to function both in the domain of theory development and for understanding
the world. But to treat this extension of the powers of the mind as a kind of exper-
iment requires not only some credible evidence of such model usage in economics
but also a convincing analysis of how such work goes on.
e development of an eective supply and demand model, and of its usage, is
usually associated with Alfred Marshall, who was an English economist of the late
nineteenth and early twentieth centuries, famous for his writings about the nature
and workings of industry. But, as historians of economics have shown, there are
several important predecessors for this work, dating from the mid-nineteenth cen-
tury.2 eir histories tell us that in 1838, the French economist Antoine-Augustin
Cournot was the rst to make a supply and demand diagram, and to experiment
1 I want to avoid the label “thought experiments” since commentators tend to treat these as a rather
distinct category; see particularly Margaret Schabas (2008) and Julian Reiss (2002) for discussions
of thought experiments in economics.
2 is chapter does not provide a history of exchange theory (on which see Creedy [1992 or 1998],
the latter having extracts from original texts) or of the use of supply/demand diagrams (on which
see Humphrey [1992], who retains the original diagrams in his commentary). Both of these authors
cover French, German, and English literature. For a neat account of the French tradition in geo-
metric analogies beginning with the pyramid analogy to demand, and considering Dupuit’s work,
Model Experiments? 259
with it in a discussion of tax incidence. He was closely followed in 1841 by the
German contributor, Karl Heinrich Rau, who built and used the diagram to discuss
how market adjustments occur. ough the use of the diagram remained uncom-
mon until the later nineteenth century, two other contributors, Hans von Mangoldt
and Fleeming Jenkin, are particularly important for my discussion of the devel-
opment of model experiments as the way to construct arguments with models.
Mangoldt worked in the classical tradition in Germany (and cited Rau’s work), but
found his analytical approach overlooked by the historical economists dominant in
his country in that later part of the century. Jenkin’s work was also overlooked, pos-
sibly because he beat his more mainstream British compatriots to the new ways of
arguing with diagrams! Yet the work of both show us how the supply and demand
model and the method of reasoning with it co-evolved.
2.i Mangoldt and Jenkin
Hans von Mangoldt’s 1863 discussion of demand and supply uses the same concepts
as Adam Smith in his 1776 e Wealth of Nations. So the “natural” price (or “centre
of gravity” price) is one that supply and demand adjustments will tend to restore
following some change in the market. (And only rarely is this price called an
“equilibrium” price.) But Mangoldt, like Ricardo earlier in the nineteenth century,
found that attempting to give more general and logical answers than Smith to ques-
tions about the principles of economics produces verbal arguments that are just too
complicated to be viable. erein his turn to diagrams, equations, numerical exam-
ples – and to experiments with them – to answer the same questions as Smith, using
Smith’s concepts and terms, but with a dierent mode of reasoning using models.
Mangoldt’s discussion of the exchange ratio of goods used a large number of
demand and supply diagrams and they played an important role in demonstrating
his arguments. I use the term ‘demonstrate’ here, and take it seriously, to dieren-
tiate it from ‘illustrate’. e importance of this distinction came up explicitly in the
Edgeworth Box discussion (of Chapter 3, Section 6ii), where we saw how the inde-
pendent representational function of models goes beyond illustration in the sense
that more information is found in the diagram than in the text, and oen the text is
dependent on the mathematics or the diagram (as in Figure 7.1, showing Mangoldt’s
gures 3 and 4, 7, and 8). For example, by laying out the various dierent shapes that
the demand and supply curves might take, Mangoldt was able to explain the reason-
ing that lay behind those shapes. His diagrams and texts are mutually dependent,
even though his initial use of the diagrams did not involve experiments:
e more general and more urgent is the need satised by a particular type
of goods, and the less capable of being satised by other means, the more
see Ekelund and ornton (1991). For a more detailed and wider treatment of the French tradition
that includes supply and demand, see Ekelund and Hébert (1999). For a useful introduction to the
diagrammatic work of Marshall, see Whitaker (1975).
e World in the Model
260
slowly will demand diminish at low prices and the more quickly at high
prices. e demand curve will have a strong bulge. If, on the other hand, a
type of goods has a limited demand and is easy to dispense with or to sub-
stitute, then a rising price causes demand to contract more sharply even at
relatively low price levels and the demand curve will quickly approach the
price scale. Similar eects follow from the distribution of wealth. If wealth
is evenly distributed, demand will fall very gradually; if wealth is concen-
trated in a few hands, demand will contract sharply at rst and slowly
aerwards. In the one case the demand curve will be concave, in the other
convex (to the origin) as shown in Figure 3.
e rule of diminishing demand at rising prices is occasionally subject
to exceptions. Vanity or fear may cause demand not to fall, but to grow
when prices rise (Figure 4). (von Mangoldt, 1863/1962, p. 35)
Read carefully, these passages show how Mangoldt’s accounts of the shapes of
the curves in his diagrams enabled him to characterize, classify, and compare typ-
ical cases, an important modelling activity in itself, as we shall see later (and as I
Figure 7.1. Mangoldt’s Supply and Demand Model Experiments.
Source: Hans K. E. von Mangoldt, Grundriss der Volkswirtschaslehre, 1863, gures 3 and
4, p. 49; gures 7 and 8, p. 50.
Model Experiments? 261
argue further in Chapter 9). But though there were questions and answering stories
attendant on these dierent slopes in the demand curves, and it was these that
enabled him to dene and categorize the dierent cases, there was nothing that we
would yet want to call an experimental intervention in the model. Similarly with
his gure 7, which showed how a supply curve might fall over some range due to
economies of scale, but rise over others.
Other examples, such as his gure 8, do show how he conducted experiments
on his diagrams.
Economic progress and the advance of civilization tend to cheapen the sup-
ply of goods through better production methods and to extend it through
increased knowledge and mastery over nature. As a result the supply curve
tends to shi downwards and the point at which it goes o vertically to
innity is moved further outwards. is tendency contrasts with that other
tendency of progress which we have mentioned, namely to extend and
raise demand (see gure 8). e latter tendency is apt to push up the nat-
ural price, the former works in the opposite direction. Whether the natu-
ral price of any particular type of goods will shi upwards or downwards,
therefore depends on the prevalence of one over the other tendency of pro-
gress. (von Mangoldt, 1863/1962, pp. 36–7)
is example is beautifully clear: an implicit question about the eect of progress
answered by an experiment with the diagram. In this context, we can see how mod-
els oer the kind of power to demonstrate associated with experimental demon-
stration, just as we found Ricardo (in Chapter 2) used his arithmetical reasoning
chains to demonstrate outcomes rather than to illustrate his text discussions. is
demonstration also claries the benets of reasoning with the diagram: by separat-
ing out the two kinds of tendency and their opposing relative strengths, he provides
an explanation as to why there is no general and simple answer to what happens to
prices during a period of “progress”.
Mangoldt is particularly recognised by historians of economics for his treatment
of far more complex cases, particularly that of interdependent demand and supply
for two goods. Here, his textual discussion became exceedingly convoluted and inter-
twined with equations, numerical examples, and diagrams. For example, a verbally
conducted experiment convinces him that if demand rises for one good, it will also
rise or fall for the connected (‘dependent’) good, depending on the nature of the con-
nection and which kinds of goods are involved. But then the more dicult question
arises: What happens to the price of the dependent good? is begins a more spe-
cic discussion starting with the case of complementary goods where an increase in
demand for one good (A) led to an increase in demand for the other related good (B).
I quote the passage extensively on its own just to show how dicult it is to follow such
verbal reasoning without the help of diagrams; patience is required:
Assume that in a given state of the economy two goods whose consumption
is directly related are consumed in a certain proportion and that the price
e World in the Model
262
of both is their natural price. is means that for both goods the price
has settled at a level at which demand and supply are equal at which the
given proportionality obtains. Suppose now that nothing alters except
for a change in a price factor of the principal good A – for instance, new
productive capacity raises the volume of supply possible at each price. e
centre of gravity of the A-price would then shi, and equilibrium between
demand and supply would come about only at higher consumption than
hitherto. Given the assumed proportionality in the consumption of both
goods, demand for the dependent good, B, would also tend to rise. By
assumption, the means of payment available for the purchase of good B
remain constant; proportionality in the consumption of both goods can,
therefore, be reestablished only if the consumption of A contracts su-
ciently to liberate enough funds to raise demand for B to the appropriate
level. (von Mangoldt, 1863/1962, p. 42)
And so the text continues on, for a further twenty odd lines, densely describing the
assumptions and conditions under which the price of the dependent good will rise
in various cases of possible changes in prices and quantities, and movements in
output and consumption. is reasoning covered so many elements that it is really
dicult to follow. Nevertheless, Mangoldt manages to nish his text argument with
a general claim that the demand for the dependent good will rise so as to use up
all the funds available for the purchase of both goods and the price of B will be its
“new natural price” (p. 43).
It then turns out that all this text is merely preliminary discussion, for he then
changes his mode of reasoning: “Let us again clarify the argument by a graphical
exposition” (p. 56 in original, my translation3). As before, Mangoldt’s diagrams
serve both to demonstrate the outcomes of dierent assumptions or questions
about particular cases and to characterize dierent kinds of cases. But here the
diagrams work in conjunction with an algebraic treatment of the basic supply and
demand relations and with a mixture of analytical and numerical methods of solu-
tion.4 In these experiments, a set of supply quantity and price values for A and the
supply curve for B are assumed, but the construction of the demand curve for B
is based upon the algebraic relations and certain numerical assumptions (about
3 is is my alternative translation of the original German (the page reference is to the 1962
translation).
4 Commentators focus on dierent aspects of these methods. Schneider (1960) discusses Mangoldt’s
algebraic treatment, and quotes at length one of his numerical experiments, but in explaining
Mangoldt, he transposes his experimental numerical solution method into a four-quadrant dia-
gram, a favourite device of Schneider’s day and a sure indication of the dimension of diculty!
Creedy (1992) pays attention to the numerical method and oers an alternative interpretation of
what he did in algebraic form. Creedy also points out that the English translation alters the way the
numerical experiment is reported from the original German, making the historical interpretation
even more dicult.
Model Experiments? 263
the demand ratio of the goods and total funds available) which enable him to use
numerical methods of solution. ese experimental results are reported on the dia-
grams, so, for example, we can see the calibrated values from one of his numerical
experiments mapped onto his gure 16 (our Figure 7.2), even though the calibrated
numbers are not written onto the gure. e accompanying discussion gives a ser-
ies of little numerical examples or experiments to motivate the claim that the price
of B goes up as the supply quantities of A move rightwards. Further experiments
consider dierent cases so that in all, he provides diagrams, equations, and numer-
ics, for changes in demand and in supply of both substitute and complementary
goods.
Mangoldt’s analysis as a whole has been described as brilliant and innovative
in content (see Schneider 1960 and Humphrey, 1992), and so it is. It is equally
innovative in its reasoning mode: it bears the hallmarks of a scientist understand-
ing the value of models, indeed arguing and reasoning with models and mak-
ing experiments with them, but still, holding no strong grip on the concept of a
model. Unfortunately for the history of economics, Mangoldt’s diagrams and equa-
tions and his experiments with them were cut out of the 1871 reprint of his book
by the editor who thought that “it is utterly inconceivable to me that graphs or
Figure 7.2. Mangoldt’s Model Experiment for Complementary Goods (his gure 16,
where hm is the assumed supply curve for good B; the supply curve from the numerical
experiment for good A is labelled with successive fn; and the demand curve for good B
derived from the numerical experiment is labelled with successive gn, where the n represent
successive numbers.)
Source: Hans K. E. von Mangoldt, Grundriss der Volkswirtschaslehre, 1863, gure 16, p. 56.
e World in the Model
264
mathematical formulae could facilitate the understanding of economic laws”.5 is
surely made his text even more dicult to follow – at least it does for modern
economists! Mangoldt’s innovatory use of models seems to have been lost until
Edgeworth found it in the later part of the nineteenth century and then historians
rediscovered his work in the following century.
Fleeming Jenkin’s arguments with diagrammatic models of the laws of sup-
ply and demand of 1870 are equally brilliant, but much more condently model-
oriented and the text is rather an addendum to the diagrammatic work, for all of
Jenkin’s model work is demonstrative. Like Mangoldt’s, many of Jenkin’s diagrams
laid out various cases and categorized them. For example, he created representa-
tions of Henry ornton’s discussion of the behaviour of buyers and sellers of single
goods such as horses, and spoiling goods such as sh. Other diagrams demon-
strated the dierences between Dutch and English auctions. Elsewhere (1871–2, in
his 1887) he used the diagram to demonstrate tax incidence. Like Mangoldt, Jenkin
used his diagrams in explicitly experimental mode, making use of the internal
resources of the diagram to answer questions. In the initial design of his diagram,
Jenkin had dened the “whole supply” as the amount for sale “then and there”,
while the supply and demand curves were functional relations in which the supply
or demand depended on a given price. We see his “laws of supply and demand”
demonstrated in his gures 3 to 6 (our Figure 7.3 and 7.4) where the diagrams were
designed and used to distinguish the “rst law”, namely that the market price will be
where the “curves cut”, from the “second law”, namely the eect of a change in the
whole supply or demand. e experiments with the rst law diagrams (his gures 3
and 4) demonstrated the eects of alterations in the slope of the functions in the
graphic relations, while the experiments on the second law diagrams (his gures 5
and 6) demonstrated a whole set of “probable eects”: changes that followed from
“an increase in the whole supply” or “in the purchase fund” (i.e., amounts available
for demand). As we can see, each diagram showed the analysis of the experiment by
labelling the lines and giving a written list underneath of the elements in the exper-
iment and how they change, almost like a laboratory notebook reporting what hap-
pened in the experiment.
e marketplaces envisaged in Jenkin’s model world were still dominated by
competition amongst buyers and amongst sellers but the language of discussion
was no longer entirely Smithian, for example, the intersection point in the rst law
is referred to in his text as the “theoretical price” (p. 79 of 1887/1996) and the dia-
grams were presented as showing “a pair of imaginary demand and supply curves
for corn” (p. 77) useful for his demonstration of aspects of the “laws of supply and
demand”. Yet these curves are also quite empirical, for they, like Ricardo’s arith-
metic chains, showed that the corn was to be bought and sold in “quarters” and
priced in plausible amounts of shillings per quarter. e corn law battles over the
5 Quoted in Creedy (1992, p. 46); this section was the rst part of his text to be translated into English
in 1962.
Model Experiments? 265
Figures 7.3 and 7.4. Fleeming Jenkin’s Supply and Demand Curve Experiments.
Source: Fleeming Jenkin, “e Graphic Representation of the Laws of Supply and Demand,
and eir Application to Labour” in his Papers Literary, Scientic, etc, Vol. II, edited by
S. Colvin and H. A. Ewing, 1887, London: Longman and Green. Figures 3, p. 80; 4, p. 81;
5, p. 82; 6, p. 82 (Reprinted facsimile, 1996, London: London School of Economics and
Political Science Reprints of Scarce Tracts in Economics, No. 3.)
e World in the Model
266
Figures 7.3 and 7.4. (see previous page for details)
Model Experiments? 267
tari on wheat, which had kept the price high in Ricardo’s day, were over, for the
tari had been abolished by 1846. However, wheat remained the main staple for the
British consumer at this time, and its price an important political fact. In parallel to
Ricardo’s hypothetical farm accounts, Jenkin’s imaginary set of curves, demonstrat-
ing how the laws of political economy worked in the market for wheat, oered not
an abstract argument, but one with immediate relevance.
