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115
IN THE FIRST CHAPTERS of Capital III, Marx presents his
transformation of values into prices of production. The
transformation is necessary because, unless all capitals
have the same organic composition or profits are uniformly
zero, a theory of value and price based on social labour cannot
explain the exchange ratios between commodities. The
transformation marks an analytical shift in Capital, from the
analysis of capital-in-general to many capitals. At this level of
analysis, the organic composition of capitals in different
branches may be distinct, and capital migration is possible. For
Marx, these are the most important factors underlying the
tendency towards the equalization of profit rates across the
economy. Competition between capitals in different branches
implies that the surplus value produced is pooled, and
distributed as profit according to the size of each capital. As a
result, commodities receive prices of production that are not
proportional to values.
The centrality of the transformation, given the structure
and aims of Marx’s work, and his seemingly counter-intuitive
approach, have brought this issue to the attention of a vast
This article analyses the transformation of values into prices of
production from the point of view of differences in the organic
composition of capital. Marx’s transformation has two stages. In the first,
the value of the means of production used up is irrelevant; in the second,
the economy is analysed at the level of price. The transformation helps
to explain the distribution of labour and surplus value across the
economy, and substantiates the claim that value is produced by
labour alone. However, it does not allow the vector of prices of
production to be calculated.
An Alternative Reading of the
Transfor mation of Values i nto
Prices of Production
by Alfredo Saad-Filho
array of writers of widely different persuasions. Interest on
this problem remains alive even after one hundred years of
the publication of Capital III, and the polemic with respect to
its analytical status and the impact of the various ‘solutions’ has
become increasingly sophisticated.1Some writers claim that the
transformation reveals fundamental flaws in Marx’s method,
and shows that analyses based on his value theory are doomed
(see, for example, Bohm-Bawerk 1949 [1896], Samuelson 1957,
1971 and Steedman 1977). Writers from within the Marxian
tradition have tended to attribute the difficulties to minor
problems or ambiguities in Marx’s analysis, that can be rectified
easily (although in different ways), or claimed that Marx’s
approach to the transformation is cogent and needs to be
understood properly rather than corrected (see, for example,
Dumenil 1980, Foley 1982, Kliman and McGlone 1988 and
Yaffe 1974).
In this article, I approach the transformation from a different
angle. Most writers have discussed this problem as if the
transformation were due to differences in the value composition
of the advanced capitals. In contrast, it is well-known that
Marx attributes it to differences in their organic composition. I
have already compared and contrasted these concepts in a
previous C&C article (Saad-Filho 1993b), and will now outline
their implications for the transformation. The reading presented
here follows an approach first proposed by Fine (1983). In
taking this route I do not seek to deny the importance of the
previous literature, that has greatly advanced our understanding
of Marx’s critique of the capitalist economy. On the contrary,
my aim is to enrich our understanding of Marx by building on
a cogent, interesting, and relatively undeveloped reading of
his transformation procedure. As I am not claiming that this
reading is the only correct one, nor that it is better than any
other, only a small part of this paper confronts other
interpretations of Marx.
This article has six sections. The first briefly introduces the
concepts of surplus value, profit, and rate of profit. The second
reviews the differences between the organic and value
compositions of capital. The third and fourth explore the
implications of OCC differences for the transformation. The
fifth discusses the transformation of input values. The sixth
concludes this study with an assessment of the implications of this
reading of Marx, and its implications for traditional views.
116 Capital & Class #63
Surplus Value, Profit, and the Composition of Capital
Marx outlines the background of the transformation in the first
part of Capital III. This volume begins with the distinction
between the concepts of surplus value (S) and profit (Π). Surplus
value is the difference between the newly produced value and the
value of the labour power purchased, and profit is the excess of
the value of the product over the value of the constant (C) and
variable (V) capital advanced. (I call ‘value’ the money-expression
of the labour time socially necessary to reproduce commodities,
and ‘price’ is a shorthand for price of production. Both are
measured in money. Therefore, the transformation of value into
price is a change in the form of expression of social labour in
money, rather than a transformation of labour time into
quantities of money (Elson 1979, Kliman and McGlone 1988).
The reader should beware of the possible confusion caused by the
need to conform with the literature.)
From these definitions, it follows that the value of constant
capital is irrelevant for the determination of surplus value, but it
affects the magnitude of profit. The same holds for their rates. The
rate of surplus value, e = S/V, measures the surplus value created
per unit of variable capital; in contrast, the rate of profit (R)
measures the increase in capital’s size, and ultimately in its ability
to produce value. R does not reflect the distinct role of the means
of production (MP) and labour power (LP) in (surplus) value-
production. It is given by:
Se
R = ____ =______ + 1
C+V (C/V)
where C/V is the value composition of capital (K/III: 161).2
Marx subsequently considers the effect of changes in the
quantity, quality and value of the inputs, and of changes in
turnover time and the rate of surplus value, upon the rate of
profit. In chapter eight of Capital III, Marx points out that the
same factors that affect the general rate of profit may also lead to
differences between the profit rates of capitals in distinct sectors:
[T]he rates of profit in different spheres of production that exist
simultaneously alongside one another will differ if, other things
remaining equal, either the turnover times of capitals invested
differ, or the value relations between the organic components of
these capitals in different branches of production. What we
The Transformation ‘Problem’ 117
Section 1.
