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The evolution of Patinkin’s interpretation of

Keynes’ principle of effective demand

Jochen Hartwig

To cite this article: Jochen Hartwig (2022) The evolution of Patinkin’s interpretation of Keynes’

principle of effective demand, The European Journal of the History of Economic Thought, 29:3,

505-522, DOI: 10.1080/09672567.2022.2037683

To link to this article: https://doi.org/10.1080/09672567.2022.2037683

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The evolution of Patinkin’s interpretation of Keynes’

principle of effective demand

Jochen Hartwig

ABSTRACT

Don Patinkin (1922–1995) was both an eminent theoretical econo-

mist and a great historian of economic thought. In the latter field,

his focus was on Keynes’“principle of effective demand”from

Chapter 3 of the General Theory. Having submitted a first inter-

pretation of the “principle”in 1976 –in which he claimed that it

contains major flaws –Patinkin revisited the subject several times

over the next couple of years. In this process, his interpretation

changed markedly. The aim of this paper is to trace (and to com-

ment on) the evolution of Patinkin’s interpretation of the theory

of effective demand.

KEYWORDS

Patinkin; Keynes; principle

of effective demand;

D/Z model

JEL CLASSIFICATION

B22; B31; E12

1. Introduction

“Keynes’Chapter 3 on ‘The Principle of Effective Demand’”, Patinkin (1979a, 155)

writes, “is at one and the same time the most important and the most obscure chapter

in the General Theory: most important, because it contains the major innovation of the

book …”. And obscure, indeed, it is also –as is evidenced by the incessant debate on

the “correct”interpretation of the model of effective demand Keynes presents in this

chapter –the D/Z model –to which I have contributed in a dozen publications over

the past 20 years.

1

That this debate soldiers on bears evidence to the utmost importance

–as pointed out by Patinkin –of understanding the “major innovation”of the

General Theory.

Revisiting Patinkin’s interpretation seems rewarding, not only because he is “widely

regarded as one of the leading experts”on the Keynesian revolution (Backhouse 2002,

186), but also because his interpretation of Keynes’principle of effective demand

changed substantially over time. Having submitted a first interpretation of this model

in 1976 –in which he claimed that it contains major flaws –Patinkin revisited the D/Z

ß2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.

This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives

License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in

any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way.

CONTACT Jochen Hartwig jochen.hartwig@wiwi.tu-chemnitz.de Faculty of Economics and Business

Administration, Chemnitz University of Technology, Th€

uringer Weg 7, Chemnitz, 09107, Germany; KOF Swiss

Economic Institute, ETH Zurich, Switzerland; Forum for Macroeconomics and Macroeconomic Policies, Hans B€

ockler

Foundation, D€

usseldorf, Germany

1

King (1994) scrutinizes the early stages of this debate. “To conclude that there was some confusion about

aggregate supply and demand analysis in the early 1950s would be a grotesque understatement”, he sums

up (14).

THE EUROPEAN JOURNAL OF THE HISTORY OF ECONOMIC THOUGHT

2022, VOL. 29, NO. 3, 505–522

https://doi.org/10.1080/09672567.2022.2037683

model several times over the next couple of years. In this process, his interpretation

changed markedly. The objective of this paper is to describe and to comment on the

evolution of Patinkin’s interpretation of Keynes’principle of effective demand over a

period of time that covered more than thirty years of his academic career.

In reconstructing the evolution of Patinkin’s interpretation of Keynes’principle

of effective demand, the paper covers a niche in the literature on the economics

of Patinkin that –unlike many other aspects –has not come under much scru-

tiny yet. Earlier literature has compared Patinkin’s views with those of his contem-

poraries Haavelmo, Klein, Lange, Marschak, and Modigliani (Boianovsky 2002;

Rubin 2002,2004; Hagemann 2017).

2

Patinkin’s impact on the development of

disequilibrium macroeconomics in the 1970s is also well-researched (Rubin 2012;

Backhouse and Boianovsky 2013). The only other contribution that deals with

Patinkin’s interpretation of Chapter 3 of Keynes’General Theory is Arthmar and

Brady (2009). These authors, however, instead of systematically reconstructing the

evolution of Patinkin’s interpretation, rather “briefly review certain points raised

by Patinkin”(Arthmar and Brady 2009, 128). In particular, they confine them-

selves to discussing Patinkin’s (changing) interpretation of the aggregate supply

function Z, remaining largely silent about his views on the aggregate demand

function D, which were also in flux.

3

The paper is structured chronologically. The next section discusses Patinkin’s

early engagement with the matter, that is, before the publication of volumes XIII

and XIV of the Collected Writings of John Maynard Keynes. It will be seen that

these early contributions do not address Keynes’Chapter 3 model yet. Section III

scrutinises Keynes’Monetary Thought (KMT) and two subsequent articles that

appeared in the journal History of Political Economy in 1977 and 1978 in which

Patinkin published a correction of an error in and a reply to a reviewer of the

1976 book, respectively. Taken together, these three writings present a coherent

interpretation of Keynes’theory of effective demand that Patinkin moved away

from, however, in his 1979 Economic Inquiry article already mentioned above. In

Patinkin (1982a) he consolidated his new interpretation. Section IV examines this

reorientation. Section V concludes.

2. Early views

In Chapter 3 of the General Theory, Keynes introduces two functions, the aggregate

supply function (Z) and the aggregate demand function (D), both being functions of the

level of employment (N). So the title of Patinkin’s(1949) article “Involuntary

unemployment and the Keynesian supply function”seems to indicate that he wanted

to make inroads into the theory of effective demand set out in this chapter. However,

Chapter 3 is not Patinkin’s point of reference in his 1949 article. He rather suggests to

2

Rancan (2017, 162, fn. 28) considers especially Lange’s and Marschak’s influence on Patinkin as “already

reconstructed”.