Note that contrary to the earlier work by Mangoldt and to modern conven-
tion, but consistent with the mathematical conventions of the day about the plac-
ing of dependent and determining variables, prices were shown on the horizontal
axes. Jenkin was a classic Victorian polymath – a well-recognised engineer who
wrote literary criticism, plays, medical tracts, political economy, and so forth. By
his mathematical economic analysis with his diagrams, he scooped Marshall, as
the latter recognised.6 Yet Jenkin’s work was to be snubbed by Marshall and Jevons,
who both claimed priority with the “scissors diagram” or “Marshallian cross” as it
later came to be known.7 Marshall developed the use of the diagram and obtained
a particular facility in experimenting with it compared with Mangoldt and Jenkin.
Indeed, it is his smoothness of experimental method with the model, rather than
any particular original nding with the model, that I wish to stress in the discussion
that follows.
2.ii Marshall
In the chapter of Marshall’s Principles of Economics (1890 and many later editions)
that I analyse here (book 5, chapter 13), Marshall used the now standard version
of a supply and demand diagram in which, by convention, prices are given on the
vertical axis, and quantities on the horizontal. Six of these diagrams are shown in
Figure 7.5, where the DD′ curve represents the potential demand by consumers for
a good at various prices and the SS′ curve the potential supply by producers over
the same price range. In an analysis that was typical for him (the argument went
on in the text, and the model manipulations were shown in footnotes), Marshall
asked four questions, conducted ten model experiments and six associated mental
experiments (all in less than ten pages), and then used the answers to provide a
commentary on both the policy and theoretical implications of the answers. I have
taken any case where the diagram was used to demonstrate a point as a ‘model
experiment’, and any case in which Marshall did not bother to work through the
diagram, but pointed directly to the answer, as a ‘thinking’ or ‘mental’ experiment.
ese mental experiments are cases where the question asks the reader to think of
the reverse of the just conducted model experiment. So he does not actually dia-
gram them, but the reader’s ability to do these mental experiments depends on the
original ones in the small world model being already understood. is means that
6 According to the later account by Foxwell, see Whitaker (1975).
7 See Humphrey (1992).
e World in the Model
268
the dierence between his mental experiments and his model experiments is not as
clear-cut as it sounds. Overall, however, the number of experiments is indicative of
the classicatory work going on – it takes sixteen cases to answer four questions.
e rst question Marshall asked is: What would happen in an industry when
there was some “great or lasting” change in normal demand? To answer this, the
model is manipulated: an increase in demand at all prices means that the demand
DD′ curve shis upwards to the right to the position dd′ (see his gures 24–6, the
top row of Figure 7.5). is experiment shows the curves’ new intersection point
(the point at which all exchanges are believed to take place, or the “equilibrium
point”): a, compared to the old intersection point: A. In the rst case, where the
commodity supply “obeys the law of constant return”, the price is determined on
the production side and the new point shows a rise in quantity (H to h), but no
change in price (A is the same height as a). However, according to Marshall’s text
and diagrams, there are two other alternative shapes that the supply schedule can
take: either upward sloping, or downward sloping like the demand curve (respect-
ively his gures 25 and 26). In the former case, the experiment shows that equilib-
rium quantity and price both rise, while in the latter case that quantity rises but
price falls. us, one question and three similar experiments with diagrammatic
models reveal that equilibrium quantity always rises, but that price changes depend
on the shape of the supply function. He is also able to rank the size of the quan-
tity changes in the three cases. e rst two of these three experiments could have
been done mentally, but only once the model diagram was already suciently well
known to the economists to be seen in their minds’ eyes, and its rules for manipu-
lation understood. When Marshall rst produced his Principles text, this would
not of course have been so. But the third case is dicult to treat, and to produce
the answer to his question, without the actual diagram and its manipulation, even
when the model is well known. Marshall then asks his second question: What hap-
pens if there is a decrease in normal demand? He does no model experiments here;
knowing the answers to the rst question provides immediate answers for each
case: the simple mental experiment is sucient.
Marshall’s third question is: What happens if there is an increase in the facilities
of supply? is question prompts a further three model experiments in which there
is a shi to the right or downwards of the supply curve from SS′ to ss′ (as shown in
his gures 27–29, the bottom row of Figure 7.5). ese model experiments allow
him to answer that regardless of the shape of the supply curve, equilibrium price
falls and quantity rises, though there is a range of price changes in the three cases.
ey also enabled him to classify the relatives sizes of the changes in the three cases,
and this turned into a discussion of elasticity of demand and (in his gure 29) of
whether the new equilibrium point would be stable or not:
e three gures 27, 28, 29 represent the three cases of constant and dimin-
ishing and increasing returns, respectively. In each case DD’ is the demand
curve, SS’ is the old position, and ss’ the new position of the supply curve.
Model Experiments? 269
A is the old, and a the new position of stable equilibrium. Oh is greater
than OH, and ah is less than AH in every case: but the changes are small
in g. 28 and great in g. 29. Of course the demand curve must lie below
the old supply curve to the right of A, otherwise A would be a point not of
stable, but of unstable equilibrium. But subject to this condition, the more
elastic the demand is, that is the more nearly horizontal the demand curve
is at A the further o with a be from A, and the greater will be the increase
of production and the fall of price. (Marshall, 1890, p. 466, fn1)
Marshall’s fourth question is: What happens if a tax or bounty is placed on
the price of the good? Here the reasoning necessary to follow through the answers
to the question requires quite complicated model experiments, but using exactly
the same set of diagrams. e answers hinges on what happens to the “consumers’
surplus” which is the triangle dened by, for example, the points DAS on his g-
ure 24. If a tax is placed on a good, the price paid by consumers will rise, and their
share of this “surplus” (the dierence consumers would have been willing to pay
and the amount they will actually pay at the market equilibrium price, A or a) will
Figure 7.5. Marshall’s Diagrammatic Model Experiments.
Source: Alfred Marshall, Principles of Economics, 1st edition, 1890. London: Macmillan & Co.
Book V, chapter XIII, gures 24–26, note 1, p. 464 and gures 27–29, note 1, p. 466. Reproduced
with acknowledgement to Marshall Library of Economics.
e World in the Model
270
consequently fall. e answers given by the model experiments lead to two further
sets of observations in which Marshall relates the ndings to wider issues. On the
one hand, the experiments prompt a discussion of the principles of taxation in
relation to both the model’s nal outcomes and the indirect changes in elements
in the model revealed by the experimental manipulations. On the other hand, the
model work leads to theoretical discussions on the validity of general claims about
the nature of the equilibria involved and to certain general issues of ethics and dis-
tributive justice.
In introducing his rst set of diagrams, Marshall suggests that diagrams are of
“special aid in enabling us to comprehend clearly the problems” (Fn 1, p. 464) of
his chapter. But as things get more dicult, Marshall’s dependency on the diagrams
and their manipulation get stronger so that on the next set of diagrams, he argues
that his explanations “can be most clearly seen by the aid of diagrams, and indeed
there are some parts of the problem which cannot be satisfactorily treated without
their aid” (Fn1, p. 466). Marshall was famous for railing against the unnecessary
use of mathematics – he only wanted mathematics that helped in understanding
economic problems; otherwise he had no use for it. Here we nd him advocating
the use of diagrammatic models as such helpful mathematics, rst in understand-
ing economic problems and then in using the models to demonstrate answers to
his questions.
2.iii Conceptual Work: Dening Generic Categories
While all these three authors, Mangoldt, Jenkin, and Marshall, developed and used
the same basic diagram, their conceptual apparatus and understanding of demand
and supply and their notion of the intersections were not entirely the same. What is
shared is that they took very little for granted in their style of reasoning. e prac-
tice of asking questions and manipulating diagrams to demonstrate the answers
to questions was foreign to the majority of economists of the day, and no doubt
that is why their texts make such a point of laying out the method of reasoning.
Some of Mangoldt’s and Jenkin’s quoted examples are rather clear, though others
(as we can see from the second example of Mangoldt) were much more laboured.
With Marshall, the method of reasoning begins to seem natural to the material.
My interpretation of these activities as ‘model experiments’ seems to t easily onto
all three economists’ usage of the supply and demand diagram, even though the
term ‘model’ was not yet in use and the style of reasoning had not yet been labelled
‘modelling’.
For both Mangoldt and Jenkin, the use of specic numbers on the graphs
remains important; as for Ricardo and his model farm numbers, their model
experiments function as examples in which the claims are partly general and partly
designed to t likely problems, causes, and plausible numbers of their day. ough
the examples have this dual quality, their reasoning with the models is consistently
demonstrative, not illustrative: they could not have made these arguments without
Model Experiments? 271
their diagrams, that is, without their models.8 For Marshall, the diagrams and their
demonstrations have become just a little more abstracted from the immediate
world, but he too, like Mangoldt and Jenkin before him, uses them to compare,
categorize, characterize, and classify during his analysis of the dierent cases. And
for each dierent kind of case, he produces ‘generic’ claims, by which I mean claims
that are not completely general (about the law of demand) nor entirely specic
(about the demand for sh or horses), but about markets in which demand curves
have certain kinds of shapes and certain characteristics.
e ability to dene kinds of cases is an important outcome of the way models
are used. Marshall’s ability to answer his “What happens when or if . . .?” questions
require that he commits himself to the shapes of the curves in his diagrams. Once
these dierent possible shapes have been given form in the model, the experiments
on the model immediately take him not to one answer, but to a set of answers
matching the set of cases he had laid out: remember he had four questions and it
took sixteen experiments to answer them for the dierent cases. Even when empir-
ical examples prompt the question, such as in Jenkin’s consideration of a market
for a single horse, or for sh at the end of the day, the economist must conceptu-
alise the form of the law of demand for such a case in the diagrammatic model.
us model questions and experiments take economists not so much to general
answers or very particular cases, but more oen to relevant categories of cases, or
generic cases, which prompt them to develop the conceptual details of the laws of
demand and supply relevant for those categories in their model experiments.
is analytical and categorizing work of model experiments ts in neatly with
the late-nineteenth-century notion of what it meant to do “formal work” in eco-
nomics. For example, W. E. Johnson’s taxonomy of methods from the encyclo-
paedia of the day (Old Palgrave, 1894–6), refers to formal methods as those that
“analyse and classify” concepts and involve the “logical processes of denition and
divi sion”. (ese formal methods were contrasted with “constructive” methods that
“establish laws and uniformities”.) is is not so very dierent from modern com-
mentaries on models. As Hausman (1992) and others have argued, mathematical
model work is conceptual theorizing work, concerned with classifying and char-
acterizing. In earlier chapters, we saw how economic concepts were formed in the
creation of models – as for example, the indierence curve and the contract curve
in the Edgeworth Box case. Here, we have found another aspect of how this con-
cept developmental work gets done consistent with Johnson’s and Hausman’s ideas;
namely in using models, the process of analysis prompts denition and division
to produce more specialised versions of the general laws of demand and supply
and so more closely specied models. So their model experiments enabled these
economists to explore the laws of demand and supply by dening and dividing into
dierent generic kinds the materials to which those laws applied, and by classifying
and categorizing the generic ways in which they applied. In so doing their model
8 See Chapter 3 for a discussion of the independent representational function played by models.
e World in the Model
272
experiments, Mangoldt, Jenkin, and Marshall created new kinds or categories of
relations by dierentiating them, and generally characterizing the shape and behav-
iour of supply and demand curves in ways that developed the conceptual content of
economic theories about markets.
Perhaps then we can regard modelling experiments in economics as a kind of
testing ground, not for seeking to prove or disprove the general law of demand, for
a model experiment could hardly do this, but one more like that of a creative design
workshop. Such model experimental work allows the economist to test out intu-
itions and ideas and so come to understand what their laws of demand and sup-
ply mean in dierent circumstances much as architects use experiments with their
models in the process of designing buildings, either to see how dierent designs
might look or how their buildings might be constructed.9 Another useful compari-
son may be found in material sciences and pharmaceuticals, where the aim of much
experimentation is to make new substances; indeed hundreds of thousands of new
things are made each year in laboratories: they are ‘synthesized’ and then ‘analy-
sed’. is creative, exploratory, character of experiments in such elds seems to be
paralleled in the model experiments of economics10. Economists create, in their
small model worlds, new categories and new manifestations of the basic demand
or supply relations, which can then be analysed in further model experiments. is
is how and why model experiments were instrumental in generating new elements
that developed the much older ‘laws’ of supply and demand.
3. Models in ‘Laboratory’ Experiments
ese historical cases of the late nineteenth century show how model reasoning
involves experimental work on the model or in the world of the model. e eco-
nomic relations of interest – the supply and demand curves – are represented in the
model, questions are asked, and the manipulation of the resources of the model is
used to provide answers. But if this way of using models is a form of experiment, we
need to ask how experimental controls are instantiated, and what type of demonstra-
tion is involved in such experiments. To answer these questions, it helps to have the
comparison case of economists’ classroom experiments ready to hand. is brings
our history to the years just aer the mid-twentieth century, when such experiments
on the supply and demand model began in economics. e classroom was the initial
site of the economist’s laboratory, its students the people in the modelled economy.
Here we will see how models typically came into the experimental design, and we
might even conceive of them as part of the experimental apparatus. But at the same
9 See Yaneva (2005) and Valeriani (forthcoming) for two examples from the literature on the use of
architectural models in the creative and construction process.
10 e hybrid experimental work of Hommes and Sonnemans (to be discussed in part 5 of this chap-
ter) contains the same combination of exploratory and classicatory work as they vary combin-
ations of inputs and models to see what happens to the outputs from their experiments.
Model Experiments? 273
time, the models are still the object of experimental interest: Do people really behave
as had been assumed in those Marshallian diagrammatic model experiments?
Economists have long assumed that market outcomes will have certain char-
acteristics, in particular that a group of buyers and sellers in a market will arrive at
an equilibrium price, that is, at the intersection of the demand and supply curves in
Marshall’s diagram. is assumption has now driven almost a century of research
into the conditions under which this assumption will hold, relying on mathemat-
ical work and modelling experiments to investigate the features of this theory.
However, many questions remain about how markets work and how the indepen-
dent individual buyers and sellers arrive at a price in the real world as opposed
to in the idealized markets portrayed in economists’ theory and in their models.
ese questions were the rst ones to be investigated in a classroom experiment in
economics and there is now a record of more than y years of such experiments
on this topic. Let us pass the argument to Edward Chamberlin, who conducted the
rst such experiments in economics at a time when modelling had just become well
established. He opened his experimental report in 1948 thus:
It is a commonplace that, in its choice of method, economics is limited
by the fact that resort cannot be had to the laboratory techniques of the
natural sciences. On the one hand, the data of real life are necessarily the
product of many inuences other than those which it is desired to isolate –
a diculty which the most rened statistical methods can overcome only
in small part. On the other hand, the unwanted variables cannot be held
constant or eliminated in an economic “laboratory” because the real world
of human beings, rms, markets and governments cannot be reproduced
articially and controlled. e social scientist who would like to study in
isolation and under known conditions the eect of particular forces is, for
the most part, obliged to conduct his “experiment” by the application of
general reasoning to abstract “models.” He cannot observe the actual oper-
ation of a real model under controlled conditions
e purpose of this article to make a very tiny breach in this position:
to describe an actual experiment with a “market” under laboratory condi-
tions and to set forth some of the conclusions indicated by it. (Chamberlin
1948, p. 95, his italics)
e last part of the rst paragraph is particularly signicant in our context: for
Chamberlin, experimenting with “a market” is a way to observe “a real model” in
place of the “abstract models” of mathematics and diagrams.