previously viewed as changes that the same capital underwent in
succession, we now consider as simultaneous distinctions between
capital investments that exist alongside one another in different
spheres of production. (K/III: 243, emphasis added)
This is a very important passage, because it marks a shift in the
level of analysis, from capital-in-general to many capitals. This
shift posits the logical necessity of the transformation (Burkett
1986, Rosdolsky 1977 [1968]). It may therefore come as a
surprise that Marx does not immediately address this issue.
Rather, he dedicates the following pages to the analysis of
(differences between) the technical, organic and value
composition of capital (TCC, OCC and VCC). It is only after this
apparent detour that Marx presents his transformation, in
chapter nine of Capital III.
Technical, Organic and Value Compositions of Capital
This section briefly reviews the meaning and significance of the
concepts of technical, organic and value composition of capital
(for a more detailed analysis, see Saad-Filho 1993b). This will
substantiate my claim that, while Marx presumes that the
transformation is due to the diverse organic compositions of
the advanced capitals, most writers see it as being caused by
their distinct value compositions.
Marx defines the technical composition of capital as the
material ratio between the means of production used up and
the labour time socially necessary to transform them into the
output. Even though the TCC is conceptually clear, the ratio
between a heterogeneous bundle of commodities and a number
of hours of labour cannot be calculated easily. It may therefore be
impossible to compare the technical composition of capitals
invested in different sectors (e.g., agriculture and shipbuilding)
directly, because of the distinct use value of the MPs used up.
Marx bypasses this difficulty through his definition of the
organic composition of capital (OCC). For him, the OCC is the
‘[d]ifferent ratios in which it is necessary to expend constant
capital in the different spheres of production in order to absorb
the same amount of labour’ (TSV/III: 387; see also p.382 and
TSV/II: 276). In other words, the OCC is the ratio between the
value of the (fixed and circulating) constant capital and the (paid
118 Capital & Class #63
Section 2.
and unpaid) labour time socially necessary to transform the
inputs into the output.
The concept of OCC is very important for value analysis.
However, Marx’s definition is problematic. The value of the MP
consumed per hour of labour is the product of the quantities used
up and the values of its components. It seems therefore impossible
to tell whether a change in the organic composition of one
particular capital stems from a change in the productivity of
labour in this firm (such that a different quantity of MP is
processed in one hour of labour), or from a change in the
productivity of labour in other industries (which changes the
value of the MP used up by our firm). How does Marx eliminate
this potential ambiguity? He does two things. First, he defines the
OCC more clearly. For Marx, the OCC is a ‘technological
composition’, or a value-reflex of the TCC. It follows that the
OCC does not vary if the underlying technology of production is
kept constant, even if the value of the elements of capital changes
(see, for example, TSV/III: 382-6).
Second, he introduced in Capital the concept of value
composition of capital (VCC) . The VCC is the ratio between the
value of the circulating part of the constant capital (inclusive of
the depreciation of fixed capital) and the variable capital (paid
labour) required to produce a unit of the commodity (thus, the
VCC is the ratio between the two components of the commodity’s
cost price).3This allows Marx to distinguish between the effects
of the application of distinct technologies (using the OCC), and the
consequences of the use of inputs with different values (using the
VCC). Following the traditional terminology, the OCC is a
concept of production, while the VCC is a concept of circulation.
Marx uses several examples to distinguish the OCC from the
VCC. In many of them, he discusses the same basic problem:
suppose that two capitals used exactly the same technology to
produce wool and cotton clothes (or iron and copper
instruments). What can be said about their TCC, OCC and
VCC? Whenever he poses this problem, Marx always draws the
same conclusion. As the technologies of production are identical,
these capitals have equal TCCs. Therefore, says Marx, their OCCs
are also equal. However, because of the different value of the
MP used up, their VCCs are different.4
The question that naturally comes to mind at this point is,
which values does Marx use to calculate the OCC, such that
capitals producing wool and cotton clothes have the same OCC,
The Transformation ‘Problem’ 119
even though wool is more expensive (say) than cotton? In this
(static) comparison of capitals employing the same technology
but producing different goods, Marx abstracts from (differences
in) the values of the inputs, such that differences in their TCCs can
be brought to light, even if only intuitively. In contrast, in the
dynamic case matters are different, and both the OCC and VCC
of a capital undergoing technical change can be calculated (this
case is the relevant for the derivation of the law of the tendency
of the rate of profit to fall; see Fine 1992).