3

Also note that Arthmar and Brady’s main intention it is to prove that the slope of Zcan be derived mathemat-

ically from Chapter 20 of Keynes’General Theory. Their section on Patinkin, which serves as a “preamble”

(Arthmar and Brady 2009, 127) to that proof, sets the stage for Arthmar and Brady’s rebuttal of Patinkin’s

claim as to “Keynes’supposed lack of mathematical proficiency”(Arthmar and Brady 2009, 129).

506 J. HARTWIG

augment the familiar “Keynesian cross”–which he calls “standard Keynesian analysis”

(Patinkin 1949, 364) without making any reference to Samuelson (1948) who passes for

the originator of that model

4

–with an aggregate supply function built up from

“Walrasian supply functions”in individual markets (Patinkin 1949, 365). Patinkin calls

it the “aggregate desired-supply function”(Patinkin 1949, 365) and suggests that this

function S¼Q(Y) might be a horizontal line in the Keynesian cross diagram.

5

However, he prefers to give it a small positive slope with respect to real income/output

(Y). At any rate, the aggregate supply function normally (except in wartime that

means) lies above the expenditure function E¼F(Y) (being the vertical sum of the con-

sumption and the investment function) so that it intersects the 45-line at a higher level

of output than the expenditure function (Figure 1).

The point of intersection of the aggregate supply function with the 45-line Patinkin

defines as full employment output (g). He suggests measuring involuntary unemploy-

ment by the difference between this full employment output and the actual level of out-

put that results from the intersection of the expenditure function with the

45-line (Y

0

).

6

In a situation where g>Y

0

, prices would start falling according to Patinkin. Only if

price reductions have absolutely no effect on spenders, involuntary unemployment

would persist amidst a deflationary spiral (Patinkin 1949, 372). However, thanks to the

real-balance effect and the depressing impact of excess supply on interest rates, the

expenditure function moves upward, ideally so much that it intersects the 45-line at

Figure 1. Aggregate supply curve in the Keynesian cross I (source: Patinkin 1949, Figure 3).

4

Already in his PhD thesis (submitted in 1947), Patinkin adopted Samuelson’s theory of income determination.

“This conception probably derived from Lange’s teaching and a careful reading of Samuelson’s 1941 paper

‘The Stability of Equilibrium’” (Rubin 2012, 244).

5

“It can be shown that the assumptions made in aggregating the supply function imply that the real return to

productive services is constant; that is, the price of finished goods is always proportionate to the price of pro-

ductive services. …(S)ince the real return is constant, suppliers might desire to provide the same amount of

goods regardless of the level of income. In that case the aggregate supply function would be a horizontal line-

…” (Patinkin 1949, 366). Patinkin abandoned this argument in the reprint of his article (Patinkin 1981)

because it contradicts the law of diminishing returns. See also Boianovsky (2002, 230–232)

6

In modern terms we would call Patinkin’s suggested measure of involuntary unemployment the “output gap”.

THE EUROPEAN JOURNAL OF THE HISTORY OF ECONOMIC THOUGHT 507

the full employment output level (Patinkin 1949, 368, reiterating Patinkin 1948).

However, it may also be that the upward push of the expenditure function peters out

before full employment is reached. In this case, some involuntary unemployment per-

sists despite falling prices (Patinkin 1949, 372–373).

Also Patinkin’s magnum opus Money, Interest, and Prices (Patinkin [1956]1991)

contains some clues to aggregate supply. Here, Patinkin drops the idea of a positively

sloped (or horizontal) “aggregate desired-supply function”from which he had dis-

tanced himself in an unpublished note one year earlier already (Boianovsky 2002, 236).

He replaces it with a “familiar aggregate supply function”which had already been pre-

sent in section 14 of Patinkin (1949) and which results from the production function.

For a given real wage, that determines labour input, and a given capital stock a certain

output level results from the production function. Therefore, the aggregate supply

curve is vertical in the Keynesian cross diagram (Figure 2). “It follows that, for any

given real wage rate, the aggregate commodity supply function must appear …as a

vertical line drawn at the level of gross national product …for that specified wage

rate. As long as this rate remains unchanged, so, too, must this vertical line”(Patinkin

[1956]1991, 211). He goes on stating that a rise in the real wage will shift the aggregate

supply function to the left and vice versa. As in Patinkin (1949), a drop in demand can

result in involuntary unemployment if producers are unwilling to permit their invento-

ries to build up. However, this would lead to a deflation of money wages and prices

that restores full employment through the interest-rate and real-balance channels.

“Keynesian economics”, Patinkin concludes, “overlooks the direct influence of the real-

Figure 2. Aggregate supply curve in the Keynesian cross II (source: Patinkin [1956] 1991, Figure

IX-3).

508 J. HARTWIG

balance effect on this demand. Similarly, it overlooks the supply side of the commodity

market which, by its excess over the demand, generates this effect”(Patinkin [1956]

1991, 325). Interestingly, unlike in his 1949 article, Patinkin in Money, Interest, and

Prices does not mention the possibility that the upward push of the expenditure func-

tion might peter out before full employment (point Bin Figure 2) is reached. On the

contrary, Patinkin [1956]1991, 324–328) explains that the dynamic process caused by

falling wages and prices “cannot stop”(Patinkin [1956]1991, 325) at a position below

full employment.