Chamberlin described a set of forty-six classroom experiments in which class
students were divided into groups of ‘buyers’ and ‘sellers’. ey were each given a
dierent card showing either the maximum price they, if buyers, would be will-
ing to pay (their ‘reservation’ prices) for a unit of a good or the minimum price,
if sellers, they would be willing to accept for a unit. (ese reservation prices for
buying:B and selling:S are listed in the column titled “Market Schedules” in his
table 1 on our Figure 7.6.) Each participant could trade one unit during a short
e World in the Model
274
period when “the market” was in operation by circulating through the marketplace
(the classroom) and trying to strike a bargain to buy or sell privately with another
participant. Once a contract was concluded, the transaction price (third column of
the le side of his table 1) was written on the class board, but not their reservation
prices. is is Chamberlin’s “real model” operating under controlled conditions.
In these experiments, the reservation prices (for buying and selling) writ-
ten on the cards were even numbers drawn from a supply and demand model
with conventional shaped curves, that is, downward sloping demand and upward
sloping supply, that were neither particularly steep nor at. If drawn out, how-
ever, as Chamberlin did in his report (see his gure 1, in our Figure 7.6), we see
Figure 7.6. Chamberlin’s “Real-Model” Experimental Results.
Source: Edward H. Chamberlin (April 1948), “An Experimental Imperfect Market”, Journal
of Political Economy, 56:2, 95–108; table 1 and gure 1 on p. 97. Reproduced with permission
from University of Chicago Press.
Model Experiments? 275
immediately that unlike the smooth continuous curves drawn by Marshall in his
diagrams and assumed in most models, these schedules have steps, for these prices
were set at even numbers and for trades at quantities in whole units, so a sched-
ule does not provide a smooth line. Since Chamberlin’s experiment oen went on
with a less than full set of price cards handed out (because of a limited number of
class participants), the schedules sometimes also had considerable gaps (or larger
steps) in them.
In most of his experimental outcomes, Chamberlin found that the average price
of transactions in this laboratory market was lower than the equilibrium price pre-
dicted by the Marshallian model (i.e., at the intersection of the demand and supply
curves used in his experiment) and sales were higher than the amount predicted,
as can be seen from the exhibit showing the actual transactions in the experiment
and the numbers given out to students forming the demand and supply “market
schedules” (see foot of his table 1, in Figure 7.6).
Much of the rest of Chamberlin’s paper was given over to further experiments
with dierent instructions or rules for trading in the classroom ‘market’ to explore
why these ndings might have arisen. He particularly sought to explain the die-
rence between average prices found in the experiments and the equilibrium price
expected from theory as the intersection of the two schedules of the model used
in his experimental design. From his experiments, Chamberlin came to doubt that
there was even a tendency towards this equilibrium:
It would appear that in asserting such a tendency, economists may have
been led unconsciously to share their unique knowledge of the equilib-
rium point with their theoretical creatures, the buyers and sellers, who, of
course, in real life have no knowledge of it whatsoever. (Chamberlin, 1948,
p. 102)
In 1955, Vernon Smith started his rst series of classroom experiments, or, as
they were known then: “experimental games”, meaning role-playing experiments
(see Chapter 8) in which the
. . . experimental conditions of supply and demand in force in these mar-
kets are modeled closely upon the supply and demand curves generated by
limit price orders in the hands of stock and commodity market brokers at
the opening of a trading day. (Smith, 1962, p. 111, italics added)
Smith followed an experimental design very similar to Chamberlin’s11. Each class
participant was given a card labelled as buyer or seller and each had a reserva-
tion price drawn from the schedules of a supply and demand model. But every
11 Vernon Smith’s contributions in developing the eld of experimental economics have been rec-
ognised by a Nobel Prize in economics. At the time he started such work, few other economists
were undertaking experiments, though by the late 1950s and early 1960s, experimental work had
begun to ourish in a small way in economics, partly in cooperation with experimental work by
psychologists, a point briey discussed again in Chapter 8 in the context of Shubik’s work. See
Guala (2008) for a short history of experimental economics.
Figure 7.7. Smith’s First Classroom Experimental Results with the Market Model.
Source: Vernon L. Smith (April 1962), “An Experimental Study of Competitive Market Behavior”, Journal of Political Economy, 70:2, 111–37;
chart 1 on p. 113. Reproduced with permission from University of Chicago Press.
Model Experiments? 277
experiment had several periods during which “the market” operated, and in each
time period, each person could make one new trade. In addition, contracting was
conducted openly by students raising their bids and oers in public so that every-
one knew what all the bids and oers were. ese two features meant that students
had more chance to learn about the demand and supply reservation prices held
by others in ‘the market’. Smith carried out ten sets of experiments, varying the
shapes of the demand and supply schedules, sometimes changing their levels in
mid-experiment, and sometimes letting participants trade two units. With these
design features, Smith found overall a much greater evidence of convergence of
exchange prices, than had Chamberlin, towards the ‘equilibrium’ prices indicated
in the various supply and demand models that he used to generate the reservation
prices in each of the experiments he conducted. We can see in the report of Smith’s
rst experiments, shown in his chart 1 (in Figure 7.7), both the stepped model
schedules that generated the prices on the cards that he gave to participants and the
convergence to that model market equilibrium over time in the sequence of runs of
his rst experimental market.
ese early experiments from Chamberlin and Smith are regarded as classics in
the eld, and their charts of the model curves and numerical outcomes have become
totems within the experimental community used both to motivate the rationale for
experiments and to convey succinctly the kinds of experimental results that opened
up investigation of long held assumptions within economics. I will come back to
this sequence of classic classroom experiments later in the chapter.
4. Comparison: Model Experiments and Laboratory Experiments
4.i Controls and Demonstration
To compare these two kinds of experiments: economists’ model experiments and
their classroom experiments, we need some grip on the notion of experiment in its
ideal form namely, in the laboratory. ese ideals might be most easily communi-
cated by thinking about the example of chemistry, which provides the typical idea
of the layperson’s laboratory science with test tubes, Bunsen burners, a range of
apparatus, jars of chemicals, and a workbench12. In this ideal experimental milieu,
the environment is controlled (e.g., all the apparatus is clean), the inputs to the
experiment are controlled (e.g., the amounts are of specied quality and care-
fully weighed quantity) and the experimental intervention itself requires a level
of control in order that the eectiveness of the change can be properly assessed.
at is, for example, the amount and process of adding chemical A to chemical B
12 Chemistry has also provided the basis for one of the most convincing accounts of tacit knowledge
in creative laboratory work in the form of Collins’ investigation into crystal growing (see Collins,
1990).
e World in the Model
278
(under the controlled conditions) must itself be carefully controlled in order for
the eect of the experimental intervention to be properly assessed. In such labora-
tory experiments, a particular process of interest cannot be isolated, accessed, and
assessed without rigorous attention by the experimenter to all kinds of control.
e experimental scientist must work hard to take account of all conditions
and factors that are likely to interfere with the process of interest. Here it is useful to
draw upon Marcel Boumans’ (1999) dissection of ceteris paribus conditions, which
extends the analysis of such factors by distinguishing between three sorts of control
conditions: ceteris paribus, ceteris neglectis, and ceteris absentibus.13 Some disturb-
ing causes may be declared absent if the experimenter can physically rule them
out of the setup (ceteris absentibus). Of the causes that are present but are not the
subject of experiment, some may be thought to be so minor in eect that they can
be neglected (ceteris neglectis), while others that are present have to be controlled
for by procedures that hold them constant during the experiment (ceteris paribus).
ese control conditions make the setup of the laboratory experiment somewhat
(more or less) articial, but it remains of the real world for all that because however
ingenious the scientist, the material world can be controlled only to an extent. Of
course, the subject of interest is not the controls, but the process and outcomes of
the experimental manipulation: the careful adding of A to B and its assessment.
Experimentalists in economics follow the same ambitions as in other labora-
tory sciences, and indeed, soon came to refer to their classrooms as “laboratories”.14
ey sought to remove or control interfering factors in the environment that might
invalidate the experimental results and to conduct the experimental intervention
in such a way that economic behaviour could be isolated and its experimental vari-
ation become known. In economics, as in other elds, these controls are enforced
in economics as much through experimental design choices as through direct
physical means. Chamberlin and Smith exerted little control over the environment
of the open classroom, but exerted control over the behaviour of the participating
subjects by limiting what they could know and how they could trade, thus control-
ling both inputs and allowable variations in behaviour. For example, Chamberlin
used his experimental design to set separate limits on the contract price for each
person and he controlled the distribution of those limits using the schedules from
his demand and supply model. He also set controls on the amount that could be
13 Boumans’ work on this problem in the context of the functioning of economic models as measur-
ing instruments connects to Hasok Chang’s (2001) discussion of the development of thermometers.
Both works are outcomes of the joint “Measurement in Physics and Economics” research project
at the London School of Economics (Centre for Philosophy of Natural and Social Science) and
University of Amsterdam’s History and Philosophy of Economics group. For a much fuller treatment
of these issues in the measurement context, see the books by Chang (2004) and Boumans (2005). For
a discussion of ceteris paribus assumptions in the supply and demand context, see especially Hausman
(1990); and in the general economics context, see Boumans and Morgan (2001) and Mäki and Piimies
(1998) and the references in both.
14 Such experiments later moved into computer ‘laboratories’ (where much greater levels of control
over personal interaction and so environments and inputs are possible) when experimental eco-
nomics really took hold in the 1980s and 1990s.
Model Experiments? 279
contracted in each period by each person and the amount of information made
publicly available. We can think of these controls as “rules” (known to economists
as “institutions”) that participants had to follow. But he le room for variation in
action because he le open how bargaining negotiations were conducted.
How such controls are instituted forms one of the dimensions of contrast
between model experiments and laboratory experiments. As we see in Table 7.1,
in the laboratory experiment, the experiment is in the real world and elements are
controlled physically and by rules of behaviour. In contrast, in the model experi-
ment, the experiment is in the world of the model, where controls are made by
assumption in the process of creating and using the model. e model experimen-
talist has control over the design of the model: he or she decides its elements and
their relationships, ‘isolates’ them by excluding other factors (as Edgeworth did in
choosing a desert island economy, as in Chapter 3), and ‘idealizes’ away awkward
features (as in the history of economic man, Chapter 4). e modeller assumes
that minor causes can be neglected; that certain things are zero; and that certain
things are unchanging. In fact, economists state the phrase ceteris paribus to imply
that all three of Boumans’ conditions hold by assumption without discriminating
between them. In contrast, the laboratory economist has to enforce physically these
dierent types of conditions: in the design of the experiment to ensure an adequate
experimental procedure and on the environment within the laboratory. Whereas
the modeller can impose, by assumption, a total independence between two or
more elements in the model (however implausible that might be) in order that the
model will be tractable for experimental manipulation, that degree of independ-
ence might not be obtainable in the equivalent real material system. Related elem-
ents or confounding causes may prevent experimental isolation and demonstration
in the laboratory experiment whereas they can so easily be assumed away in the
model experiment: everything else may not be the same or may not be ruled out
when manipulating the real world system whereas it can be held the same or set at
zero when manipulating the model.
Table 7.1. Model Experiments and Laboratory Experiments
Model Experiment
(Mangoldt, Jenkin, and
Marshall)
Ideal Laboratory and
Classroom Experiment
(Chamberlin and Smith)
Materials of the
Experimentable World
Create an articial world in a
model
Create a controlled real
world within an articial
environment
Experimental Control By model design and assumption
of ceteris paribus conditions
By experimental design
and physical controls/rules
Demonstration Method Deductive in model Experimental in laboratory
Note: is and the following Table 7.2 were developed from comparisons rst made in Boumans and
Morgan (2001), Morgan (2002a, 2003), and nally in Morgan (2005), some of which also bring in the
econometrics comparison but not those of eld and natural experiments.
e World in the Model
280
We can see how these model controls work if we go back to our late-nineteenth-
century experimentalists. ere were certain things in Marshall’s model experiments
that he did not bother to make any specic assumptions about. For example, he moti-
vated his rst experiment by listing ve reasons why normal demand might have
risen: change in fashions, new use for the good, new market for the good, decline in
supply of a substitute good, and increase in wealth or income. But it made no die-
rence to the model experiment which of these were relevant for he assumed that all
these causes had the same eect, namely, a rise in normal demand that was the start-
ing point of the experiment. He also assumed away all sorts of potentially disturbing
factors, such as events in closely related markets (though he did consider these in
other chapters). ere were also many hidden assumptions, such as that of automatic
adjustment to equilibrium, that the curves were smooth, cut the axes, and so forth,
which were required to make his model experiments work neatly.
e importance of these assumptions becomes particularly evident if we com-
pare Chamberlin’s laboratory experiment with Marshall’s earlier model experi-
ments. We can see that Marshall’s outcomes depended on the assumption that
before the experiment (as it were) trading was at the intersection point of a supply
and demand curve and that there was an automatic adjustment to the new inter-
section (or equilibrium) point whenever one of the curves was shied in the exper-
imental manipulation within the model. In Chamberlin’s classroom experiments,
by contrast, reservation prices were controlled by a design based on a pair of imag-
ined curves of potential supply and demand from Marshall’s diagrammatic model.
But while those numbers on the stepped curves limited each participant’s range of
behaviour, there was nothing in the experimental design that enforced buyers and
sellers to trade at those prices, or for their behaviour in ‘the market’ to lead to the
intersection point of those curves. As Smith wrote about his chart 1 (Figure 7.7),
participants were free to trade within the shaded area of the graph, but,
We have no guarantee that the equilibrium dened by the intersection
of these sets [of reservation prices – the stepped lines] will prevail, even
approximately, in the experimental market (or any real counterpart of it).
e mere fact that, by any denition, supply and demand schedules exist in
the background of a market does not guarantee that any meaningful rela-
tionship exists between those schedules and what is observed in the market
they are presumed to represent. All the supply and demand schedules can do
is set broad limits on the behavior of the market. (Smith, 1962, pp. 114–5)
is dierence between the materials of the laboratory and model experiments
is summarized in the top row of Table 7.1: the laboratory scientist creates a con-
trolled real world within an articial environment while the modeller creates an arti-
cial world in a model.15 But in the laboratory case, it is not only the experimenter
15 Boumans (2002) shows how this latter idea is now the self-conscious aim of many economists. See
also the discussion of “credible worlds” in Chapter 6. e terminology of “articial worlds” has been
Model Experiments? 281
who places controls on the experiment, for the agency of nature also creates bound-
aries and constraints on the experiment. ere are constraints in the mathematics
or diagrammatics of the model too of course, but the critical point is whether the
assumptions that are made there happen to be the same as those of the situation in
the world that the model is held to represent, and there is nothing in the materi-
als of the model to ensure that they are. is fundamental dierence between the
‘experimental world’ and the ‘model world’ has considerable implications, as we
shall see in later Sections 5 and 6.
Another fundamental point of dierence between model experiments and
laboratory experiments lies in the nature of their demonstration (the third line
of Table 7.1). It is easier to recognise, and to label, this dierence as that between
experimental demonstration and deductive demonstration than it is to provide a
characterization of the dierence. It is tempting to portray model demonstration
as superior on the view that it is grounded in some form of abstract diagrammatic
or mathematical logic, compared to experimental demonstrations that, as we have
learnt from modern science studies, depend on all sorts of technological and human
and social attributes that defy philosophical codication.16 But this apparent super-
iority of mathematics may be regarded as doubtful since Lakatos’s seminal Proofs
and Refutations (1963) recognised that mathematical argument too has its own
informal nature. And, as we have already seen, the kinds of diagrammatic model
reasoning that Marshall used depended critically on all sorts of shared disciplinary
views from economics (some labelled ‘theory’) about the economic elements rep-
resented in the model, about automatic adjustment processes, and, most critically,
on what constitutes a valid manipulation of the elements in the model.