In sum, the distinction between OCC and VCC corresponds
to the contrast between differences in the TCC and differences in
the values of its components (the differences between fixed and
circulating capital, and between paid and unpaid labour, are
also taken into account). The contrast between OCC and VCC is
important, because the OCC allows the study of technical
differences in production regardless of the distinct value of the
elements of capital, while the VCC synthesizes both effects. If one
takes into account Marx’s well-known view that the sphere of
production predominates vis-à-vis circulation, distribution and
consumption, it comes as no surprise that he considers differences
in TCCs and OCCs more significant than differences in VCCs.
The OCC and the Transformation Problem
The profit rates of capitals invested in distinct sectors may be
different because of their distinct organic or value compositions.
The OCC connects the rate of profit to the sphere of production,
where living labour produces (surplus) value, while the VCC
links this rate to the sphere of circulation, where the growth of the
advanced capital is measured by the newly established values
(see Saad-Filho, 1993a). Marx describes the impact of differences
or changes in the OCC and the VCC on the rate of profit saying:
Fluctuations in the rate of profit that are independent of changes
in either the capital’s organic components or its absolute
magnitude are possible only if the value of the capital advanced
… rises or falls … If the changed circumstances mean that twice
as much time, or alternatively only half as much, is required for
the same physical capital to be reproduced, then given an
unchanged value of money … the profit is also expressed
accordingly in twice or only half the monetary sum. But if it
120 Capital & Class #63
Section 3.
involves a change in the organic composition of the capital, the
ratio between the variable and the constant part of the capital,
then, if other circumstances remain the same, the profit rate will
rise with a relatively rising share of variable capital and fall with
a relatively falling share. (K/III: 237-8; see also pp.142-5 and
246–8, and TSV/II: 28, 383-8 and 426-7)
Thus, a variation in the value of the MP consumed in one hour of
labour (because of technical changes in another sector, say)
immediately modifies the VCC, the value of the output and the
rate of profit, but it does not affect the TCC nor the OCC. In
contrast, the effect of a change in the quantity of simple labour
necessary to produce one unit of the output (because of technical
changes in this industry) is more complex; first, it modifies the
TCC, the OCC and the quantity of (surplus) value created; in the
sequel, it changes the value of the output and the rate of profit.
If Marx was primarily interested in the impact on prices of
differences in the value of the elements of the advanced capital,
or the effect on the rate of profit of the distinct expenditure
ratios in constant and variable capital, he would focus on the VCC
in the transformation. Even though most of the literature
approaches the problem from this angle (see section 6), Marx’s
procedure is different. His emphasis on the OCC shows that he
is primarily concerned with the effect on prices of the distinct
(surplus) value-creating capacity of the advanced capitals, or
the impact on prices of the different quantities of (paid and
unpaid) labour necessary to transform the means of production
into the output, regardless of the value of the (fixed or circulating
parts of the) MP.5This is only natural for a labour theory of
value; but let us discuss this point in more detail.
As we have seen in section 2, when OCCs are compared
differences in the value of the MP and LP, and the impact of the
conditions of circulation upon the rate of profit, are netted out,
and only differences in the conditions of production are
influential. This leads Marx to a very simple yet powerful
conclusion: the capital with the lowest OCC employs relatively
more workers, produces more surplus value, and has the highest
profit rate, regardless of the commodity produced.6
This is very important for Marx, and it points to two reasons
why the analysis of profit through the OCC is important; first,
because it pins the source of surplus value and profit firmly
down to unpaid labour performed in production. This helps Marx
The Transformation ‘Problem’ 121
to substantiate his argument that machines do not create value,
and that industrial profit, interest and rent are merely shares of
the surplus value produced. Second, it connects the concepts
being introduced (rate of profit, distribution of labour and
surplus value, and price of production) with the sphere of
production. This is important because for him production is the
determinant sphere, both in reality and in analysis. For Marx,
these concepts cannot be grounded upon circulation or
distribution because these spheres are relatively less important,
and express in a possibly distorted manner categories determined
in production (see Marx 1981b [1953]: 85-108). In the aftermath,
Marx illustrates how the general rate of profit is formed, and
how prices of production are determined, through a comparison
of five capitals with distinct OCCs.
From Values to Prices of Production
In his transformation tables in chapter 9, Marx works with five
capitals worth £100. He states that these capitals have different
profit rates because of their distinct OCCs. From the individual
rates of profit he calculates an average and, from this average,
Marx derives the prices of production. In spite of its importance,
the reason why Marx uses capitals of £100 in the transformation
has escaped the literature; this has probably been attributed to
convenience or ease of exposition. However, since Marx is
interested in the OCC, this is a necessity:
[T]he organic composition of capital … must be considered in
percentage terms. We express the organic composition of a capital
that consists of four-fifths constant and one-fifth variable capital
by using the formula 80c + 20v. (K/III: 254, emphasis added)
Marx uses the percent form several times, in the transformation
and elsewhere. He does this because this is the only way to assess
the OCC in the static case, when it cannot be measured directly
(as shown in section 2 above). If we assume, as Marx does, that
all workers are equally skilled and that the rate of surplus value is
identical across the economy,7when capitals are put into the
percent form (60c+40v rather than 180c+ 120v; 80c+20v rather
than 240c+60v, etc.) the consequences are striking: variable
capital becomes an index of the quantity of simple labour power
122 Capital & Class #63
Section 4.