7

3. “Keynes’Monetary Thought”

Patinkin (1976) marks a reorientation in his preoccupation with aggregate supply and

demand analysis. Although the most common view that, with this book, he turned

away from being a mathematical economic theorist towards becoming a historian of

economic thought is an oversimplification (Backhouse 2002, 198), the publication of

volumes XIII and XIV of the Collected Writings of John Maynard Keynes (in 1973)

prompted him to refocus from “Keynesian economics”to “the economics of Keynes”

(Rivot 2016, 1002). “Patinkin set himself to the task of reviewing the progress of

Keynes’ideas towards the principle of effective demand, an endeavor that resulted in a

monograph titled Keynes’Monetary Thought. A Study of its Development”(Arthmar

and Brady 2009, 130).

8

Patinkin describes the relationship between his new approach and the work dis-

cussed above with great candour: “(T)he contention of my 1949 article that there is

no supply curve in the General Theory was based on a complete an inexcusable fail-

ure at the time to understand Keynes’notion of aggregate supply price”(Patinkin

1976, 84, fn. 3).

9

In KMT, Patinkin displays a deeper understanding of the aggre-

gate supply curve. However, for him, “some basic logical difficulties remain”

(Patinkin 1976, 84).

Although readers of the present article are probably familiar with the passages from

the General Theory where Keynes states his aggregate-demand-aggregate-supply (D/Z)

model, these must nonetheless be reproduced here. Keynes writes:

Let Zbe the aggregate supply price of the output from employing Nmen, the

relationship between Zand Nbeing written Z¼/(N), which can be called the aggregate

supply function. Similarly, let Dbe the proceeds which entrepreneurs expect to receive

from the employment of Nmen, the relationship between Dand Nbeing written

D¼f(N), which can be called the aggregate demand function.

7

See also Boianovsky (2006) on the topics covered in this paragraph.

8

From what he quotes in KMT we can infer that three types of items published in volumes XIII and XIV of the

Collected Writings of John Maynard Keynes were instrumental for Patinkin in reconsidering his ideas towards

the principle of effective demand: (i) the correspondence between Keynes and his colleagues Roy Harrod,

Ralph Hawtrey, Richard Kahn, Nicholas Kaldor, Bertil Ohlin, Dennis Robertson, and Joan Robinson, (ii) lec-

tures contributed by Keynes in the early 1930s, and (iii) the drafts of the General Theory.

9

Further down, Patinkin acknowledges that Keynes’upward-sloping Zcurve was similar to his own right- or

leftward-shifting vertical aggregate supply function in Patinkin ([1956]1991). “Accordingly, my criticism then

of the General Theory on the grounds that it did not provide for an analysis of supply was not well taken”

(Patinkin 1976, 91, fn. 12).

THE EUROPEAN JOURNAL OF THE HISTORY OF ECONOMIC THOUGHT 509

Now if for a given value of Nthe expected proceeds are greater than the aggregate

supply price, i.e., if Dis greater than Z, there will be an incentive to entrepreneurs to

increase employment beyond Nand, if necessary, to raise costs by competing with one

another for the factors of production, up to the value of Nfor which Zhas become

equal to D. Thus the volume of employment is given by the point of intersection

between the aggregate demand function and the aggregate supply function; for it is at

this point that the entrepreneurs’expectation of profits will be maximised. The value of

Dat the point of the aggregate demand function, where it is intersected by the aggregate

supply function, will be called the effective demand (Keynes [1936]1973, 25, italics

in original).

This quote spells out some fundamental differences between Keynes’aggregate-

demand-aggregate-supply (D/Z) model from Chapter 3 of the General Theory and the

Keynesian cross as alternative ways of representing Keynes’theory. First, the two curves

as defined by Keynes are in nominal terms while those of the Keynesian cross are in real

terms. Furthermore, Keynes speaks of expectations and profit-maximising. Those ele-

ments are absent from the Keynesian cross. Most importantly, Keynes’aggregate supply

function Zis not the 45-line of the Keynesian cross. Zdepends on employment, the 45-

line does not; Zhas a distinguishable price- and quantity-component, the 45-line has

not. In short: unlike Z, the 45-line is no autonomous supply function, it is a “helping

line”(Samuelson 1948, 257). It is just there to find out which level of income is consistent

with the aggregate demand it supports, given the assumptions made about the aggregate

demand schedule.

As will be seen, the “evolution of Patinkin’s interpretation of Keynes’principle of

effective demand”consisted to a large extent in Patinkin adopting changing views as to

the meaning and especially the slope of the aggregate supply function Z. With respect

to the latter, another passage from a footnote in the General Theory is crucial:

For example, let us take Z

w

¼/(N), or alternatively Z¼W./(N) as the aggregate

supply function (where Wis the wage-unit and W.Z

w

¼Z). Then, since the proceeds

of the marginal product is equal to the marginal factor-cost at every point on the

aggregate supply curve, we have

DN¼DAwDUw¼DZw¼D/ðNÞ,

that is to say /0(N) ¼1; provided that factor cost bears a constant ratio to wage cost,

and that the aggregate supply function for each firm (the number of which is assumed

to be constant) is independent of the number of men employed in other industries, so

that the terms of the above equation, which hold good for each individual entrepreneur,

can be summed for the entrepreneurs as a whole. This means that, if wages are constant

and other factor costs are a constant proportion of the wages-bill, the aggregate supply

function is linear with a slope given by the reciprocal of the money-wage (Keynes [1936]

1973,55–56, fn. 2).

Key for Patinkin’s understanding of the aggregate supply function is Keynes’state-

ment that /0(N) ¼1. If /0(N) ¼DZ

w

/DN¼DZ/(WDN)¼1, it follows that DZ/DN¼

Wand that Z¼WN. This means that Zis a cost function in which Nrepresents all

variable-factor inputs. “(T)he aggregate supply price equals total variable costs”

(Patinkin 1976, 87, fn. 7).