Knowledge of what counts as a valid experimental manipulation of elements
in a model can be understood as equivalent to a knowledge of valid experimen-
tal protocols in the laboratory. In laboratory experiments, some protocols are
about conditions and control, but others are about the order and range of permit-
ted interventions. e situation is similar with model experiments. As discussed
in Chapter 1, the deductive resources in model demonstrations depend on both
the language of the model and its economic content, so its manipulation is subject
not only to the protocols of legitimate mathematical manipulation but also to the
legitimate subject-specic rules about what can be done to what, what ranges a
parameter might take, and so forth. For example, in Marshall’s diagrammatic sup-
ply and demand model, the curves can be shied only in certain ways in response
to particular questions raised, and if a sequence of changes is involved, the order of
this is not open. e use of the model resources are also shaped, as we have seen in
independently applied to understand Marcel Lenoir’s work on the supply and demand model; see Le
Gall (2007), chapter 6.
16 On the one hand, science studies has debunked experiment for us (e.g., see Gooding et al., 1989;
Gooding, 1990; Hacking, 1983; and Franklin, 1986, 1990) while at the same time philosophers
have also moved away from dening experiment in any simple way (see Heidelberger and Steinle,
1998; Radder, 2003; and Rheinberger, 1997).
e World in the Model
282
Chapter 6, by the need to provide a plausible or meaningful economic account of
the sequences of changes and outcomes demonstrated in the model experiment. So
the validity of demonstration depends on following valid subject matter protocols
in both model and laboratory experiments.
4.ii Experimental Validity and e Inference Gap
In Chapter 1, I argued that models served as an instrument of enquiry rather than
a mode of truthmaking, and that models were both objects to enquire into and to
enquire with. In experimenting on models, economists enquire directly into the world
of the model, and only indirectly into the world represented in the model. e ques-
tion of whether an experimental result in any eld, and for any kind of experiment,
can be taken as valid for the uncontrolled real world is an important and complicated
problem. Model experiments are no exception. e worries appear dierent because
couched in dierent terms, but for communities of both model users and labora-
tory experimentalists, they are directly related to issues of control and representation.
For laboratory scientists, the main problem can be seen as one of ‘external valid-
i t y ’. 17 Do the processes and results obtained in the laboratory hold true in the world?
Has the world been suciently well replicated in the laboratory? Does the articial,
controlled environment created for the laboratory experiment nevertheless allow the
experimentable materials to behave suciently naturally to justify inference from the
laboratory to the world? For economists using models, this same issue can be under-
stood as a question of ‘similarity’ or ‘parallelism’. Has the real world been well enough
represented in the created, circumscribed and parallel world in the model for infer-
ences to be made from the model experiment to the world. ese two related points
of contrast in the materials of the experimentable world – control and representa-
tion – have implications for the range of potential inference from the two types of
experiment. ese dierences are displayed in Table 7.2, an extension of Table 7.1.
In experimental economics, the validity of experimental results is defended
by referring to the design of the experiment. Experiments are designed to recreate
or replicate part of the real world in the classroom ‘laboratory’. Control is depen-
dent on the choice of experimental setup, circumstances, and procedures (institu-
tional rules, rewards, and so forth). ese choices are guided by the experimenter’s
need to design the experiment in such a way that real economic behaviour is made
17 In Morgan (2005), I discuss Harré’s (2003) argument that there are two dierent kinds of experi-
ment, ones that intervene on natural objects, and others that create artefacts that are not paralleled
in the natural world. It was this that suggested to me that the inference problem of parallelism
(from the latter kind of experiment) might be considered dierently from that of external validity
(for the former kind), and that this has relevance for how to think about inferences from models.
On ‘parallelism’ in experimental economics, see the work of Francesco Guala (another member of
the “Modelling” and “Measurement in Physics and Economics” projects at LSE), particularly his
1999b. He also treats experiments as playing the same kind of mediating function as models (see
Guala, 1999a, 2002, 2003 and his 2005 book). Conversations with Francesco Guala have helped
me clarifying my thinking about many aspects of laboratory experiments in economics.
Model Experiments? 283
manifest in the experiment. Although there are arguments as to whether experi-
mental subjects, such as the students in Chamberlin’s and Smith’s classroom exper-
iments, really do behave ‘naturally’ in such articial environments, nevertheless
they share the quality of being humans in economic action. is ‘natural’ claim is
obviously more of a problem where the students are asked to role play, for example,
managers in industries. Nevertheless, this element in the inference gap is surely
less than for model experiments, where the humans are represented by model men,
symbols that behave as programmed by the economists (see Chapter 4).
e quality of economists’ experimental design and their real human inputs
can be adduced as reasons why the results experimentalists nd in their con-
trolled situations might carry over and be considered valid in the external, that is,
the uncontrolled real world. ese qualities may make it possible to infer to very
similar situations (in terms of behaviour, objects, rules, and circumstances) in the
world, but that very same tightness of controls and the high levels of specicity
involved in the laboratory experimental setup make inferences to situations and
circumstances in the world that are not exactly the same more problematic. us,
Chamberlin could make some inferences about the behaviour of people (acting
under similar market rules and within a similar kind of demand and supply market
as given by his model) in the world, but could not say much about their behav-
iour in markets with dierent characteristics or where the rules are very dierent.
Smith found it possible to make somewhat wider inferences about behaviour under
his rules because he found stable results over a set of experiments with consider-
able variation in supply and demand curves. Taking the Chamberlin and Smith
cases together, economists might perhaps make comparative inferences about how
people behave, and the eects of this, under two dierent kinds of market rules of
Table 7.2. Model Experiments, Laboratory Experiments, and Inferential Scope
Model Experiment
(Mangoldt, Jenkin, and
Marshall)
Ideal Laboratory and
Classroom Experiment
(Chamberlin and Smith)
Materials of the
Experimentable World
Create an articial world in a
model
Create a controlled real
world within an articial
environment
Experimental Control By model design and assumption
of ceteris paribus conditions
By experimental design and
physical controls/rules
Demonstration Method Deductive in model Experimental in laboratory
Inference to World Dierent materials:
“casual”* but wider range, weaker
validity; relies on accurate
representation
Same materials:
specic but narrower range,
stronger validity; relies on
accurate replication
Potential of Results** Surprise Confoundment
* is term derives from Gibbard and Varian’s 1978 description.
** See Section 6 of this chapter.
e World in the Model
284
interaction. But still, the validity of their results was limited in scope because, their
experimental work had shown them that the details of rules or ‘institutions’ matter
to outcomes. eir results have a certain strength in external validity, but that val-
idity is narrowly limited to like situations in the world.
In contrast, for mathematical modellers the problem of inference from model
experiments is understood as directly related to the kinds of assumptions involved in
creating their small world models. eir model versions of the world are not already
given; they have to be created. As we know from the rst half of the book, this involves
processes of imagination, abstraction and simplication in representing the economic
relations and events into a model. In Marshall’s cases, these processes created a model
world of supply and demand relations in which the economist gains experimental
control by making assumptions about the connecting, confounding, and disturbing
factors in that model world. It is these assumptions and simplications that make the
model world tractable so that experiments on it will produce results.
While these abstractions, simplications, and controls by assumption all limit
the applicability of the model-experimental results to any particular concrete events
in the world, yet paradoxically, it is these same qualities that make it easier for econ-
omists to ‘apply’ the results of their model experiments ‘approximately’, or even as
Gibbard and Varian (1978) suggest, “casually”, to a wider number of objects and
circumstances in the economic world: namely, to all those that share some common
traits with the model world. us, for example, Marshall’s experiments on models
provide potential inferences about the direction of change in quantity in response
to a shi in the demand curve due to a whole range of causes. But, unless – to con-
tinue with Marshall’s example – an economist knows the exact shape and slope of
the curves, he would be hard pressed not only to make general inferences from
such experiments, but equally to provide narrative explanations or useful infer-
ences about any particular case in the real world. is is where the dividing and
categorizing work of modelling comes in. As we saw, Marshall broke down the gen-
eral case into dierent sub-cases or classes – of dierent shaped and sloped curves,
suggesting that inference could be valid back to a set of applications in the world
where those generic kinds of curves might hold. But at the same time, this infer-
ence is relatively weak, because such models still lack the host of details required for
vaid inferences in any particular concrete case. e generic level at which models
operate – at the level of a class or typical kind – means that their experiments attain
a degree of particularity at the same time as a degree of generality.18 is explains
why the range of inferences from model experiments is less than that from general
theory, but broader than from laboratory experiment (where inferences are bound
by the specics of experimental design) and than econometric modelling (where
inferences apply only to a specic time and place), both of which have narrower
domains but stronger claims to validity.
18 is classication element of modelling is nicely reected in John Sutton’s ‘class of models’ approach
that relies on modelling to categorise industries into dierent kinds that can then be more eec-
tively worked with than by taking the set as a whole (see Sutton, 2000 and Morgan, 2002b).
Model Experiments? 285
At this point in the discussion of inference, it is worth returning to the four
steps of model reasoning outlined in Chapter 6: create a model for the problem
of interest, ask questions, make experimental demonstrations in the world of the
model, and tell narratives of inference and explanation. ese must necessarily
be connected: so the possibility for making inference from a model experiment
depends upon the question that prompts the experiment. An entrance to this con-
nection comes from considering May Brodbeck’s aphorism: “Model ships appear
frequently in bottles; model boys in heaven only” (1968 [1959], p. 579). We can’t get
much help in understanding how ships can transport goods or explain why boys
are naughty from these models. Why not? To understand exactly how a ship can
oat, simplifying into a model that ts into a bottle doesn’t help, but simplifying to
capture the relations among length, dra, and displacement may do. Similarly, an
idealization process that provides a model of the behaviour of a boy in heaven may
not be very useful to social scientists seeking to answer questions about real boys in
the world. Rather, scientists need to represent or denote in their model some of the
essential characteristics relevant for understanding boys in the real world if experi-
ments with the model are to help them answer questions about real boys. Scientists
have to capture the elements and relations in their model that are relevant to the
question asked if they are to provide a model demonstration in answer to that par-
ticular question: that is, the question (the external dynamic) and the resources of
the model (the internal dynamic) have to be aligned.
e challenge to economists then is to make their model world descriptively and
analytically useful at precisely that point where the question is to be answered. If the
problem at issue is how dierent pricing strategies aect a supply and demand mar-
ket outcome, then the market input strategies have to be considered very carefully.
If questions are about what happens when the demand curve shis, both demand
and supply curves need to be eectively represented, but particularly, as Marshall
showed in his experiments, the latter, since the experimental manipulation of the
demand curve traces out the shape of the supply curve on which the experimental
results for that kind of model depend. is is the classic ‘identication problem’,
as it is known in econometrics.19 And in this respect, model experiments have the
same structure as laboratory experiments, for it is the elements of the model or
classroom manipulation that are the focus of the economists’ questions, and that
require careful model or experimental design, in order for the experimental inter-
ventions to provide informative output.
Both kinds of experiments depend on controls of some part of the system as
well as the environment to make their interventions work, even though these con-
trols make those aspects of the laboratory or the model world articial. And both
kinds of experiments have problems in isolating and capturing the part of the world
that they want to interrogate. A comparison emphasises these aspects in common.
19 For a history and analysis of that problem, in the same supply/demand domain, see Morgan
(1990), and Boumans (2005).
e World in the Model
286
We might say that in the case of laboratory science, successful experiments depend
on accurate replication in the articial environment of the laboratory of the ele-
ments, changes, and outcomes in that part of the world relevant to the question. Or,
as Cartwright has suggested, “when features of the situation of the [experiment]
are just right to manifest the natural characteristics of the process”, then infer-
ences might be made from the results of experiment to teach something about the
world.20 In the case of a modelling science, a parallel claim would be that successful
experiments depend on accurate representation in the articial world of the model of
the parts of the world relevant for the questions of interest.
But there is of course a serious catch-22 situation here. Economists create mod-
els in an eort to nd out how the world works and it is because they don’t already
know how it works that they also don’t know whether they have an accurate model
representation! e real problem therefore lies in that the sciences do not have for-
mal procedures and inference criteria for deciding when a representation is a good
one. is might be called ‘forward inference’ from the world to the model dur-
ing the process of model-making, in contrast to ‘back inference’, from the model
experiment to the world when using the model. If a model is a good representation,
an experiment with it may well be informative. But, this back inference too lacks
formal criteria.21 is is not just a problem for model experiments, for the methods
of back inference from laboratory experiments are mostly informal too.22 And even
when economists do have formal back inference procedures based on statistical
theory (as in econometrics) these do not mean that it is easy to make valid infer-
ences in practice. is general lack of principles and procedures for making infer-
ences from models are why, as we found in Chapter 6, economists using models to
comment on, or act in, the world fall back on the credibility and plausibility of their
narratives.
Strangely perhaps, the most obvious element in the inference gap for models (in
comparison with that for laboratory experiments) lies in the validity of any infer-
ence between two such dierent media – forward from the real world to the arti-
cial world of the mathematical model and back again from the model experiment
to the real material of the economic world. e model world is at most a parallel
world.23 is parallel quality does not seem to bother economists. But materials do
20 Cartwright (2000, p. 6), a sentiment that goes back to Bacon.
21 It is generally agreed that this requires some kind of outside evidence or additional information
for models as well as for hybrid experiment setups, and simulation procedures (see Oreskes et al.,
1994 and Oreskes, 2000). What kind of evidence is not agreed: for example, economists take the
accuracy of the representation to depend on the realism of the model assumptions; Cartwright
(2000) suggests we need outside knowledge of causes; and Hartmann (1996) argues that we need
independent reasons for believing the model to be used.
22 See, however, Deborah Mayo (1996).
23 It is because the model world is a parallel world that the inference problems for model experi-
ments can be labelled as ‘parallelism”, in comparison to the laboratory experiment where the infer-
ence question is one of ‘external validity’. is ‘parallel world’ terminology can be found also in the
discussion of “credible worlds”, see Chapter 6.
Model Experiments? 287
matter: it matters that economic models are only representations of things in the
economy, not the things themselves.
e inference gap is not just a matter of language, important though that is,
but also a matter of the distance this creates in the experimentable materials. In
Chapter 1, I characterized the modelling tradition of economics as one concerned
with thin men acting in small worlds. Early discussions of the supply and demand
diagram were premised on an economic man who still had some content and feel-
ings, so that we found Mangoldt arguing about people behaving from vanity or
fear. Jenkin’s discussion of buyers at auctions tells us their judgement of the market
depends “partly on the quickness of the bids, and partly on their former expe-
rience and general knowledge” (Jenkin, 1887/1996, p. 84). But as my Chapter 4
history of this model of economic man recounts, the fatter character of the nine-
teenth century gave way to a more thinly characterized rational economic man in
twentieth-century economics who became the animating device assumed to be
acting inside small worlds like these market demand and supply diagrams. is
model economic man is predictable, for he behaves, as Merkies (1997) suggested
about the people in the Edgeworth Box, “according to the wishes of the econo-
mist” (see my Chapter 3). But the implications of his behaviour have to be worked
out for each model in which he is placed (as we shall see in Chapter 9). Economic
man is not any real economic man, any more than the supply and demand curves
are the real marketplace.