purchased, labour performed, and value and surplus value created
(see K/III: 137, 146, 243-6). In addition, there is a direct
relationship between the quantity of (paid and unpaid) labour put
in motion, the value of the output and the rate of profit (see
appendix). This is precisely what Marx wants to emphasize in
the transformation; all else is secondary. As these relations are
established in production, they involve the organic (not the
value) composition of capital:
As a result of the differing organic compositions of capitals
applied in different branches of production, as a result therefore
of the circumstance that according to the different percentage that
the variable part forms in a total capital of a given size, very
different amounts of labour are set in motion by capitals of equal
size, so too very different amounts of surplus labour are
appropriated by these capitals, or very different amounts of
surplus-value are produced by them. The rates of profit prevailing
in the different branches of production are accordingly originally
very different. (K/III: 257)
The use of the percent form in the transformation has three
interesting implications, other than those mentioned in the
previous paragraph. First, the ‘adjusted’ surplus value extrated in
each industry (surplus value per £1 of advanced capital, si*, ) is
equal to the profit rate, and it can be determined from the
quantity of labour power purchased. The analysis of profit from
the point of view of the adjusted surplus value is important,
because it illustrates the principles that profit is created in
production, and that the rate of profit depends primarily upon the
quantity of labour power put in motion. Second, the output of
every £1 of advanced capital has the same price, regardless of the
commodity produced.8This substantiates the argument that
competition between capitals in different branches determines
prices of production such that the average capital of every branch
has the same profit rate. For Marx, this shows that profit is a
‘dividend’ drawn from the social surplus value (see K/III: 258,
298-9). Finally, the adjusted or percent form can help
demonstrate that total value equals total price of production,
and total surplus value equals total profit.
These aggregate equalities are essential for Marx. They should
not be understood as two independent conditions, for they are
one and the same (albeit influential at distinct levels): total price
The Transformation ‘Problem’ 123
is equal to total value because total profit is equal to total surplus
value. The abstraction of the transformation of the value of the
inputs and the value of the money-commodity (see below) shows
that these equalities should be understood in the conceptual
(rather than algebraic) sense; they express the relationship between
value and surplus value with their own forms of appearance, price
and profit. Total profit = total surplus value because profit is
redistributed surplus value, while total price = total value because
price is merely a form of value. In other words, the prices of
production derived by Marx are a relatively complex form of
value, where price-value differences redistribute surplus value
across the economy until all capitals have the same profit rate (see
Weeks 1981: 171).
We have seen above that the percent form is convenient,
because it highlights the effect of differences in the OCCs on
the profit rate. However, because it equalizes all capitals to £1
the percent form changes the average rate of profit and
modifies the quantities produced by each capital. Consequently,
the adjusted value and price of the product of a capital may be
different from the actual, and total adjusted surplus value,
price and profit are different from the original magnitudes. It
is therefore impossible to calculate the price vector, unless
the technologies of production are specified—which Marx
does not consider to be necessary for the analysis of the
transformation.9
As the percent form is necessary to assess the OCC, and
since its use precludes the calculation of prices, it cannot be
argued that Marx’s primary objective in the transformation is to
devise a method for the calculation of the price vector, given the
value of the means of production and labour power. Although
some may find this disappointing or worse it is hardly
surprising, for the issue in the transformation is not quantitative
(the calculation of unit prices), but qualitative (the claim that
price is a more complex form of expression of social labour than
value, since it takes into account the distribution of labour and
surplus value across the economy).10 The input values are
irrelevant to this end. In the light of the ensuing controversy,
Marx’s objectives are important for another reason: they can be
fulfilled only if the transformation departs from differences in
the OCC, and not the turnover times or the VCC. One problem
remains to be addressed: the transformation of the value of
the inputs.
124 Capital & Class #63
The Transformation of Input Values
The distribution of surplus value such that profit rates are
equalized, and the consequent determination of prices of
production is the first logical stage of the transformation, the
only one which Marx discusses in detail. The second logical stage
involves the transformation of the input values and the value of
money. It received much less attention from Marx, and it has been
the source of most disagreement about the meaning and
significance of his approach. It is often argued that Marx ignores
the transformation of the input values in his procedure. However,
this statement is at best incomplete. Marx abstracts from the
input values themselves (as far as an OCC-analysis allows him to
do), for two reasons. First, because they are irrelevant for the
argument that profit is the form of appearance of surplus value;
second, because the simultaneous transformation of input and
output values would make undetectable the process of distribution
of surplus value, which is the core of the transformation. If inputs
and outputs are transformed simultaneously, only two opposing
and seemingly unrelated systems would be visible, one measured
in values and the other in prices. Price and profit could not be
assessed in the former, and value and surplus value would be
absent in the latter; their mutual relationship would be invisible.