510 J. HARTWIG

Combining Zwith the aggregate demand function Dyields Figure 3.

The Z

w

curve has a slope of 1; hence it is the 45-line (DZ

w

¼DN). At employment

level N

1

,“(t)he corresponding ordinate OA represents actual costs of production of

that output. In contrast, the ordinate OB represents not the actual proceeds but the

expected ones. Why, then …does Keynes treat the difference between OA and OB as

if it represented actual, realized profits that motivate the entrepreneur to expand out-

put? And even more puzzling, why does Keynes contend that profits are at a maximum

at the point of intersection of his demand and supply curves, where profits as measured

by the foregoing difference are zero?”(Patinkin 1976, 90, italics in original).

So Patinkin’s interpretation of the D/Z model is in conflict with Keynes’claim that

producing an output corresponding to the effective demand maximises expected prof-

its. This is not the only interpretative problem, however. Also, in the last sentence of

the “footnote”, Keynes suggests that the slope of the aggregate supply curve equals “the

reciprocal of the money-wage”. Surely, the slope cannot both be equal to 1 and to the

reciprocal of the money-wage, unless the latter also equals 1. Or does Keynes mean

the slope of the Zcurve as opposed to the Z

w

curve in the last sentence? This is what

Patinkin (1976, 88) believes to be true. However, as was shown above, if the slope of

the Z

w

curve equals 1, then the slope of the Zcurve equals the money wage-unit (W),

not its inverse. Therefore, Patinkin claims that the word “reciprocal”“should not

appear here, or else it refers to the measurement of the slope with respect to the vertical

axis”(Patinkin 1976, 88, fn. 8).

Figure 3. The D/Z diagram I (source: Patinkin 1976, Figure 9.1).

THE EUROPEAN JOURNAL OF THE HISTORY OF ECONOMIC THOUGHT 511

If the system converges to N

0

in Figure 3, then proceeds will just cover costs. This,

in Patinkin’s(1976,87–88) reading, Keynes means by “proceeds which will just make it

worth the while of the entrepreneurs to give that employment”(Keynes [1936] 1973,

24). However, this ignores that Keynes adopted Marshallian microfoundations, which

assume that entrepreneurs maximise profits not that they aim at covering costs.

10

Also,

Keynes explicitly states in the passage quoted above that “the entrepreneurs’expect-

ation of profits will be maximised”at the point of effective demand. Patinkin therefore

suggests “that these words should simply be deleted from the General Theory”

(Patinkin 1976, 93).

As was mentioned in the Introduction, two journal articles complement Patinkin’s

analysis in KMT. The “correction”Patinkin (1977) found necessary to make refers to a

minor issue. In Figure 3 (reproduced from Patinkin 1976) he placed income in wage-

units in square brackets below the employment levels. Patinkin soon realised that with

respect to real income, the 45-line no longer measures the minimum proceeds (costs)

on which firms will insist since its unitary slope now represents the marginal return

from this output. By definition, if output rises by one unit, its total value rises by one

unit. Hence, with respect to Y

w

the 45-line represents the total market value of output

(variable costs plus profits in wage units) and not the aggregate supply price as defined

by Patinkin in KMT (total variable costs). Since he did not attribute this part of his

argument to Keynes, this error does not bear on Patinkin’s interpretation of the theory

of effective demand in the General Theory.

11

Patinkin (1978) is a defence of his interpretation of the Zfunction in KMT against a

(mostly critical) review by Roberts (1978). Patinkin reiterates that, based on the

“footnote”–or rather the upper part of it –the Zfunction (in wage-units) must be

interpreted as representing total factor costs (Patinkin 1978, 585). But then he makes a

concession that paves the way for his reinterpretation of Keynes’theory of effective

demand vis-

a-vis KMT that will be discussed in the next section. He writes that

“Keynes incorrectly defines a supply curve as identical with the total-variable-cost

curve”(Patinkin 1978, 586, italics added). Vaguely, he allows the aggregate supply

curve to be derived from profit-maximisation. It then no longer coincides with the

45-line. The proposition “that every point on the aggregate supply curve is a point of

maximum profits”he declares “valid”(Patinkin 1978, 590, italics in original). This is all

quite surprising against the background of KMT. Patinkin refrains from explaining

these statements, but refers (in fn. 24) to his forthcoming article (Patinkin 1979a) for

“a more systematic and detailed discussion of these points”. He summarises his new

view as follows: “There can be little doubt that aggregate supply price as specified in

10

Asimakopulos (1982, 18) insists that “Keynes accepted implicitly Marshall’s microeconomics, and …they

provided the foundations for his aggregate supply function”. He also notes that Keynes’choice of words in

the General Theory just “echoes Marshall’s definition of the supply price for a particular commodity, ‘the nor-

mal supply price of any amount of that commodity …is the expectation of which will just suffice to main-

tain the existing aggregate amount of production’” (Asimakopulos 1982, 23 citing Marshall 1920, 342–343).

The proceeds which will just make it worth the while of the entrepreneurs to give that employment “include

all the elements, other than user costs, to be found in industry supply curves, that is, labour, other factor costs

and profits”(Asimakopulos (1982, 25). Asimakopulos (1982, 32) also criticizes that Patinkin’sZcurve in

Figure 3 becomes vertical at full employment N

F

because Zis derived from individual firm’s curves which are

drawn “without reference to possible constraints on output due to shortages of labour or other variable

inputs”. So if the individual curves do not have vertical parts, their aggregate counterpart should neither.

11

In the German translation of KMT (Patinkin 1979b), the Y

w

terms in square brackets are gone.