We can express this in a more philosophical way by adopting the language that
Rom Harré (2003) used when he made this same point about his “domesticated
world” experiments, those conducted using colonies of fruit ies that scientists have
captured and tamed to live in their laboratories.24 In contrast to the representations
provided by mathematical models, these fruit ies can be taken as representatives
of fruit ies in the world and may even serve as representatives for other kinds of
ies.25 ere are epistemological consequences of this shared ontology. It is because
real experiments are made of the same stu as the world that their epistemological
power is greater: inference back to the world is likely to be easier and more convinc-
ing than for the case of model experiments where there is no shared stu, no shared
ontology of things and materials.26 e inference gap is much harder to bridge –
for example – for model economic man than for his domesticated version in the
economists’ classroom or laboratory. I will return to this point when I up take up
the hint of the last row in Table 7.2 on “surprise versus confoundment”. Meanwhile,
24 See Weber in Creager et al. (2007) and references therein.
25 See Morgan (2003) on these issues of representing; and Baden-Fuller and Morgan (2010) for the
representativeness idea with respect to ‘business models’.
26 My commentary in this chapter is concerned with the dierence between experiments on math-
ematical models (and, later on, computer models) of natural or social systems and experiments
directly in the material of the natural or social worlds. ere are other kinds of experiments
wherein the materials of experiment dier from those of the focus of interest and I discuss experi-
ments with analogical models in Chapter 5 and in Morgan and Boumans (2004).
e World in the Model
288
I turn to my nal case of model experiments in economics. e discussion so far
suggested we could make a rather clean cut between experiments in mathemati-
cal, small-world, models and those where models featured in experiments in class-
rooms and laboratories. But as experimentalists became more ambitious, and their
techniques of experiment developed further, they wove models more deeply into
their experimental designs. us the distinctions that I have made between experi-
ments in the world of the model and models that play a role in experiments, or
between model experiments and laboratory experiments, have become increas-
ingly dicult to make.
5. Hybrids
e ideal of experiments given above suggests that successful laboratory experi-
ments rely on the object or process of interest having a high degree of detachabil-
ity (so that the ceteris paribus, absentibus, and neglectis conditions hold) and of
manipulability (so that the scientist can vary or manipulate the process of interest
in a controlled way in order to make an experimental demonstration and get some
results). But many of the things scientists want to learn about cannot be studied
in a laboratory experiment because those things do not have these joint qualities
of detachability and manipulability: the weather system and the economic system
are two obvious examples of systems that are neither isolatable nor controllable
in the laboratory.27 Economists can reproduce reasonably complex situations and
induce certain kinds of economic behaviour in the laboratory (see Guala, 1999b),
but cannot easily recreate the open environment of market forces and laws in which
those actions occur. As we saw in the classroom experimental work of Chamberlin
and Smith, models can oer substitute controls for the market, but these are oen
far from the open market institutions of interest to economists. Yet mathematical
models of these systems are equally likely to be insoluble and intractable for ana-
lysis. And even where a system has the qualities necessary to enable model investi-
gation, the ways in which the model’s elements and capacities can be manipulated
may not be at the level the scientist wants to investigate. It is in these situations,
where real-world experiments and model experiments are both equally problem-
atic, that various forms of hybrid experiments and simulations – all of which use
models in some way or other – have become important in scientic work.
5.i Virtually Experiments
I take as my case here the work of two of my colleagues at the University of
Amsterdam: Cars Hommes and Joep Sonnemans, who wanted to learn about mar-
ket behaviour at a level of complexity beyond that which could be easily investigated
27 On climate models, see Dahan Dalmedico in Creager et al. (2007).
Model Experiments? 289
in straightforward lab experiments and that was also too complex for mathematical
model work (which is typically where simulation comes in; see Chapter 8).28 In a
series of three experiments (see Sonnemans et al., 1999 and Hommes et al., 1999),
they joined Hommes’ mathematical experiments and numerical simulations using
a model to Sonnemans’ laboratory experiments on learning. eir aim was to
allow role-playing participants to behave as if operating in a market, but to t their
behavioural inputs together in ways that model a market. So here the model device
that brought these experiment participants together was an active element in the
experiment itself.
e individuals in their laboratory experiments are told that they are each
advising a hypothetical supplier who operates in a market where he or she must
make output decisions based on the expected price (because of production lags)
while buyers made decisions on the actual price. So, the experimental subjects are
asked to predict the price for the following year (and to design strategies for predict-
ing future prices) for the supply of the good, knowing only the current and previ-
ously realized prices (that is, not knowing how anyone else in the market will act).
Such experiments are now conducted in ‘laboratories’ where ‘market’ participants
are linked via computers rather than ‘trading’ in an open classroom. ese one-
period-ahead predictions (or the alternative written down strategies) are then used,
either individually or in randomly selected groups, by the experimenting scientists
as inputs into a market model, for unknown to the experimental participants, the
hypothetical market has demand and supply functions that are already specied
by the researchers in mathematical form. But while the model gives a structure of
relations to the market, it also functions as the calculation instrument in the exper-
iment, taking the experimental subjects’ expected prices as inputs and using them
to determine the ‘realized’ market prices for each period.29 ese model outputs are
then taken as existing prices relevant for the prediction of the next period’s price,
as the experiment runs over several periods.
e values of the parameters in the two functional relations in the model are
also varied experimentally so that, according to the participants’ predictions, a
sequence of prices over time may behave nicely (converge towards a stable market
equilibrium level), or get stuck in a cycle, or result in chaotic behaviour, but in the-
ory at least, the participants should be able to learn from their experience to reach
the stable level. But there are a number of twists in the experimental design that
complicate the ability of the experimental subjects to learn about the mathemat-
ical model market in which they are participating over the experimental runs. For
example, random ‘noise’ is added to the demand side, and the demand and supply
28 Cars Hommes worked at CeNDEF – Centre for Nonlinear Dynamics in Economics and Finance
and Joep Sonnemans at CREED – the experimental unit in the Faculty of Economics and
Econometrics at the University of Amsterdam.
29 In fact, this part of the experiment is computerized, so that the computer also acts as the interface
among participants, the model, and the experimental outputs.
e World in the Model
290
functions change levels (but not shape) during, or even within, the course of the
experimental sessions so that realized prices and the market equilibrium level both
change.30 So variations in the model create some of the experimental variation to
which the individuals respond.
Like all laboratory experiments in economics, these ones have both an air of
articiality about them (stemming from the combination of strict rules and struc-
tured responses) and a real-world quality (stemming from the natural variation that
comes from the participants’ behaviour and their predicament). e controls in
the experimental situation meant, for example, that participants’ price predictions
had to be within a xed range determined by the mathematical model, although
they could write down any pricing strategy they liked – so long as it could be pro-
grammed.31 e mathematical model of the market used was a ‘cobweb model’,
well understood from decades of empirical work.32 But here, the parameter values
that govern its shape were chosen by Hommes and Sonnemans to allow for a range
of outcomes according to the participants’ responses, thus enabling the variation
in participants’ inputs to be reected in variations in experimental outputs. e
experimental participants were students given small monetary incentives to predict
prices in the experimental environment rather than industry managers whose jobs
might depend on their abilities to predict prices in the market. Yet, just as in the
real world, they had to make decisions about pricing, and pricing strategies, with-
out knowing either the demand relation in the market model or about their rival
suppliers’ pricing strategies.
e presence of such real-world inputs in these kinds of experiments has led me
to describe them as ‘virtually experiments’ (based on a comparable example on the
structural strength of bones tested in computer experiments).33 By this I mean that
although certain aspects of the experimentally dened world are articially con-
structed, other aspects are of the real world, or so close to it, that the experiment
is virtually a laboratory experiment. Here the human subject inputs are real-world
material, while the world they operate in is a model world. Because of this real-
world input, the experimental setup allows for unexpected variations in the exper-
imental outcomes. For example, in these experiments in which the participants
wrote down their strategies for responding to realized prices, those strategies were
fed into the model to calculate long period dynamics of the equivalent realized mar-
ket prices. e 102 strategies proposed by the experimental participants were all
dierent, and though they could be grouped according to certain types, there was no
30 Further variability is provided by varying the number of suppliers (in one experiment there are
many and in another, only one); and in learning (in one experiment, subjects can learn as they go
along, in the other, they can plan out a strategy in advance and learn only between experiments).
31 ey were checked by the experimenters to make sure they were clear, complete, provided unique
predictions for each situation, and used only the information available at that time.
32 e cobweb model is based on empirical work in the 1930s on agricultural goods markets, see
Morgan (1990).
33 See Morgan (2003) for an analysis of this comparable example.
Model Experiments? 291
‘typical’ strategy; there was no one strategy that could be taken as ‘the’ representative
strategy. is variability in turn limited the inferences that could be made from the
experiments. Even when the eect of their dierent predictions and strategies were
combined together via the mathematical model of the market, the patterns were
suciently ordered only to infer a vefold classication. ese results could then
be compared with other results obtained by simulations and analytical work with
the model, where the inputs were mathematically modelled people that ‘behave’
according to certain theoretical or hypothesized rules, such as following “ratio-
nal” or “adaptive expectations”.34 By using real people, not model economic men,
in their experiments, Hommes and Sonnemans enabled a legitimate comparison
to be drawn between these real-people experiments and the equivalent model-men
experiments where ‘the market’ was characterized only in a model.
ese hybrid forms stretch into simulations: experiments with statistical or
mathematical models that generally rely on iterative, rather than deductive, modes
of demonstration. Simulation has a comparatively long tradition in economics that
predates the computer simulations of the type so familiar nowadays, and oen such
models may not be built as small world models but only aim to mimic something
in the world. ese models are used as raw materials in experiments to see whether
they generate particular kinds of data patterns that look like those produced by the
world. (I discuss simulation models at greater length in Chapter 8 and consider
their inferential possibilities there.)
Experiments conducted by Cars Hommes, this time in conjunction with William
Brock, provide a example of the range of elements involved in simulating models to
mimic patterns in stock market prices (see, e.g., Brock and Hommes, 1997). Such
studies use, as inputs, mathematical decision rules appropriate for dierent kinds of
behaviour, labelled with classications that separate “fundamentalists’: those who
believe that stock prices reect fundamental values of the companies concerned,
from “technical traders” or “chartists”: those who trade on observed patterns of
price changes, and “trend followers”: those who follow trends (and may overreact in
doing so). Hommes and Brock (amongst others) use model experiments to explore
what happens when various dierent such kinds of mathematically described ‘trad-
ers’ are put together in simulated ‘markets’. And to the extent that traders in the
real stock market act on the decision rules as proposed in the models, or that the
mathematical rules real traders use are those used in the model experiments, then
we might also accord these model experiments the status of ‘virtually experiments’.
It appears here that, rather than the model oering a representation in a dierent
kind of material of the rational behaviour decisions made by humans, the math-
ematical model is itself an input of the real world: that is, the mathematics here
is not a model of the behaviour, but provides model-based rules on which eco-
nomic action is taken, including computer-based trading directly on such models
34 ese mathematical modelling comparisons drew on Hommes’ earlier work (see, e.g., Brock and
Hommes [1997] and text below).
e World in the Model
292
without intervening human traders. ese models have become “performative”, for
as Mackenzie (2006) argues, these nance models are “an engine not a camera” –
they do not represent what is happening the nancial markets; they are the active
power in those markets. e models themselves have become part of the market.35
5.ii e Status of Hybrids
e range of experiments discussed in this chapter – laboratory, model, and hybrid
experiments – have used versions of the same basic supply and demand apparatus
and framework. In the exploratory, analytical tradition represented by Marshall’s
model work (see Section 2), experiments consisted of manipulations of the model
enabling the economist to explore deductively what happens in the model when
specied events, policy interventions or structural changes aect certain variables.
is branch of model-experiment activity relies on small abstract models based on
assumptions that oen have limited correspondence with the real-world economy.
Such model-based experiments are designed to explore the range of possibilities
in answering questions posed by various theoretical hypotheses about economic
behaviour. In using their internal resources to answer their questions, economists
come to understand how the elements of the model t together; they learn the
range of forms the model can take and the variations in response to experimental
manipulation that they exhibit, and how to classify them in terms that are generic:
they are neither completely general, nor particular to individual cases, but specic
for a kind of case. In Marshall’s experiments, the model world was both the subject
and the object of experiment.
In the laboratory experimental work of Chamberlin and Smith, the active
resources were provided by the experimental subjects while the model was largely
passive, for it was neither the subject nor object of experiment but part of the experi-
mental design. Even there though, it played two roles; namely, it placed rather loose
limits on each participant’s behaviour and it acted as a benchmark to assess their
experimental results against those obtained from Marshall’s model experiments.
So the experimental work into the nature of real economic activity depended also
on the world conceived in the model, both in performing such experiments and in
making inferences from them.
e hybrid cases show us how models and experiments come together in ways
that mix real-world and abstract elements. In some of these experiments, there are
no people and we are close to the model experiment except that the dynamic of
demonstration operates in simulation mode not in deductive mode. In others – the
virtually experiments of Hommes and Sonnemans – elements of both laboratory
35 is thesis, and the term “performativity”, are due to Michel Callon (1998); MacKenzie’s (2004,
2006) account oers many insights into this in the case of economic market-making, in particular
how the use of models may make a market more ecient at one point, but then be blamed for its
failure at another – “counterperformativity”. See also MacKenzie (2009), MacKenzie et al. (2007),
and Callon et al. (2007) and further discussion in Chapter 10.
Model Experiments? 293
and model experiments are embodied at both the design and experimental stage,
for the ‘market’ consists of real people (laboratory inputs) operating in conjunction
with a mathematical model and each part is subject to its own kinds of ‘control’. In
a pragmatic mixture, Hommes and Sonnemans instituted laboratory control where
real-world material could be isolated and manipulated and substituted model-
based controls in those areas that could not be isolated by experimental means. e
demonstration method also involved a mixture of experimental and mathematical
methods (of calculation). e model was part of the structure of the experimental
world, and was itself varied in an experimentally controlled fashion. (It was also
part of the experimental apparatus, used as an instrument to calculate the outputs
depending on the various real-world inputs.) e model behaviour was of interest,
but so was the behaviour of the participants.36
When we add the hybrids to the dierent kinds of experiments using the sup-
ply and demand models in this chapter, it becomes much harder to make clear
distinctions between the dierent kinds of experiments and the role of models in
them. Rather, as we have seen, models play many dierent roles in experiments;
sometimes they are the object of experiment, sometimes part of the experimental
apparatus, sometimes both, and sometimes models may even create the part of the
economic world that they represent.
6. Materials Matter: Surprise versus Confoundment
Let me return, however, to the hard and fast distinction in order to make a nal
point about inference from model experiments. e archetype of experiment
assumes that however much the experimental situation is constrained, controlled,
and even constructed, it is nevertheless an experiment on a real-world system.
However articial the environment that is created, however articial the outcome,
the experimental intervention itself involves an action upon or the creation of a
material object or phenomenon in the same kind of stu as the world it investi-
gates. In contrast, much of modern economics functions by using extended model
experiments in which the material world of the economy remains absent: model
experiments are investigations into a world made of bits of mathematics, diagrams,
and so forth, not real people in real markets.
It is tempting to see this contrast between model and real experiments as
one between a system in which the outcome to the question is already built into
the model that is created and another where experiments may give really new
36 Finally, it is worth mentioning briey another hybrid or intermediate case provided by the kind of
model-based experiments found in the econometrics in the same domain of demand and supply
models; see Morgan (1990, part II) for discussion and examples. e typical econometric model
incorporates a mathematical model as its structure and ‘real-world’ statistical observations from
the economy are used for valuing its parameters. It thus incorporates a lesser degree of control
but some greater degree of real-world materiality than a mathematical model experiment (see
Boumans and Morgan, 2001).
e World in the Model
294
information. On this view, economists should not be surprised by their model
experiments because, of course, they know the resources that created their results
because they built the model that provides the experimental setup.