In contrast, if we follow Marx and abstract from the value of
the MP, the dichotomy is broken and the change in the level of
abstraction can be ‘seen’ through the shift of surplus value across
the industries.
In other words, the abstraction from the value of the MP
reveals the process of distribution of surplus value and the
ensuing determination of prices of production, regardless of the
systematic modification of the exchange ratios brought about by
the transformation. In addition, it nets out the effect of the
transformation of the value of the money-commodity, that would
complicate further the relationship between values and prices and
obscure the concepts being introduced (see K/III: 142). To sum
up, there are three reasons why the price vector cannot be calculated
from Marx’s transformation procedure: (a) because Marx works
with the price of production of the mass of commodities
produced per £ l advanced, and not unit prices; (b) because he
abstracts from the transformation of input values, and (c) because
he abstracts from the transformation of the value of the money-
commodity.11
The Transformation ‘Problem’ 125
Section 5.
It follows that the age-old objection that Marx’s transforma-
tion is wrong because he failed to transform the value of the
inputs is beside the point. For, if the value of the MP is immaterial
in the transformation, their (changing) level cannot affect the
result. The same argument can be used to dismiss the critique that
Marx ‘forgot’ to transform the value of the money-commodity (or
was mathematically incompetent to handle this problem), or
that he ‘unwarrantedly’ failed to define the problem in terms of
unit values and unit prices of production.
Marx’s procedure is adequate for the derivation of the concept
of price of production (although not for its calculation), because
it separates cause (the performance of labour in production and
exploitation through the extraction of surplus value) from effect
(the existence of a positive rate of profit, which tends to be
equalized across branches). When the concept of price of
production is introduced, Marx’s analysis reaches a more
complex level; the second stage of the transformation may then
be analysed. When the realm of the OCC is superseded and the
prices (no longer values) of the MP and LP enter into the picture,
there are two reasons why the price of the commodity may be
different from its value:
1) because the average profit is added to the cost price of a
commodity, instead of the surplus-value contained in it;
2) because the price of production of a commodity that diverges
in this way from its value enters as an element into the cost price
of other commodities, which means that a divergence from the
value of the means of production consumed may already be
contained in the cost price, quite apart from the divergence that
may arise for the community itself from the difference between
average profit and surplus-value. (K/III: 308-9)12
This change in the point of view, from the conceptual derivation
of price to the study of the economy at the level of price, leads to the
further determination of the concept of price of production,
concludes the transformation and signals a major step forward in
the analysis.13 Whilst the derivation of the concept of price
departs from the distribution of the surplus value produced in
abstraction from the value of the MP and LP, the calculation of the
price vector involves (as is well-known) the current price of the
inputs and the (price-) rate of profit.14 In sum, Marx’s method
involves not only the progressive transformation of some concepts
126 Capital & Class #63
into others, but also gradual shifts in the meaning of each concept,
whenever necessary to accommodate the evolution of the
analysis.15 Having done this, Marx can now claim that his prices
of production are:
the same thing that Adam Smith calls ‘natural price’, Ricardo
‘price of production’ or ‘cost of production’, and the Physiocrats
‘prix necessaire’, though none of these people explained the
difference between price of production and value … We can
also understand why those very economists who oppose the
determination of commodity value by labour-time … always
speak of prices of production as centres around which market
prices fluctuate. They can allow themselves this because the
price of production is already a completely externalized and
prima facie irrational form of commodity value, a form that
appears in competition and is therefore present in the
consciousness of the vulgar capitalist and consequently also in
that of the vulgar economist. (K/III: 300; see also p.268 and
K/I: 678-9).
The impact of the transformation on the structure of Capital is
two-fold; first, it explains why market exchanges are not directly
regulated by the labour time socially necessary to reproduce
each commodity; second, it shows that price is a relatively
complex form of social labour. The virtue of Marx’s approach, as
it has been outlined here, is that it accounts for both aspects of the
problem, even though it does not lend itself to the calculation of
unit prices or the general rate of profit. In the context of Capital,
Marx’s procedure is important because it develops further the
reconstruction in thought of the capitalist economy, and
substantiates the claim that living labour alone (and not the dead
labour represented by the value of the means of production)
creates (surplus) value.
In contrast, approaches that argue that the input values should
be taken into account from the start, and that they should be
transformed together with the output values, often conflate the
roles of living and dead labour in the production of value, and can
hardly distinguish between workers and machines in production.
It follows that the ‘non-transformation of the inputs’ cannot be
considered a defect; it is, rather, a feature of Marx’s method. By
abstracting from (changes in) the value of the inputs and the
money-commodity, Marx locates the source of profit in the
The Transformation ‘Problem’ 127
performance of labour in production, and carefully builds the
conditions in which circulation may be brought safely into the
analysis and add positively to its development.