512 J. HARTWIG

this footnote is equal to total variable costs. And though this specification is analytically

incorrect …, no clear evidence has been supplied that Keynes specified aggregate sup-

ply price in any other way at other points in the General Theory”(Patinkin 1978, 591).

The next task Patinkin set himself to was to specify the aggregate supply function

correctly. The next section will show that Patinkin dropped his claim that the aggregate

supply curve is the 45-line. His new claim is that Keynes did not properly understand

his own Zfunction.

12

4. “A Study of Keynes’Theory of Effective Demand”

In Patinkin (1979a), he argues more formally than in his earlier contributions on

aggregate supply. He opens up his argument stating: “let us first derive an aggregate

supply function from the principle of profit-maximization. Accordingly, let the produc-

tion function be

Y¼wðNÞ”(1)

(Patinkin 1979a, 158).

As stated in the Abstract, my aim in this paper is not only to trace the evolution of

Patinkin’s interpretation of the theory of effective demand, but also to comment on it.

Patinkin’s attribution of a macroeconomic production function (from which to derive

the aggregate supply function) to Keynes might be questioned. Keynes, in Chapter 4 of

the General Theory, expressed concern over the concept of aggregate real output –Yin

formula (1) –because real output was not homogeneous. He declared that he wanted

to use only two units for measuring macroeconomic aggregates, namely money and

labour. Therefore, authors such as Hayes (2007) and Ambrosi (2011) have denied the

admissibility of the aggregate production function for a reconstruction of Keynes’the-

ory.

13

However, Keynes occasionally used the notion of aggregate real output himself –

on p. 209 of the General Theory, for instance, he calls it O–; and it is a very useful and

established concept in macroeconomics.

14

So I would go along with Patinkin in taking

the aggregate production function with labour as the only variable factor of production

as starting point.

15

Next, Patinkin writes down the first-order condition as

w=p¼w0ðNÞ(2)

and calls it the “labor-demand function”(Patinkin 1979a, 158).

12

“(M)y basic criticism of Keynes’presentation of his aggregate supply function is that it is a confused one”

(Patinkin 1978, 588).

13

An anonymous reviewer for this journal seems to agree claiming that the use of a production function implies

that the variables appearing in Figure 2 above and in Figure 4 below are defined in terms of a single good

produced that can be consumed or invested. According to the reviewer, in such an economy, the aggregate

demand function would not be independent of the aggregate supply function or the 45-line in the Keynesian

cross; and Say’s Law would apply.

14

See Hartwig and Brady (2008) for a critique of Hayes (2007). Froyen (1976) argued that Keynes finally opted

for a single measure of output in the General Theory.

15

In fact, I did exactly this when I reconstructed the Zfunction in Hartwig (2000, 174–179). At that time, how-

ever, I was unaware of Patinkin (1979a) and used Chick (1983) as my main point of reference.

THE EUROPEAN JOURNAL OF THE HISTORY OF ECONOMIC THOUGHT 513

Arguably, if Keynes had accepted the neo-classical labour-demand function, it would

hardly have been necessary for him to devise a new (“General”) theory of employment.

I fully agree with Asimakopulos (1982, 30) that “(t)here is no separate independent

demand curve for labour in Keynes’model. …(The) inverse relationship [between

employment and the real wage] should not be confused with a labour-demand curve

…There is no labour market in Keynes’model in which labour demand and labour

supply curves interact to determine the equilibrium level of employment and the real-

wage rate”.

16

Nonetheless, the first-order condition is very important as it picks up the

idea of profit-maximisation. Following Chick (1983), my approach in earlier publica-

tions has been to solve Equation (2) for the price level, to call this the “supply price lev-

el”, then to multiply this supply price level with the output level from Equation (1) to

get Z¼wwN

ðÞ

w0N

ðÞ

or Zw¼wðNÞ

w0ðNÞ:

17

Patinkin argues slightly differently. He first expresses

the production function (1) “in money terms”and deflates it by the wage-unit (w) to get

Yw¼pwðNÞ

w:(3)

“Upon substitution from profit-maximizing condition (2), this becomes the aggre-

gate supply function

Zw¼wðNÞ

w'ðNÞ”(4)

(Patinkin 1979a, 159–160).

Applying the quotient rule and assuming diminishing marginal productivity (wʺ(N)

<0) it is easy to show that the slope of the Z

w

curve is greater than unity.

18

So Z

w

lies

above the 45-line, which represents variable costs. This is Patinkin’s new insight vis-

a-vis Patinkin (1976).

From the perspective of the Chick-Hartwig interpretation –if I may call it that way

–as detailed in Chick (1983), Hartwig (2000) and elsewhere, Patinkin’s approach to

substitute Equation (2) into Equation (3) is not quite satisfactory as it ignores that there

are two price levels involved in the D/Z model, not just one.

19

The supply price is not

the market price level an entrepreneur expects, but the proceeds he must have for the

last unit of output at each level of employment to satisfy the profit maximising condi-

tion. This unit supply price will grow with employment under conditions of decreasing

16

The English translation of Hartwig (2000)isKeynes vs. Pigou. Reconstruction of an Employment Theory

Beyond the Market Paradigm. See also Davidson (1983).

17

Note that for employment to rise by one unit the “supply price level”has to increase under conditions of

diminishing returns. Hence, the real wage must fall and income must be transferred from the previously

employed workers to the entrepreneurs. This principle enshrined in Keynes’aggregate supply function is in

keeping with Pigou’s([1933]1968)Theory of Unemployment (see also Arthmar and Brady 2009, 139–140).