However, this mistakes the case. Economists do nd themselves surprised by the
results of their mathematical model experiments. ey know the elements that they
put into their model so that the outcomes of model experiments are already built
into the model. But the answers to their questions found from experiments on their
models are not fully known, or not fully understood, in advance. ey created the
model because they could not gure out how a number of elements behave together,
or how a variation in one thing will aect all the other elements and relationships
that they are juggling. As we found in the history of the supply and demand model,
model experiments extend the possibilities for scientists to gure out those compli-
cated problems. Scientists want their experiments with models to tell them things
they know already – because that way they gain condence in the model’s quality.
But they really want their experiments with their models to surprise them for this
betokens that they have learnt something new from their model experiments. In
principle though, having been surprised, economists can go back through the model
experiment and understand why such surprising results occurred.
We saw this in the models built to understand the new macroeconomics of the
1930s. Recall (from Chapter 6) Samuelson’s expression of surprise in experimental
results as he varied the parameter values in a very small macro-model:
A variety of qualitatively dierent results emerge in a seemingly capricious
manner from minor changes in hypotheses. Worse than this, how can we
be sure that for still dierent values of our coecients new and stronger
types of behaviour will not emerge: Is it not even possible that if Table 2
[his simulation experiment results] were extended to cover more peri-
ods, new types of behaviour might result for these selected coecients?
(Samuelson, 1939, p. 76)
Samuelson’s reaction to the “capricious” results of experimenting with his
model was to solve the model analytically and classify and characterize all the pos-
sible kinds of results (according to dierent values of the parameters). It is more
doubtful that such ‘surprise’ was something that Marshall would admit too, but we
see in his classication work, as in Mangoldt’s work, the same desire to character-
ize, to classify, and to develop concepts interpreting the varying dierent kinds of
results that come from their experiments with models. Surprise marks the unex-
pected things that economists learn from enquiring into the world of their model
and that are associated with the kinds of conceptual development work that we
noted in this chapter.
In model experiments, surprise comes from ignorance about the model world.
In laboratory experiments, ignorance comes in a dierent place – it is ignor-
ance not about the model behaviour, but about the world behaviour. So econo-
mists experimenting in their classrooms and laboratories might have the wrong
Model Experiments? 295
account or hypothesis about what they expect to happen in the economy, or their
knowledge of the economic behaviour of the subjects they are investigating might
be seriously incomplete. We can characterize the contrast between these dier-
ent kinds of experiments – in the model and in the laboratory – by saying that in
experiments on mathematical models of physical, biological, or economic systems,
scientists may be surprised, but in real-world experiments directly on those sys-
tems, they may be confounded. at is, in the laboratory, there is always the pos-
sibility not only of being surprised but of being confounded because the scientists’
greater level of ignorance may prevent them from explaining why a particular set
of results occurs, and the limits on experimental manipulability may prevent them
easily reaching an understanding of why such results occur.
In our examples from Hommes and Sonnemans, it is the unexpectedness
which results from their real-world inputs, revealed (by the participants) to the
experimenters but not designed or known by them beforehand, which creates the
possibility of genuinely experimental outcomes, that is, ones that might confound
the experimenters’ expectations. Recall that they found so much variation in one
part of their experiment that though they were able to suggest interpretations for
some of the patterns of behaviour that emerged, others were even without pattern.37
Chamberlin too was confounded by many of his results. For example, some showed
that aer a movement towards the expected equilibrium level, the path then diverged
further from it. ere were others in which “the most diverse patterns appear, with
no apparently predominant tendencies to be noted” (Chamberlin, 1948, p. 101).
Another set of results appeared to contradict an analytical point that “proved at the
time exciting at least to the writer and to one particular group of students” (1948,
p. 98). e more that the behavioural inputs are of the real world, the more empir-
ically rich they are, the more possibilities there are for confoundment, that is, for
turning up unexpected regularities (or even none at all), or for results that don’t t
either the standard theory, or the existing knowledge of the economy, or even cer-
tain intuitions about the economic world, and so for genuine learning from experi-
ments. is points to the importance of maintaining as much real-world input as
possible into economic experiments, and so of allowing participants in the experi-
ments a certain degree of the freedom to behave within the experimental setup.
e danger for the economic experimentalists is that they control the behaviour of
their participants so closely to their models of how people should behave that those
subjects have no freedom to act in ways not dictated by economic science.38 In such
a case those economists might as well have conducted the experiment in the world
of the model rather than the laboratory of the real world.
In the contrast between model experiments and laboratory experiments in
Section 4, it was suggested that inference from model experiments is weak but
37 See Sonnemans et al. (1999, p. 20).
38 See Santos (2007), who has taken up the challenge of discussing the trade-o between control and
agen cy.
e World in the Model
296
wide and from real experiments is strong but narrow. ese were comparisons
of the scope of inference to apply to more or less detailed cases and circum-
stances in the world. Here I am pointing to a dierent aspect of inference: its
focus. Real experiments, in the same materials as the world, have a potentially
greater epistemological power than model ones with respect to the world – such
experiments give the possibility of observing new patterns, of establishing new
stable regularities and so uncovering new phenomena unexplainable given the
existing body of knowledge and so confounding the scientist (see Morgan, 2005
for further discussion of this). Model experiments oer less inferential power
to learn about the world. But the possibility of model experiments to surprise,
that is, to produce results that are unexpected against the background of exist-
ing knowledge and understanding, remains an important, even powerful, way in
which economic theories and concepts are developed and rened. e surprising
results of model experiments lead not to the discovery of new phenomena in the
real world, but to the recognition of new things in the small world of the model,
and thence to the development of new categories of things and new concepts and
ideas in economics.
Acknowledgement
I thank the British Academy for supporting my research during the initial work on this
topic. is chapter has grown out of several papers. e rst was prepared for the work-
shop “Towards a More Developed Philosophy of Scientic Experimentation” (Amsterdam,
June 2000) at the invitation of Hans Radder and appeared as Morgan (2003). e paper
was prompted by two events: Tony Keaveny’s seminar on bone experiments at UC Berkeley
in Fall 1999 which formed the example for my commentary on Nancy Cartwright’s paper
on experiments prepared for the Princeton Workshops on “Model Systems, Cases and
Exemplary Narratives” during 1999–2000. I was able to present these ideas to the British
Association Festival of Science in 2002. My thanks go to Tony Keaveny and his colleague,
Michael Liebschner, and the Princeton workshop organisers, Angela Creager, M. Norton
Wise, and Liz Lunbeck. e second was a joint paper with Marcel Boumans written at
the invitation of the editors of Journal of Economic Methodology entitled “Ceteris Paribus
Conditions: Materiality and the Application of Economic eories” (2001). I thank Marcel
for an extremely stimulating joint writing experience! e third paper, drawing on the
previous two, was prepared for “Model Based Reasoning” (Pavia, May 2001), given also
at “Language, Logic and Logistics: Modeling and Cross-Disciplinary Discourse” (State
University of New Mexico, January 2001) and published as Morgan (2002a). I thank Cars
Hommes for discussions about his experiments. e extension of materials on catego-
rization were developed for a session on models at the ASSA 2005; and those on “con-
foundment versus surprise” for a meeting on experiments (Nottingham, 2003) that led
to Morgan (2005). I particularly thank Marcel Boumans, Francesco Guala, Rom Harré,
Arthur Petersen, Hans Radder, Norton Wise, Angela Creager, Rachel Ankeny, Margaret
Morrison, Dan Hausman, and participants at the above meetings and subsequent seminars
at Nijmegen, INEM (Amsterdam), Melbourne, ANU, and A Coruña for all their useful
questions and comments.
Model Experiments? 297
References
Baden-Fuller, Charles and Mary S. Morgan (2010) “Business Models as Models”. Long Range
Planning, 43, 156–71.
Boumans, Marcel (1999) “Representation and Stability in Testing and Measuring Rational
Expectations”. Journal of Economic Methodology, 6, 381–401.
(2002) “Calibration of Models in Experiments”. In Lorenzo Magnani and Nancy J.
Nersessian (eds), Model-Based Reasoning: Science, Technology, Values (pp. 75–94).
New York: Kluwer Academic/Plenum Press.
(2005) How Economists Model the World to Numbers. London: Routledge.
Boumans, M. and M. S. Morgan (2001) “Ceteris Paribus Conditions: Materiality and the
Application of Economic eories”. Journal of Economic Methodology, 8:1, 11–26.
Brock, W. A. and C. Hommes (1997) “Models of Complexity in Economics and Finance”.
In C. Heij, J. M. Schumacher, B. Hanson, and C. Praagman (eds), System Dynamics in
Economic and Financial Models (pp. 3–44). New York: Wiley.
Brodbeck, May, 1968 [1959] “Models, Meaning and eories”. In M. Brodbeck (ed), Readings
in the Philosophy of the Social Sciences (pp. 579–601). New York: Macmillan.
Callon, Michel (1998) e Laws of Markets. Oxford: Blackwell.
Callon, Michel, Yuval Millo, and Fabien Muniesa (2007) [eds] Market Devices. Oxford:
Blackwell.
Cartwright, N. (2000) “Laboratory Mice, Laboratory Electrons, and Fictional Laboratories”.
Paper for Princeton Workshop on Model Systems, Cases and Exemplary Narratives,
January 2000.
Chamberlin, E. H. (1948) “An Experimental Imperfect Market”. Journal of Political Economy,
56:2, 95–108.
Chang, Hasok (2001) “Spirit, Air and Quicksilver: e Search for the ‘Real’ Scale of
Temperature”. Historical Studies in the Physical and Biological Sciences, 31, 249–84.
(2004) Inventing Temperature: Measurement and Scientic Progress, Oxford: Oxford
University Press.
Collins, Harry M. (1990) Articial Experts, Social Knowledge and Intelligent Machines.
Cambridge, MA: MIT Press.
Cournot, Augustin (1838/1960) Researches into the Mathematical Principles of the eory of
Weal th. Translated by Nathaniel T. Bacon. New York: Kelley reprint.
Creager, Angela, Elizabeth Lunbeck, and M. Norton Wise (2007) [eds], Science Without
Laws: Model Systems, Cases, and Exemplary Narratives. Durham, NC: Duke University
Press.
Creedy, John (1992) Demand and Exchange in Economic Analysis. Aldershot: Edward Elgar.
(1998) Development of the eory of Exchange. Cheltenham: Edward Elgar.
Dahan Dalmedico, Amy (2007) “Models and Simulations in Climate Change: Historical,
Epistemological, Anthropological and Political Aspects”. In Angela Creager, Elizabeth
Lunbeck, and M. Norton Wise (eds), Science Without Laws: Model Systems, Cases, and
Exemplary Narratives (pp. 125–56). Durham, NC: Duke University Press.
Ekelund, Robert B. and Robert F. Hébert (1999) Secret Origins of Modern Microeconomics;
Dupuit and the Engineers. Chicago: University of Chicago Press.
Ekelund, Robert B. and Mark ornton (1991) “Geometric Analogies and Market Demand
Estimation: Dupuit and the French Contribution”. History of Political Economy, 23:3,
397–418.
Franklin, Allan (1986) e Neglect of Experiment. Cambridge: Cambridge University Press.
(1990) Experiment, Right or Wrong. Cambridge: Cambridge University Press.
e World in the Model
298
Gibbard, A. and Varian, H. R. (1978) “Economic Models”. e Journal of Philosophy 75:11,
664–77.
Gooding, David (1990) Experiment and the Making of Meaning. Dordrecht: Kluwer
Academic.
Gooding, David, T. Pinch, and S. Schaer (1989) e Uses of Experiment. Cambridge:
Cambridge University Press.
Guala, Francesco (1999a) Economics and the Laboratory. Ph.D. thesis, University of
London.
(1999b) “e Problem of External Validity (or ‘Parallelism’) in Experimental Economics”.
Social Science Information, 38:4, 555–73.
(2002) “Models, Simulations, and Experiments”. In Lorenzo Magnani and Nancy J.
Nersessian (eds), Model-Based Reasoning: Science, Technology, Values (pp. 59–74).
New York: Kluwer Academic/Plenum Press.
(2003) “Experimental Localism and External Validity”. Philosophy of Science, 70,
1195–1205.
(2005) e Methodology of Experimental Economics. New York: Cambridge University
Press.
(2008) “History of Experimental Economics”. In S. Durlauf and L. Blume (eds), e New
Palgrave Dictionary of Economics, Vol. 3 (pp. 152–6). London: Palgrave-Macmillan.
Hacking, Ian (1983) Representing and Intervening. Cambridge: Cambridge University
Press.
Harré, Rom (2003) “e Materiality of Instruments in a Metaphysics for Experiments”. In
Hans Radder (ed), e Philosophy of Scientic Experimentation (pp. 19–38). Pittsburgh:
Pittsburgh University Press.
Hartmann, Stephan (1996)“e World as a Process: Simulations in the Natural and Social
Sciences”. In Rainer Hegselmann, Ulrich Mueller, and Klaus G. Troitzsch (eds),
Modelling and Simulation in the Social Sciences from the Philosophy of Science Point of
View (pp. 77–100). Dordrecht: Kluwer Academic.
Hausman, Daniel M. (1990) “Supply and Demand Explanations and their Ceteris Paribus
Clauses”. Review of Political Economy, 2, 168–87.
(1992) e Inexact and Separate Science of Economics. Cambridge: Cambridge University
Press.
Heidelberger, M. and F. Steinle (1998) Experimental Essays: Versuche zum Experiment.
Baden-Baden: Nomos Verlagsgesellscha.
Hommes, Cars, J. Sonnemans, J. Tuinstra, and H. van de Velden (1999) “Expectations Driven
Price Volatility in an Experimental Cobweb Economy”. University of Amsterdam
CeNDEF Working Paper, 99–07.
Humphrey, omas M. (1992) “Marshallian Cross Diagrams and eir Uses before Alfred
Marshall: e Origins of Supply and Demand Geometry”. Economic Review, 78:2,
3–23.
Jenkin, Fleeming (1887) “e Graphic Representation of the Laws of Supply and Demand,
and eir Application to Labour”. In Papers Literary, Scientic, etc, Vol. II. Edited by
S. Colvin and H. A. Ewing. London: Longan and Green; and as LSE Scarce Tracts in
Economics, III (1996). Routledge/oemmes Press.
Johnson, W. E. (1894–6) “Method of Political Economy”. In Robert H. Inglis Palgrave (ed),
Dictionary of Political Economy, Vol. II (pp. 739–48). Reprinted 1917. London: Macmillan.
Lakatos, Imre (1963) Proofs and Refutations. Edinburgh: Nelson.
Le Gall, Philippe (2007) A History of Econometrics in France: From Nature to Models.
London: Routledge.
Model Experiments? 299
MacKenzie, Donald (2004) “e Big, Bad Wolf and the Rational Market: Portfolio Insurance,
the 1987 Crash and the Performativity of Economics”. Economy and Society, 33, 303–34.
(2006) An Engine, Not a Camera. Cambridge, MA: MIT Press.
(2009) Material Markets. Oxford: Oxford University Press.
MacKenzie, Donald, Fabian Muniesa, and Lucia Siu (2007) Do Economists Make Markets.
Princeton, NJ: Princeton University Press.
Magnani, Lorenzo and Nancy J. Nersessian (2002) Model-Based Reasoning: Science,
Technology, Values. New York: Kluwer Academic/Plenum Press.