Concluding Remarks
This article has shown that Marx’s presentation of the
transformation of value into price of production has two distinct
stages. In the first, he abstracts from (differences in) the value of
the means of production, to highlight the principle that value is
produced by labour alone. His unambiguous conclusion is that
the greater is the quantity of living labour put in motion, the
higher is the profit rate. The averaging out of these rates distributes
surplus value according to the size of each capital, and this forms
prices different from values. In the second stage, the economy is
analysed at the level of price; all commodities are sold at price, and
the input prices are taken into account. The role of transformation
is to allow a greater determination in the form of social labour, and
explain the distribution of labour and surplus value across the
economy.
The use of the organic composition of capital is essential to
distinguish these stages, because it helps to identify the cause of
the transformation, and describe the process that gives rise to
prices distinct from values. In addition, it shows that Marx’s
interest lies in the conceptual relationship between labour, price
and profit, and not the algebraic calculation of prices nor the rate
of profit. Moreover, it indicates that equilibrium (or simple
reproduction) assumptions are unwarranted in the study of the
transformation. It follows from Marx’s transformation that, even
though workers are exploited as they produce specific
commodities, the capitalist class as a whole (and not individual
capitalists) is the agent of exploitation, and the results are evenly
divided among its members. The reading of the transformation
outlined here shows that the presentation in Capital III is
consistent with Marx’s method, and is part of his reconstruction
of the main categories of the capitalist economy.
In contrast, the use of the value composition of capital in
the transformation would tend to conflate these stages, in which
case the process would collapse. The transformation would
appear to be the external relation between two contrasting
exchange value systems, one in which the exchange ratios are
128 Capital & Class #63
Section 6.
determined by the labour time socially necessary to produce the
commodities, and another where an equal (price-) rate of profit
prevails (similar criticisms can be found in Fine 1980, Kliman and
McGlone 1988, Moseley 1993b and Wolff, Roberts and Callari
1982, 1984). Because of the arbitrary separation of value from its
form of appearance, this type of approach may lead to irrational
relations between the value produced and its expression as price,
and/or between surplus value and its form of appearance as
profit.
Most of the literature has investigated the transformation
through the VCC. Whilst this is not in itself wrong, and may lead
to important theoretical developments, this approach has no
direct implications with respect to Marx’s own problem. The
various solutions to which this approach has led can be
distinguished from each other by the processes that they
contemplate, the relations that are put to the forefront, and the
treatment which is given to them (in other words, the nature
and form of the normalization condition adopted, the use of
interactions or simultaneous equations, etc). In my view, most
transformation procedures found in the literature are alternative
to Marx’s; they cannot claim to ‘correct’ the latter, because they
address different issues and conceive of the relation between
values and prices distinctly from Marx.
The inadequate understanding of Marx’s own transformation
procedure has often led to the complaint that he unwarrantedly
omitted the specification of the technologies of production or,
more often, that he did not transform the value of the inputs.16
This article demonstrates that these objections are misplaced,
because they emphasize issues that are not the primary object of
Marx’s concern in the transformation, and may obscure, rather
than reveal, the subject of his inquiry.
______________________________
I am grateful to Ben Fine, David Harvie, Costas Lapavitsas and John
Weeks for their helpful comments to previous versions of this paper. The
usual disclaimers apply.
______________________________
The Transformation ‘Problem’ 129
Acknowledgment
APPENDIX
Let us assume that there are n capitals in the economy and that
they produce m different commodities. Because of the
technologies adopted, capital ispends cij buying means of
production and employs Lij workers to produce quantity xij of
commodity j. If we assume that the workers are identical and that
the unit value of labour power is β, variable capital is:
(A.1)
In the aggregate, V = βL. The value of the mass of commodities
jproduced by capital iis:
(A.2)
where µjis the unit (money-)value of commodity j, kij is the
cost price, and sij is the surplus value extracted. In the aggregate,
M = C + V + S. The total surplus value is equal to:
=>
(A.3)
where m = (M–C)/L is the (money-)value produced per unit
time, which is constant across the economy. At the individual
level, sij = (m–β)Lij. From Marx’s definition and equations A.1
and A.3 the individual rate of profit is:
(A.4)
We can adjust the advanced capitals to the percent form
(k*=c
*ij +v
*ij =1,∀i,j) simply by defining:
(A.5)
From A.1 and A.5, the adjusted labour power, L*(labour power
hired per £1 advanced), can be determined as:
(A.6)
while the adjusted surplus value is:
(A.7)
130 Capital & Class #63
S = M–(C+V)=M–(C+βL)
S = – β L = (m–β) L
M–C
L
(
)
sij (m–β)Lij
rij = =
cij + vij cij + βLij
c*ij = cij /(cij + vij); v*ij = vij /(cij + vij)
Lij
L*
ij =
cij + βLij
s*ij = (m–β)L*
ij
µjxij = cij + vij + sij = kij + sij
vij = βLij
Equations A.4, A.6 and A.7 show that rij = s*ij This follows from
the definition of the profit rate as the surplus value extracted
per £1 advanced. However, A.7 is particularly useful because it
shows that the (adjusted) labour power purchased is an index of
the surplus value extracted and the rate of profit. This is why
Marx considered the percent form useful.