18

dZw

dN ¼1wN

ðÞ

w00 N

ðÞ

w0ðNÞ

½

2>1:

19

Interestingly, Patinkin had seen that in KMT, where he wrote: “In graphical terms …Keynes seems to have

treated the difference between OA and OB in Figure 9.1 [Figure 3 in this paper] as if it represented the differ-

ence between two different per-unit prices that actually existed in the economy at a given level of aggregate

output”(Patinkin 1976, 92).

514 J. HARTWIG

marginal returns to labour. P

s

, the price level implicit in Z, is in a way purely hypothet-

ical. If, for a certain N

1

, the entrepreneurs expected the price level Ps¼wdN1

dY to rule

in the market they would employ N

1

men because they knew that profits would thereby

be maximised. But which price level do they really expect? This question is not

answered by the aggregate supply function at all but by the aggregate demand function.

The price level implicit in D, which I call the “demand price level”P

d

, is the price level

the entrepreneurs really expect to rule in the market and which they must “take”under

free competition that Keynes assumes. Being profit-maximizers, the entrepreneurs

must be on the aggregate supply curve –they cannot be off that curve. All points on Z

are profit-maximising. The aggregate demand curve Dpicks the “right”profit-maxi-

mising level of employment where it intersects Zat the point of “effective demand”.

In my most recent contribution to the D/Z controversy (Hartwig 2017), I use spe-

cific functional forms for the Dand Zfunctions and run numerical simulations which

allow study of the comparative statics of the model in the face of various “shocks”.I

use the production function Y¼N

a

with a¼0,7 as starting point. As chance would

have it, Patinkin (1979a, 161) uses almost the same function Y¼AN

a

(with 0 <a<1)

for illustrative purposes.

20

This production function gives rise to the following Z

w

func-

tion (depicted in Figure 4)

Zw¼ANa

aANa1¼1

aN(5)

The slope of Z

w

,(1/a), is greater than unity, which is the slope of the total variable

cost (TVC) curve. “By construction, every point on this aggregate supply curve is a

point of maximum profits –for the real-wage rate to which it corresponds”(Patinkin

1979a, 161).

21

For the aggregate demand curve D

w

¼

1

f(N) in Figure 4,0A ¼N

1

Tare

total proceeds, N

1

Uare wages and UT are profits (all in wage-units). “In accordance

with the property of a Cobb-Douglas function, the share of wages in the total value of

output …is constant and equal to

a¼N1U=N1T¼N2S=N2R”

(Patinkin 1979a, 162).

This means that the slope of the Zcurve is equal to the inverse of the wage share (a)

or, in other words, equal to the inverse of the output elasticity, which is equal to the

wage share for a Cobb–Douglas production function. Although this insight pre-dates

Patinkin (1979a),

22

it was Ambrosi (2011) who seems to be the first to have suggested

20

I did not quote Patinkin (1979a) in Hartwig (2017) because I discovered his article only recently when collect-

ing literature for the present paper. Patinkin (1979a) has not received much attention. The article has received

only 12 citations in Scopus (as of November 2021); and no reviewer or editor has ever pointed my attention

to it. See Patinkin (1982b)on“multiple discoveries”in science.

21

I would replace “real-wage rate”with “marginal product of labour”as Patinkin’s wording reflects his substitu-

tion of the “labour-demand function”into the production function, which was criticized above. However,

since we assume that the supply price level moves to equate the real wage with marginal product, Patinkin’s

formulation is correct.

22

The earliest statement I found is by Marty (1961) who wrote: “The tangent of the angle made by drawing a

line from the supply function to the origin is the reciprocal of the relative share of labour. If the relative share

is constant as we move along the supply function we trace a linear function. Linearity of the supply function

THE EUROPEAN JOURNAL OF THE HISTORY OF ECONOMIC THOUGHT 515

that it can be used to solve one of the puzzles posed by the “footnote”on pp. 55–56 of

the General Theory. In the last sentence of the footnote, Keynes claims that the slope of

the aggregate supply function equals the inverse of the money wage. Ambrosi agrees that

this is wrong, but he claims that the statement could be corrected simply by inserting the

word “share”at the very end of the footnote. In other words, Ambrosi thinks that

Keynes “really meant”that the slope of the aggregate supply function is equal to the

reciprocal of the money wage share. Although it cannot be proved that Keynes’pen

“slipped”here,

23

this is an attractive explanation. Hartwig (2017,362–363) offers a math-

ematical proof that the slope of Z

w

is equal to the inverse of the output elasticity.

24

In section III of his article, Patinkin (1979a) collects passages from the General Theory

which accord with his new interpretation of the theory of effective demand. However, in

section IV, he rejects the idea that this was Keynes’own interpretation. His argument is

twofold. First, there is the “footnote”where Keynes states that the slope of the aggregate

supply function in wage-units equals 1. This means he must have thought that Z

w

is the

45-line. And second, neither in Keynes’Treatise on Money nor in the drafts of the

Figure 4. The D/Z diagram II (source: Patinkin 1979a, Figure 2).

implies constancy of the relative share”(Marty 1961, 561–562). Patinkin’s(1979a, 159, fn. 5) statement that

Marty has not analyzed the “slope and other properties”of Zis thus incorrect. See also Davidson and

Smolensky (1964, 125, 134–135), Asimakopulos (1982, 26) and Arthmar and Brady (2009, 140) on (1/a) being

the slope of Z

w

.

23

See Heller (2009).

24

This argues against Patinkin’s(1976, 88) conjecture that the last sentence of the “footnote”was about the

slope of Zinstead of Z

w

.