Mäki, Uskali and Piimies, Jukka-Pekka (1998) ‘Ceteris paribus’. In John B. Davis, D. Wade
Hands, and Uskali Mäki (eds), e Handbook of Economic Methodology. (pp. 55–9).
Cheltenham: Edward Elgar.
von Mangoldt, Hans K. E. (1863/1962) Grundriss der Volkswirtschaslehre, Book III, Chapter 3,
Part 1 translated as “e Exchange Ratio of Goods” by Elizabeth Henderson, International
Economic Papers, No. 11, pp. 32–59 (2nd, abridged edition of original German, 1871).
Marshall, Alfred (1890) Principles of Economics, 8th edition, 1930. London: Macmillan.
Mayo, Deborah (1996) Error and the Growth of Experimental Knowledge. Chicago: University
of Chicago Press.
Merkies, A. H. Q. M. (1997) “Zo” Afscheidscollege, September, 1997, Vrije Universiteit,
Amsterdam.
Morgan, Mary S. (1990) e History of Econometric Ideas. Cambridge: Cambridge University
Press.
(2001) “Models, Stories and the Economic World”. Journal of Economic Methodology,
8:3, 361–84 (also in Mäki, Uskali [2002] Fact and Fiction in Economics (pp. 178–201).
Cambridge: Cambridge University Press.
(2002a) “Model Experiments and Models in Experiments”. In Lorenzo Magnani and
Nancy J. Nersessian (eds), Model-Based Reasoning: Science, Technology, Values
(pp. 41–58). New York: Kluwer Academic/Plenum Press.
(2002b) “How Models Help Economists to Know”. [Commentary on John Sutton’s Marshall’s
Tendencies. What Can Economists Know? (2000)] Economics and Philosophy, 18, 5–16.
(2003) “Experiments Without Material Intervention: Model Experiments, Virtual
Experiments and Virtually Experiments”. In Hans Radder (ed), e Philosophy of
Scientic Experimentation (pp. 216–35). Pittsburgh: Pittsburgh University Press.
(2005) “Experiments vs Models: New Phenomena, Inference and Surprise”. Journal of
Economic Methodology, 12:2, 177–84.
Morgan, M. and M. Boumans (2004) “Secrets Hidden by Two-Dimensionality: e Economy
as a Hydraulic Machine”. In S. de Chadarevian and N. Hopwood (eds), Models: e
ird Dimension of Science (pp. 369–401). Stanford, CA: Stanford University Press.
Oreskes, N. (2000) ‘Why Believe a Computer: Models, Measures and Meaning in the Natural
World’. In J. S. Schneiderman (ed), e Earth Around Us: Maintaining a Livable Planet
(pp. 70–82). San Francisco: W. H. Freeman.
Oreskes, N., K. Shrader-Frechette, and K. Belitz (1994) “Verication, Validation, and
Conrmation of Numerical Models in the Earth Sciences”. Science, February 4, 263,
641–6.
Radder, Hans (2003) [ed] e Philosophy of Scientic Experimentation. Pittsburgh: Pittsburgh
University Press.
Rau, Karl Heinrich (1841) Grundsätze der Volkswirtschaslehre. Heidelberg: C. F. Winter.
Reiss, Julian (2002) “Causal Inference in the Abstract or Seven Myths about ought
Experiments”. Causality, Metaphysics and Methods Technical Report, 03/02, CPNSS,
London School of Economics.
e World in the Model
300
Rheinberger, Hans-Jörg (1997) Towards a History of Epistemic ings: Synthesizing Proteins
in the Test Tube. Stanford, CA: Stanford University Press.
Samuelson, Paul A. (1939) “Interactions Between the Multiplier Analysis and the Principle
of Acceleration”. Review of Economics and Statistics, 21, 75–8.
Santos, Ana C. (2007) “e ‘Materials’ of Experimental Economics: Technological versus
Behavioral Experiments”. Journal of Economic Methodology, 14:3, 311–37.
Schabas, Margaret (2008) “Hume’s Monetary ought Experiments”. Studies in History and
Philosophy of Science, Part A, 39:2, 161–9.
Schneider, Erich (1960) “Hans von Mangoldt on Price eory: A Contribution to the
History of Mathematical Economics”. Econometrica, 28:2, 380–92.
Smith, Adam (1776) An Inquiry into the Nature and Causes of e Wealth of Nations, edited
by R. H. Campbell and A. S. Skinner. Oxford: Oxford University Press, 1976.
Smith, Vernon L. (1962) “An Experimental Study of Competitive Market Behaviour”. Journal
of Political Economy, 60:2, 111–37.
Sonnemans, Joep, C. Hommes, J. Tuinstra, and H. van de Velden (1999) “e Instability of a
Heterogeneous Cobweb Economy: A Strategy Experiment on Expectation Formation”.
University of Amsterdam CeNDEF Working Paper 99–06.
Sutton, John (2000) Marshall’s Tendencies. Cambridge, MA: MIT Press.
Valeriani, Simona (forthcoming 2012) “Models as ‘In-Between-Knowledge’ in the
Construction of St Paul’s Cathedral”, in Proceedings of the Conference ‘e Model, a Tool
in the Architectural Project’, Ecole de Chaillot, Cité de l’Architecture et du Patrimoine,
Editions Lieux Dits.
Weber, Marcel (2007) “Redesigning the Fruit Fly: e Molecularization of Drosophila”. In
Angela Creager, Elizabeth Lunbeck, and M. Norton Wise (eds), Science Without Laws:
Model Systems, Cases, and Exemplary Narratives (pp. 23–45). Durham, NC: Duke
University Press.
Whitaker, J. K. (1975) e Early Economic Writings of Alfred Marshall, 1867–1890. London:
Macmillan/Royal Economic Society.
Yaneva, A. (2005) “Scaling Up and Down: Extraction Trials in Architectural Design”, Social
Studies of Science, 35:6, 867–94.
301
8
Simulation: Bringing a Microscope
into Economics
1. e Birth of a New Technology 301
2. Simulation: Content and Context 304
3. Shubik and Simulation 307
3.i Martin Shubik’s History 307
3.ii Models, Simulated Environments, and Simulated Behaviour 311
4. Guy Orcutt’s History and “Microsimulation” 315
5. Bringing a Microscope into Economics 320
5.i Introducing the Analogy 322
5.ii Matters of Scale and Kind 323
5.iii Specimens = Models 325
6. How Do Simulations Work as Microscopes? 327
7. e Observation–Inference Problem 331
8. Conclusion 336
1. e Birth of a New Technology
It is evident that one of primary places of use for models in modern sciences lies
in various kinds of simulation. Economics is no exception: a distinctive culture
of simulation emerged in the social sciences in the years around 1960. is sud-
den explosion in the use of the term “simulation” covered a very broad range of
practises: a variety of types of ‘experiments’ including people in role-playing exper-
iments (known then as “gaming”), computation machines, probability setups, sta-
tistical data, mathematical models, and games of chance.1 All these elements tted
under the same umbrella, and so apart from the notion of mimicking, or imitation,
1 A search of the electronic journals at JSTOR in economics (including some management), sta-
tistics, and demography journals shows that “simulation”, used in those senses, had 4 mentions
between 1951 and 1954; 36 usages in 1955–8; and 180 in the years 1959–61. (e term had other
meanings before 1950, when it was used to refer either to workers feigning sickness in insurance
schemes, or to the use of policy to create the conditions for perfect competition.)
e World in the Model
302
inherent in the meaning of the term ‘simulation’, the possibilities of giving a neat
denition are small. e extraordinary range of the term is revealed in a bibliogra-
phy in the house journal of the American Statistical Association, and in a sympo-
sium in the house journal of the American Economic Association, both in 1960.2
ese documents allow us to explore the connotations of the new term ‘simulation’
in economics and to trace back its separate roots into the interwar period. Each of
the elements has its own longer tradition, yet, like a family tree where the same rst
names keep reappearing through the generations, the elements of simulation in
economics oen tangle together and reappear.
My particular interests in this literature are twofold. e rst is to understand
the historical dynamic by which the newly emerged method of modelling came to
be combined with an older experimental tradition from statistics, a newer exper-
imental mode in social sciences, and the new research tool of the computer, to
form the technology of simulation.3 is is, not by intent but by content, a largely
American history, situated within the immediate context of the Cold War and
its research technologies. My historical enquiry focusses on two gures, Martin
Shubik and Guy Orcutt, who played an important developmental role in creating
simulation techniques in economics. eir personal histories help us to under-
stand how the new technology was broadly constituted out of some old and some
new techniques and ideas, and yet encompassed a considerable variety of simula-
tion types.
is literature of 1960 also serves my second interest, namely to understand
how models t into in the technology of simulation and to see how this technol-
ogy, in turn, ts into the history of reasoning modes in economics. In this context,
1960 is an apparently undistinguished moment in the history of social sciences
in America. It is not a moment when the world of social science changed because
simulation dropped into the tool box of methods. Rather it is a moment when the
multiple possibilities of experiments with models and real experiments (that had
emerged already in several dierent forms, as we saw in the last two chapters) coa-
lesced together as a new technology under the all-embracing single term: simula-
tion. is coalition was relatively short-lived, for as experimental economics grew
in strength, it developed into its own self-condent eld and style of reasoning. But
at this point of time, an American Economic Review (AER) Symposium of 1960, and
the 1962 publication of a book of readings entitled Simulation in the Social Sciences
2 For the bibliography in the Journal of the American Statistical Association (JASA), see Shubik
(1960a). e American Economic Review symposium (to be discussed later in the chapter) con-
tained an essay survey of simulation in the economics of rms and industries by Shubik (1960b),
Guy Orcutt’s (1960) rst substantive report of his microsimulation studies, and a paper by Clarkson
and Simon (1960) reporting their attempt to programme a computer to mimic bankers’ investment
decisions. A slightly later view of the eld might be found in the entries on “Simulation” in the
International Encylopedia of the Social Sciences in 1968 (edited by Sills).
3 Simulation is nowadays oen taken to refer narrowly to a substitute for analytical techniques in
mathematical work, but not in this time nor in the social sciences disciplines.
Simulation as a Microscope 303
(Guetzkow, 1962), provide evidence of simulation as a combined methodology. e
literature of those years around 1960 is self-conscious in a way that earlier and later
literature is not: simulation as a way of doing social science was perceived as new,
and because of its newness, it had to be explained, justied, and recommended to
readers.4
My two questions about models in relation to simulation t naturally into
broader enquiries into simulation undertaken by historians and philosophers of
science in recent years, although there seems no generally accepted denition or
account of simulation. e notion has been dicult to pin down because it has
involved dierent elements and practices at dierent times and in dierent subject
communities.5 For this 1960s group of scholars in the social sciences, simulation
was broadly perceived to be a technology of investigation that used experiments
to reveal aspects of the models under study, and from which inferences might be
made. In certain crucial respects, we can think of the technology of simulation
as bringing a microscope to economic models. Like the specimens placed under
the slide of a microscope, simulation puts the world in the model under greater
scrutiny than other modes of model analysis. Later in this chapter, I explore this
analogy of the simulation technology as taking a microscope to the models of
economics, to understand what is involved in the preparation of models for such
scrutiny and what kind of invasive techniques are used to observe the worlds in
those models.
Economic models are also instruments to enquire with into the nature of the
world (see Chapter 1). In this respect, the association of the word simulation with
that of mimicry suggests that the credibility of models relies – in some way or
other – on their ability to mimic. My analysis of simulation as a technology akin to
microscopy suggests not only how, and so why, inferences about the real world that
rely on this mimicking power of models may be misleading, but also when and why
such inferences might be justied.
4 Ten years later, an equivalent collection of essays (Guetzkow et al., 1972) betrays a much greater
degree of maturity and assumes that the simulation approach is understood and acceptable.
5 Apart from biographical and autobiographical pieces, and brief histories from eld participants,
there has been little historical evaluation of the development of the technology as a broad move-
ment, but there are a number of specic studies. For example, Peter Galison (1997), working on
physics of this period, suggests we see in simulation something that is not quite theory and not
quite experiment. Evelyn Fox-Keller (2003), on physics and AI, concentrates on the thing that is
being simulated in computer experiments, and points to the change in meaning of the notion from
something that is false to something that imitates. In Sergio Sismondo’s edited volume (1999) on
simulation and modelling, Eric Winsberg looks at the many model layers required in simulation
and Deborah Dowling portrays simulation as a method of experimenting on theories. Hartmann
(1996) discusses a variety of functions that simulation play while Humphreys (2004) focusses par-
ticularly on computer aspects of simulation. More recently, there has been an explosion of interest
in the subject with specialist meetings and at least two special issues of journals devoted to simu-
lation in the sciences (for examples, see those edited by Knuuttila et al. [2006] and by Frigg et al.
[2009]).
e World in the Model
304
2. Simulation: Content and Context
e 1960 bibliography on “Simulation, Gaming, Articial Intelligence and Allied
Topics” was prepared by the economist Martin Shubik (see his 1960b), then a con-
sultant to the General Electric Company. Looking at this material enables us to
take a wide-angled lens to the historical question: What was simulation in 1960?
e rst major point to notice is its extraordinary range of subject matters, and
while statistics is certainly one of the main roots of simulation methods (the bib-
liography was published in the Journal of the American Statistical Association),
Shubik was reporting an essentially multidisciplinary activity.6 e social sciences
and engineering sciences were linked into a network via a number of in-between
topics and elds (see Figure 8.1). e broad span of issues – from logistical ones
to individual rationality and the behaviour of organisations – cover the space from
management to political science, from decision making to weapons, and from engi-
neering to psychology. Shared between the elds, we see various kinds of games –
war games with sand tables or in logistics labs, business games based on company
histories, and role-playing games; dierent connotations attach to the term ‘games’
in relation to the subject elds.7 Economics nds its place both around and within
this circle, with a considerable number of articles about rms/markets and indus-
tries, in role-playing experiments, and in econometric and computer simulations
of models.
Shubik placed the majority of the works he surveyed into the two categories
labelled “simulation” and “gaming” (role-playing experiments), from which I have
drawn the map in Figure 8.1. But, like many undertaking such bibliographic exer-
cises, Shubik clearly had diculty in separating out his two categories and in clas-
sifying his material.8 He tried to use the following denition:
Gaming usually (though not always) makes use of a simulated environ-
ment to study the behavior of, or to teach individuals, while simulation is
directed towards studying the behavior of a system given the behavior of
the individual units or vice versa. Gaming always involves the presence of
decision-makers. Simulation does not necessarily entail the involvement
of individuals. In most instances a simulation involves only the machine
manipulation of a model. (Shubik, 1960a, p. 736)
But Shubik’s attempts to make this taxonomy of simulation work were defeated
both by the recalcitrance of his material and by the contemporary users of the ter-
minology, who understood simulation as a research approach that dened a set of
6 For a more extended discussion of the coverage of this bibliography, see Morgan (2004).
7 ere are a number of possibly interesting links (e.g., between war gaming and management games)
that have not been much researched, though see two papers by Rowley (1998, 1999).
8 Similar diculties beset the third section on Monte Carlo studies. Applied examples using Monte
Carlo were included within the simulation category in his section I and technical papers on devel-
opments in Monte Carlo appeared in his section III.
Simulation as a Microscope 305
research methods.9 At that moment of time, “simulation” covered both simulated
environments and simulated processes and these were not neatly separable.