As the percent or adjusted form equalizes the size of all capitals,
the general adjusted rate of profit is different from the
nonadjusted or original rate:
(A.8)
(A.9)
where n is the number of capitals (in Marx’s case, five) and C*,
V*, S*and R*are totals for the entire economy. From A.2, the
value of the mass of commodities produced per £1 advanced is:
(A.2a)
while their price of production is:
(A.10)
Therefore, the output of every £1 of advanced capital has the same
price, regardless of the commodity produced. From A.10 it
follows that the total adjusted price, P*, is equal to the total
adjusted value, M*.(note 1)Moreover, the total adjusted profit, Π*,
is equal to the total adjusted surplus value, S*.(note 2)Hence,
Marx’s two aggregate equalities hold.
Finally, Marx insists that a capital with average OCC produces
commodities whose price equals their value; if the OCC is greater
(smaller) than the average, the price is also greater (smaller)
than the value (see K/III: 263–4). Moreover, the price vector is
equal to the value vector if the workers absorb all the net product
(in which case both surplus value and profit are nil). All these
conditions can be expressed in one equation. Subtracting A.2a
from A. 10 and using A.7,
(A.11)
The Transformation ‘Problem’131
S (m–β)L
R = =
C + V C + βL
µjx*ij = c*ij + v*ij + s*ij = 1+s*ij
pjx*ij = k*(1+R*) = k*+ = 1+
k*S* (m–β)L*
nk* n
L*
(pj – µj)x*ij = (m–β) n
(
)
– L*
ij
S* S* (m–β)L*
R*= =
C*+V* nk* n
=
A higher than average OCC means that fewer workers than
average are employed by capital i; thus, L*/n > Lij. In this case, it
necessarily follows that p j> µj. If the workers absorb all the net
product, m= βand, therefore, p j= µjwhatever the OCCs.
______________________________
1. By definition, M*= C*+ V*+ S*and C*+ V*= n. It follows that
M*=n+S
*= n + (m–β)L*, which is equal to the sum of the terms in
A.10 across the economy.
2. By definition, profit = sale price minus cost price. Hence, Π*= P*–(C*+V*)
= P*–n . From the definition of adjusted price in A.10 and summing up
across the economy (see note 1 above), Π*= (m –β)L*= S*.
______________________________
1. The literature on the transformation is vast, and there is no need nor space
for a survey in these pages. See, however, Desai (1989), Dostaler and
Lagueux (1985), Fine and Harris (1979), Freeman and Carchedi (1996),
Mohun (1991), Steedman (1981), and Sweezy (1949).
2. In this article, I refer to Capital (Marx 1976 [1867], 1981a [1894]) as K, and
to the Theories of Surplus Value (Marx 1969 [1959], 1972 [1962]) as TSV. All
italics in quotations are original, unless otherwise stated.
3. Clarke (1994) compares Marx’s thoughts on the composition of capital
with the relatively less developed approach of Ricardo.
4. ‘In the case of capitals of equal size … the organic composition may be the
same in different spheres of production, but the value ratio of the primary
component parts of constant and variable capital may be different according
to the different values of the amount of instruments and raw materials
used. For example, copper instead of iron, iron instead of lead, wool instead
of cotton, etc.’ (TSV/III: 386; emphasis omitted; see also p.387 and
TSV/II: 289). In K/III: 244 Marx says: ‘[I]t is possible for the proportion [the
TCC] to be the same in different branches of industry only in so far as
variable capital serves simply as an index of labour-power, and constant
capital as an index of the volume of means of production that labour-
power sets in motion. Certain operations in copper or iron, for example, may
involve the same proportion between labour-power and means of
production. But because copper is dearer than iron, the value relationship
between variable and constant capital will be different in each case, and so
therefore will the value composition of the two capitals taken as a whole.’
Marx discusses the opposite situation, in which capitals with different
TCCs and OCCs have equal VCCs, in K/III: 50–51 and pp.900–01.
5. Ben Fine (1983: 522) was the first to point out this essential feature of
Marx’s transformation: ‘Because Marx discusses the transformation problem
in terms of the organic composition he is concerned with the following
132 Capital & Class #63
Notes to the Appendix
Notes
problem: what is the effect on prices of differences across sectors in the
quantities of raw materials worked up into commodities irrespective of
the value of those raw materials? The transformation problem as traditionally
concerned would wish to take account of differences in the values of raw
materials. Usually, following on from this, account is also taken of the
differences in the prices of raw materials (which differ from the differing
values).’ Fine concludes (p.523) that ‘Marx did not get wrong the problem
that he posed, although it differs from the one which he is presumed to have
failed to solve.’