516 J. HARTWIG

General Theory can references to profit-maximisation and marginal analysis be found. So

ignoring the fact that the passage from p. 25 of the General Theory quoted above is per-

fectly in line with his new interpretation, Patinkin concludes that, for Keynes,Drepre-

sents expected proceeds and Z(erroneously) total variable costs.

The last critique Patinkin offers is that “even if Keynes had correctly derived his

aggregate supply curve from profit maximisation (thus yielding, say, Z

w

¼(1/a)N in

Figure 2 [Figure 4 in this paper]), its intersection with D

w

¼

2

f(N) at Ris not a point of

maximum profits”(Patinkin 1979a, 171). To prove this, Patinkin first redefines the

aggregate demand curve D

w

¼

2

f(N) in Figure 4 as representing actual proceeds

(Patinkin 1979a, 172–173), even though he admits, that for Keynes it represented

expected proceeds.

Given that Patinkin’s aim for his article was “to determine to the best of my

ability what he [Keynes] did say”(Patinkin 1979a, 155), this departure from his

source seems odd. I can only speculate about his reasons. Maybe these had to do

with the problem of how to arrive at aggregate results starting out from the

expectation formation of individual entrepreneurs. On pp. 24-25 of the General

Theory, Keynes describes Dand Zboth as functions of N. But while Nin the

entrepreneurs’“micro”Zfunctions stands for the employment in the entrepre-

neurs’own firms, and the individual Zfunctions can be aggregated straightfor-

wardly, the Nin the “micro”Dfunctions cannot stand for the employment in the

entrepreneurs’own firms because demand expectations of individual entrepreneurs

do not depend on the employment they give themselves. Therefore, Asimakopulos

(1982) rejects the expectational Dfunction, and he quotes Patinkin (1979a,

172–174) as a point of reference (see Asimakopulos 1982, 21, fn. 10).

25

Patinkin’s

argument seems to be somewhat different, though. He accepts that individual

entrepreneurs are (demand-) price takers because they cannot observe the aggre-

gate demand function. For them, “Keynes’description of the point of intersection

of the aggregate demand and supply curves as one of maximum profits …is

correct”(Patinkin 1979a, 173). For the “firms as a whole, operating as one unit”

(Patinkin 1979a, 173), however, things are different. The “unit”can perceive the

aggregate demand curve –the actual one that is, not Keynes’expectational one –

and can move freely on it, according to Patinkin. If the “macro”Dcurve is D

w

¼

2

f(N) in Figure 4 –as Patinkin has postulated (see above) –then the difference

between actual proceeds on D

w

¼

2

f(N) and total variable costs on the 45-line –

hence profit –is higher than at the point of effective demand Rwhen employ-

ment falls below N

2

.

26

Patinkin comes to this conclusion because he treats the aggregate of firms like

a monopolist who can move freely on the Dcurve. I have doubts that the aggre-

gation problem should be solved this way. In my interpretation (see fn. 25 above),

the Dcurve is exogenous for the entrepreneurs, as is the price component

25

I think Asimakopulos’rejection of the expectational Dfunction is unwarranted. Entrepreneurs do form

expectations on overall employment –or the state of the business cycle, respectively –when they decide how

many workers to employ in their own firm. So “macro”employment and “micro”employment are interre-

lated. See Hartwig (2004,81–82) for a defence of the expectational Dfunction.

26

See also Boianovsky (2002, 248–249) on the topics covered in this paragraph and the next.

THE EUROPEAN JOURNAL OF THE HISTORY OF ECONOMIC THOUGHT 517

inherent in it. Entrepreneurs are (demand-) price takers. They cannot move freely

on D. On the other hand, being the suppliers, entrepreneurs cannot be off the

aggregate supply curve. To repeat from above, the aggregate demand curve D

picks the “right”profit-maximising level of employment where it intersects Zat

the point of “effective demand”.

27

Howsoever, Patinkin softens his criticism of Din his concluding examination of the

theory of effective demand. Patinkin (1982a) is basically a reprint of Patinkin (1979a),

albeit with some rearrangements and amendments. One such rearrangement concerns

the two criticisms from section IV of Patinkin (1979a). Patinkin (1982a) now discusses

the “inconsistency”concerning D–that profits are not maximised at the point of inter-

section with Z–first and indicates that it can be removed when Dis reinterpreted as

representing actual instead of expected expenditure (Patinkin 1982a, 143–144). It will

be remembered that this redefinition was the first step in his proof of the

“inconsistency”concerning Din Patinkin (1979a, 172–173). The “inconsistency”arose

because Patinkin assumed that the entrepreneurs “as a unit”could perceive and move

on D

w

¼

2

f(N) in Figure 4. If, however, “the aggregate demand curve is not perceived

by entrepreneurs”(Patinkin 1982a, 143, italics in original) so that D

w

¼

2

f(N) repre-

sents the total consumption and investment expenditures, and if D

w

¼

1

f(N) represents

aggregate demand as expected by the entrepreneurs, then at employment level N

1

actual demand is higher than expected demand. So the entrepreneurs have an incentive

to expand output. This triggers a quantity reaction –just like an upward shift of the

demand curve in the Keynesian cross would –which continues until the economy

reaches an equilibrium at point Rin Figure 4,“where, for the representative competi-

tive firm, market price equals marginal cost. Thus, from the viewpoint of such a firm,

Ris a point of maximum profits in the sense that the firm has no incentive to depart

from it”(Patinkin 1982a).

So with respect to D, Patinkin eases his criticism vis-

a-vis Patinkin (1979a) some-

what. He maintains, however, that “Keynes did not distinguish properly between prop-

ositions which are valid for the representative firm operating under conditions of

perfect competition and those valid for firms as a whole, operating as one unit”

(Patinkin 1982a, 144).