Shubik’s perceptions of the shared spaces of simulation were not idiosyn-
cratic. Guetzkow’s 1962 book of readings on simulation in the social sciences con-
tained accounts of dynamic ight simulators; role-playing air-defence experiments
from RAND’s Systems Research Laboratory; computer simulations of thinking; a
management game report; and examples from engineering, transport queuing, and
role playing from political science, along with computer simulations of elections.10
In contrast to the generous nature of the subject elds found within Shubik’s cat-
egories of “simulation” and “gaming”, the majority of the “Monte Carlo” section in
the bibliography came from mathematics, statistics, and computation with some
papers from natural sciences and engineering (see Figure 8.2). is forms a further
set of axes for techniques and ideas which feed into the elds outlined in Figure 8.1:
a set of elements that includes the research tools of computers and yet another kind
of game, games of chance.
Engineering
Weapons
Defense
Business
Games
War
Games
Role
Playing
Political Science
Organizations
Learning
PsychologyEconomics
Management
Operations Research
Firms, Industries,
Markets
Decision
Making
Figure 8.1. Shubik’s 1960 Bibliography: Subject Map for the “Simulation” and “Gaming”
Categories.
Source: Mary S. Morgan (2004) “Simulation: e Birth of a Technology to Create ‘Evidence’ ”
Revue D’Histoire des Sciences, 57:2, 341–77, p. 345. Reproduced with permission of Revue
D’Histoire des Sciences.
9 Even in Shubik’s own division of items between categories, we nd people-based experiments
(i.e., “gaming”) in amongst the “simulations” and machine-based research (i.e., “simulations”) in
amongst the “gaming”! He also wondered if it might be useful to separate “strategic” from “tacti-
cal” simulation, “analogue” from “digital” computer simulations, and both from “man–machine”
simulation. ough he did not make use of these classications, they are all ones that reappear in
other discussions of the day.
10 Two similarly named collections of essays provide useful contrasts: the 1972 collection (Geutzkow
et al., 1972) contained role-playing and computer-based simulations within a more restricted tra-
ditional social sciences range, whereas a 1996 collection (Hegselmann et al., 1996) contained
no gaming or experiments with people. Aer 1960, the pattern of usage of the term ‘simulation’
waxed and waned, and in settling down, its range of meaning was reduced to that of computer
simulation.
e World in the Model
306
It is also evident from the publication sources that what we have here is the
intersection between the sciences and two kinds of secretive establishments: we are
warned by Shubik that there were many other papers that could not be included in
his bibliography for either they were classied as part of the defence establishment’s
Cold War stance or they were company documents and reports considered to con-
stitute commercial secrets.11 So we must extend the military–big (natural) science
complex that grew up in World War II and the Cold War period to the social sciences
including management studies, and we must add to that the military–industrial
complex familiar to economic historians and going back to World War I (and
intermittently to the mid-nineteenth century).12 Shubik’s bibliography shows how
entrenched that military–industrial–science complex had become for the social
sciences, for U.S. Defense Department research contracts in this eld of simula-
tions and gaming employed a mix of social scientists, mathematicians, and defence
experts. is mix included not only some already known multidisciplinarians such
as John von Neumann and Herbert Simon, but also a host of younger talents who
later became leaders in their own elds in American academe. With the work of
Mirowski (2002), it is becoming increasingly clear that much of the basic and tech-
nical research in economics in the USA during the Cold War period was funded
directly or indirectly by various arms of the defence establishment.
11 Not all US Defense Department contract material was classied during the Cold War. e bib-
liography contained many RAND reports and many other research papers that originated from
Defense Department funding of various kinds. e three most populous outlets in Shubik’s simu-
lation and gaming (his Categories I and II) came from RAND, from the Journal of the Operations
Research Society of America and from a collection of management journals.
12 For recent discussions of Cold War big natural science, see Galison (1997); for the social science
and industrial side, see Hounshell (1997), Jardini (1996), and Mirowski (2002); for the manage-
ment studies connections, see Rowley (1999).
Maths
Stats
Economics Computers
Monte Carlo
Systems
Games of
Chance
Computing
Natural Sciences
and Engineering
Figure 8.2. Shubik’s 1960 Bibliography: Subject Map for the “Monte Carlo” and
“Systems” Categories.
Source: Mary S. Morgan (2004) “Simulation: e Birth of a Technology to Create ‘Evidence’ ”
Revue D’Histoire des Sciences, 57:2, 341–77, p. 347. Reproduced with permission of Revue
D’Histoire des Sciences.
Simulation as a Microscope 307
From the point of view of this newly established history of Cold War economics,
there is one striking omission from Shubik’s bibliography, namely, game theory. e
omission is striking both because game theory was fostered within some of the same
institutions leading the eld of simulation within the military–science context (e.g.,
RAND) and because – as we will see – Shubik himself was known as a game theo-
rist at this time; indeed, he surveyed the use of game theory in industrial economics
in a parallel paper in May 1960 (Shubik, 1960c). e absence of game theory in his
bibliography makes an important point for my interests. While it may be tempting
to think that the connection between game theory (the theory of games of strategy)
and gaming is a very intimate one, the former being the theory for the latter, this
quite mistakes the meaning of the term gaming as it was used during this period.
‘Gaming’ was understood to be a broad-based experimental research and training
method involving people playing roles (either simulating the behaviour of others, or
possibly playing their own usual roles) in an actual or simulated environment – for
example, to investigate how team learning took place. ‘Game theory’ was a mathe-
matical body of work about decision making in strategic interaction, as we shall see
in Chapter 9. In the late 1940s and early 1950s, mathematical game theorists, such as
Shubik, invented “playable games” of strategy to illustrate and explore their patho-
logical or paradoxical properties and played such games with each other. But Shubik
regarded this as an informal “trying-things-out” activity, a practice he separated
from the carefully designed and controlled role-playing experiments falling under
the label “gaming”.13 For Shubik, game theory was neither simulation nor experi-
ment, and there was no reason to confuse them, yet he carried out gaming (i.e., role-
playing experiments) on game theory as well as contributing to both elds.
3. Shubik and Simulation
3.i Martin Shubik’s History
A simulation of a system or an organism is the operation of a model or simula-
tor which is a representation of the system or organism. e model is amenable
to manipulations which would be impossible, too expensive or impracticable
to perform on the entity it portrays. e operation of the model can be studied
and, from it, properties concerning the behavior of the actual system or its sub-
systems can be inferred. (Shubik, 1960b, p. 908)14
13 See next section, and for this part of Shubik’s history, see his 1992, p. 159 and pp. 248–52 (in
Weintraub, 1992). For an explicit statement of the separation of gaming and games – see Shubik
1966 (p. 10), and more generally, his 1975 book.
14 One way to notice the importance of Shubik’s claim about the nature of economic models used in
simulations is by contrasting it with those models used in operations research (OR) at that same
point in time, where the aim was to be prescriptive for how rms ought to behave, rather than
accurately descriptive of how they do behave. For example, contrast our authors’ notion of a rep-
resenting model with Dorfman’s 1960 description of OR, where the activity is described as one of
e World in the Model
308
How did Shubik come to know the technology of simulation so intimately that he
could assemble an authoritative and wide-ranging bibliography on it within a few
years of his Ph.D. thesis? Shubik’s career history speaks both to the content and
context of simulation evident in his bibliography and its range in economics at that
time.
Shubik chose mathematics as his eld of study at the University of Toronto,
despite a highly variable performance in mathematics at high school.15 e choice
was instrumental: the young Shubik fancied a career in politics, and nding the
social science studies available in 1943 unimpressive, decided that at least he would
gain some useful tools. At the same time, as a navy reservist, he gained experi-
ence in electronics. is start proved eective for his continuing graduate studies
in economics, but both these and his extracurricular activities in le-wing political
parties and union schools made him disillusioned with his chances of changing
the world by using his economics within a political career. e seminal moment
in his history, according to his own hindsight, was when he picked up John von
Neumann and Oskar Morgenstern’s e eory of Games and Economic Behavior
(1944) while browsing the library one day. He gained entry to the economics
department at Princeton in 1949 and was, as he says, “swept into the excitement”
(Shubik, 1997, p. 97), the excitement of being just in the right place at the right
time, for Princeton was one of the two main research centres at which the theory
of games was being developed in the late 1940s and early 1950s. e location of
the excitement was the mathematics department’s seminar, in which a number of
economics students along with one of its professors, namely Morgenstern himself,
were active participants.16
Shubik’s enthusiasm for game theory is evident in his rst professional publica-
tions dating from the early 1950s. Only a year aer earning his Ph.D. in 1953 and
while still at Princeton, he published a book of readings in game theory, which began
“formulating [the] problem by means of formal mathematical models” and a model is dened as
“a symbolic description of a phenomenon in which its observable characteristics are deduced from
simple explanatory rst principles (ie assumptions) by manipulating symbols in accordance with
the laws of some formal logic” (p. 577). Shubik’s and Orcutt’s emphasis on the model’s representa-
tional role is the usual accompaniment to denitions and descriptions of simulations, where the
representing capacity relates to the need for validating the model. If the model does not represent
the economic system, the mimicking ‘evidence’ produced by simulation has little value in telling
us anything about that economy (but see Section 7). Where OR might use similar experimental
techniques of model solution, they do not aim to mimic and the validation issue is not important.
e OR aim of simulation is to determine what the economic system ought to be like to ensure
best performance, whereas, as discussed here, the aim is to understand the working features of the
economic system as it is. See also omas and Williams (2009) on the dierent aims of social sci-
ence simulations in this period.
15 is section draws on Shubik’s autobiographical accounts (1992, 1994, and 1997). He was born
in New York, educated in England and Canada, and was a member of the Royal Canadian Navy
(Reserve) from 1944 to 1950, starting o as “Stoker” and ending as Lieutenant (Electronics and
Radar).
16 From this seminar grew Shubik’s long-term collaboration in game theory with Lloyd Shapley, a
graduate student in the mathematics department.
Simulation as a Microscope 309
by attributing the failure of earlier mathematical thinking in the social sciences to
their basis in physical analogies (Shubik, 1954 pp. 2–4). He asserted that there were
six new interconnected theories where there was a mathematics appropriate for,
and adapted to, the social sciences.17 He had already used two of these – game the-
ory and information theory – in a short paper of 1952 (based on work funded by
the Oce of Naval Research) in which he took issue with neoclassical economics
and claimed to unify the existing economic theory of competition (in which forms
of monopolistic competition were then treated independently from that of perfect
competition).18 In doing so, he redened the rm as “an organization designed to
obtain, process, store, and act on information”, in other words, the rm as an orga-
nisation was like a computer (Shubik, 1952, p. 146).
His was not a straightforward academic career. From Princeton in 1954, fol-
lowing a year at the Center for Advanced Studies in the Behavioral Sciences at
Stanford, Shubik went to work at the General Electric Company (in the Operations
Research section) in 1956, which “changed his views about how rms actually
worked” (1997, p. 103). It grounded his earlier abstract denition of a rm as an
information processor:
In particular, at General Electric, I felt that the future of long-range plan-
ning lay in the development of good detailed computer models of rms
and the industries they were in. My vision, which still has not been real-
ized, was to see the simulation integrated into the data-gathering system of
the rm and used both for the generation of contingent forecasts and long-
range planning and for both training and operational gaming. (Shubik,
1994, p. 252)
He supposed that planning, operations, and training would all be managed using
the data that owed every day into the rm and using simulation models and man-
agement games both developed for the computer and built specially for that rm.
Meantime, Shubik’s thesis was growing into Strategy and Market Structure
(1959a), the rst full-length serious integration of the ideas of game theory into the
eld of industrial economics (see also Chapter 9, Section 4.iii). His importance in
this initiative may easily be overlooked. Economists take it for granted that game
theory is about economics. But in the early years, game theory was both a math-
ematical topic and a series of social (sometimes intensely antisocial) real games,
whose most obvious applications were found in military problems and Cold War
strategy, rather than in mainstream economics. Shubik was instrumental in mak-
ing the mathematical part of game theory into a theory for economics, particularly
17 e most well developed of these, he claimed, was game theory, wherein analogies connected
human and social activities to other human and social subject matters. With our hindsight, we can
see that the six elds he mentioned – game theory, information theory, statistical decision theory,
choice theory, learning theory, and organization theory – were all well chosen.
18 is was obviously a big claim for a Ph.D. student to make, particularly in the house journal of the
Economics Department at the University of Chicago, one of the foremost departments of the day.
e World in the Model
310
the economics of rm and industry behaviour (the subject of his Ph.D. thesis). His
contribution has been lauded as the turning point: “. . . . . in 1959 came Shubik’s
spectacular rediscovery of the core of a market in the writings of F. Y. Edgeworth
(1881). From that time on, economics has remained by far the largest area of appli-
cation of game theory” (Aumann, 1987 p. 467).19 To reinterpret the new game the-
ory concepts and results in terms of the classic eighty-year-old work of Edgeworth
(discussed in Chapter 3) was to establish game theory’s place in the heart of mod-
ern neoclassical microeconomics.
Shubik’s continuing enthusiasm for game theory was moderated from the
mid–later 1950s by his growing appreciation of the usefulness of role-playing
experiments or gaming and a growing belief that game theory could be tested by
“experimental and empirical techniques of simulation” (1959a, p. 556). Why and
how did he make this move from game theory to gaming? As early as his 1952
paper, he was considering how people in an organisation argued and came to
agreement, and thought about a little role-playing experiment to imagine how this
process occurred. But Shubik tells us that his rst attempts at experiments in the
economics of industry were undertaken with Siegel and Fouraker only in 1957–9,
aer a chance meeting with Siegel while camping at Yosemite.20 By 1960, Shubik
was undertaking such experiments on his own account (reported Shubik, 1962a),
in which he explored various theoretical solution concepts from game theory in
a series of dierent experiments in which games were played under experimental
conditions.21 Meanwhile, following a year’s leave at Yale in 1960, he had gone to
a research laboratory at IBM working on experimental and business games and
forecasting problems. He collaborated there to develop a business game that had a
suciently rich environment to make a good training tool, but with enough “clean
basic structure that it could be analyzed for many game theory and oligopoly the-
ory results” (Shubik, 1994, p. 253).22
By 1960 then, Shubik had successfully covered the grounds of simulation and
gaming experiments (including the man–machine simulations of business games)
as we see in Figure 8.3, which picks out and assembles these elements of Shubik
career. It is no wonder that he could write with such authority in surveying the topic
19 is comes from the historical survey piece on game theory in the New Palgrave (the modern
encyclopaedia of economics) and surely overstates the case both in implying Shubik (1959b)
turned the tide singlehandedly and that economics took game theory to its heart immediately aer
1959 (see Weintraub [1992]). In fact, it was rather slow at taking a general hold in the community.
Nevertheless, Shubik’s result remains fundamental in the community history.
20 See Shubik (1994, pp. 252 and 257); these experiments that Shubik participated in were reported
in Fouraker and Siegel (1963).
21 is work was undertaken while Shubik was at the Cowles Commission at Yale and was completed
by February 1961, with, again, funding from the Oce of Naval Research. In 1975, Shubik, that
student of both game theory and gaming, made the join in a book: Gaming for Society, Business
and War: Towards a eory of Gaming.
22 He seems to have specialised in making business games work as research tools: in the 1970s he
succeeded in a double aim of creating an articial player for a business game in a joint research
initiative into competitive behaviour and an exploration of the Turing test (see 1994, p. 255).
Simulation as a Microscope 311
of simulation both in his bibliographic treatment of the broad eld (1960a) and his
survey paper for the AER symposium on simulation (1960b). Both were based on
a deep, insider’s, practitioner’s, knowledge of simulation, its research methods, and
the economic topics involved.23
3.ii Models, Simulated Environments,
and Simulated Behaviour
Models are always to be found somewhere in these economic simulations though
their location is not always obvious. On the one hand, they are oen hidden in
the various combinations of factual and ctional resources that economists use
23 Shubik’