The “second inconsistency”–the “footnote’s”statement that /0(N) ¼1–“is a

much more serious one”(Patinkin 1982a, 144). Patinkin offers a new insight, how this

statement might be explained. He argues that Keynes simply confounds the aggregate

supply function /(N) with the production function w(N) in the “footnote”. For it fol-

lows from the first-order condition (Equation 2 above) that p

ww0N

ðÞ

¼1:That is, the

slope of the production function (Equation 1) “in money terms”and deflated by the

wage-unit (w) equals 1. “Was Keynes’implicit, erroneous identification of the produc-

tion and supply functions transitory or permanent?”, Patinkin asks. “Was it a chance

error of this footnote or a systematic component of his thinking? The evidence is not

clear, but I think the latter alternative is closer to the truth”(Patinkin 1982a, 145).

Which leads Patinkin to his final verdict on Keynes’theory of effective demand: “And

27

Victoria Chick was right to point out that “(e)ffective demand is an unfortunate term, for it really refers to

the output that will be supplied; in general there is no assurance that it will also be demanded”(Chick

1983, 65).

518 J. HARTWIG

this is my main point: that the obscurity with which the aggregate supply curve is pre-

sented in the General Theory is a sign not of profundity, but of obscurity”(Patinkin

1982a, 150).

5. Conclusion

The evolution of Patinkin’s interpretation of Keynes’theory of effective demand made

some turns. Patinkin started out supplementing the then-dominant way of representing

Keynesian theory –the Keynesian cross –with an aggregate supply function. His initial

version of that function, in Patinkin (1949), was nearly horizontal; later on, in Money,

Interest, and Prices, Patinkin opted for a vertical version of the aggregate supply func-

tion. Failure to include aggregate supply in the Keynesian cross let “Keynesian econom-

ics”, in Patinkin’s view, to neglect that an excess of supply over demand would

generate a deflation of money wages and prices that would restore full employment

through the interest-rate and real-balance channels.

After the publication of volumes XIII and XIV of the Collected Writings of John

Maynard Keynes (in 1973) Patinkin refocused from “Keynesian economics”to “the

economics of Keynes”. The drafts of Keynes’General Theory as well as the correspond-

ence between Keynes and his colleagues published in these volumes were instrumental

for Patinkin in recognising the importance of Chapter 3 of the published version of

Keynes’book titled “The Principle of Effective Demand”. However, Patinkin struggled

for several more years with identifying the true meaning of this “most important and

…most obscure chapter in the General Theory”(Patinkin 1979a, 155). His main inter-

pretative problem was with Keynes’aggregate supply function Z. Chiefly based on a

footnote from pp. 55–56 of the General Theory, in which Keynes states that the slope

of the aggregate supply function in wage-units (Z

w

) equals 1, Patinkin identified the

latter as the total-variable-cost curve in his book Keynes’Monetary Thought (Patinkin

1976). He was well aware, however, that several passages of the General Theory, for

instance Keynes’insistence that profits are maximised at the point of effective demand

–which is the point of intersection of the aggregate supply function Zand the aggre-

gate demand function D–were at odds with this interpretation. Therefore, in 1979, he

revisited his interpretation, integrating the first-order condition in Z. The slope of the

aggregate supply function in wage-units (Z

w

) in the Z

w

/N-space is consequently greater

than 1, and the distance between Z

w

and the 45-line measures profits (in wage-units).

This interpretation, Patinkin was convinced, was the correct version of the aggregate

supply function. This implies that the version in Patinkin (1976) is wrong.

28

I agree

with Patinkin on this point. Patinkin attributes the wrong version –the KMT version –

to Keynes, however.

29

His main evidence: the “footnote”from pp. 55-56 of the General

Theory. I tend to disagree with Patinkin on this second point because the interpretation

of Keynes’principle of effective demand developed in Patinkin (1979a) and reaffirmed

28

“The chapter is a further development –and in part a correction –of the critique of Keynes’theory of effect-

ive demand which appears in chapter 9 of KMT”(Patinkin 1982a, 123).

29

“The analysis of section 3 above not only demonstrates the invalidity of Keynes’description of the supply

curve as having a constant unitary slope, but also suggests that the immediate cause of Keynes’error was his

failure to distinguish between the supply function and the production function”(Patinkin 1982a, 145).

THE EUROPEAN JOURNAL OF THE HISTORY OF ECONOMIC THOUGHT 519

in Patinkin (1982a) is perfectly in line with the passage on p. 25 of the General Theory

quoted above in section III.

There must be something wrong with the “footnote”, however, since it makes con-

flicting claims about the slope of Z

w

, namely that the latter equals at the same time 1

and the reciprocal of the money wage. I already mentioned Ambrosi’s(2011) proposal

to rectify the last sentence of the footnote by inserting the word “share”at the very end

and Patinkin’s(1982a) suggestion that it should read p

ww0N

ðÞ

¼1 instead of /0(N) ¼1

in the upper part of the “footnote”. Another suggestion can be made. Keynes [1936]

1973, 283) writes that “if the elasticity of output is unity, no part of the increased effect-

ive demand is expected to accrue as profit”. In this special case of zero marginal profits,

the slope of the aggregate supply function in wage-units (Z

w

) equals 1. So the statement

/0(N) ¼1 is correct, but only for the special case of an output elasticity –and hence a

wage share –of 1.

30

Acknowledgements

I wish to thank Harald Hagemann, Fritz Helmedag and two anonymous reviewers for this

journal for helpful comments on an earlier draft. The usual disclaimer applies. This research

did not receive any specific grant from funding agencies in the public, commercial, or not-for-

profit sectors.

Disclosure statement

No potential conflict of interest was reported by the author(s).

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