6. ‘When the rate of surplus-value … is given, the amount of surplus-value
depends on the organic composition of the capital, that is to say, on the
number of workers which a capital of given value, for instance £100,
employs.’ (TSV/II: 376)
7. ‘The rate of surplus value exists as a social aggregate, independently of
any particular industry. This follows from the social nature of the value of
labour power, so that it is incorrect to conceive of the rate of surplus value
varying across industries and the aggregate to be a mere weighted average
of rates in different industries’ (Weeks 1981: 170).
8. See K/III: 264. This conclusion holds as long as the sum of variable plus
circulating constant capital is equal in all sectors. It lends support to the
argument that the OCC (that does not distinguish between the fixed and
circulating parts of constant capital, not between paid and unpaid labour)
is the pivot of the transformation, instead of the VCC (where only circulating
constant capital and paid labour are influential).
9. Marx was aware of this limitation: ‘In our previous illustration of the
formation of the general rate of profit, every capital in every sphere of
production was taken as 100, and we did this in order to make clear the
percentage differences in the rates of profit and hence also the differences
in the values of the commodities that are produced by capitals of equal size.
It should be understood, however, that the actual masses of surplus-value
that are produced in each particular sphere of production depend on the
magnitude of the capitals applied … [I]t is evident that the average profit
per 100 units of social capital, and hence the average or general rate of
profit, will vary greatly according to the respective magnitudes of the
capitals invested in the various spheres.’ (K/III: 261–2)
10. This has been recognized by the more careful interpreters of Marx. Schefold
(1994: 8), for example, rightly argues that ‘[w]ages, interest and rent appear
as the revenues derived from the supply of labour, capital and land, justified
by work and abstinence, but they are revealed [by Marx] to derive all from
labour and its exploitation through a chain of transformations in which the
substance of a deeper layer takes forms closer to the surface: the value of labour
power takes the form of the wage, the surplus value that of profit etc.’
(emphasis added).
11. See Mattick, Jr. (1991–92: 51–52). Lack of understanding of these features of
Marx’s approach is partly responsible for the results obtained by trans-
formation procedures that follow Bortkiewicz (1949 [1907], 1952 [1906–7]).
For a critique, see the contributions in Freeman and Carchedi (1996).
The Transformation ‘Problem’133
12. By the same token the cost price, previously equal to the value of the inputs,
is now their price: ‘It was originally assumed that the cost price of a
commodity equalled the value of the commodities consumed in its
production. But … [as] the price of production of a commodity can diverge
from its value, so the cost price of a commodity, in which the price of
production of others commodities is involved, can also stand above or
below the portion of its total value that is formed by the value of the means
of production going into it. It is necessary to bear in mind this modified
significance of the cost price, and therefore to bear in mind too that if the cost
price of a commodity is equated with the value of the means of production
used up in producing it, it is always possible to go wrong.’ (K/III: 264–5; see
also pp.1008–10, TSV/III: 167–8, Mattick, Jr. 1991–2: 47–51, Moseley
1993b: 168, and Yaffe 1974: 46).
13. ‘It is of the essence of dialectical theories that simple and abstract determina-
tions (prices proportional to values) lead to more complex and concrete ones
(prices that are not so proportional) that cannot be simply reduced to the
former.’ (Smith 1990: 167). The (changing) meaning of concepts in
dialectical theory is discussed in Arthur (n.d.), Engels’ Preface to K/III,
Murray (1988; 1993) and Shamsavari (1991).
14. Whether or not this is a limitation of Marx’s procedure depends on one’s
judgement of the purpose of the exercise and the theoretical status of value.
These issues have been debated at length and need not be considered here
(see, however, Elson 1979 and Steedman 1981). The calculation of the
(price-) rate of profit and the price vector is not discussed here either, but
it is well-known that it can be made without reference to value (which, of
course, does not mean that the concept of value is either irrelevant or wrong;
see K/III: 259–65, 308–09 and 990–920, Dumenil 1980, and Fine 1980).
15. The concepts of price of production and general rate of profit are modified
again when Marx discusses commercial capital: ‘Commercial capital thus
contributes to the formation of the general rate of profit according to the
proportion it forms in the total capital … We thus obtain a stricter and more
accurate definition of the production price. By price of production we still
understand, as before, the price of the commodity as equal to its cost (i.e.
the value of the constant and variable capital it contains) plus the average
profit on this. But this average profit is now determined differently. It is
determined by the … total productive and commercial capital together
… The real value or production price of the total commodity capital is
therefore k+p+m (where m is commercial profit). The price of production,
i.e. the price at which the industrial capitalist sells as such, is therefore
less than the real production price of the commodity; or, if we consider all
commodities together, the price at which the industrial capitalist class sells
them is less than their value … In future we shall keep the expression “price
of production” for the more exact sense just developed.’ (K/III: 398–99;
emphasis added)
16. See, for example, Bortkiewicz 1949 [1907]: 201 and 1952 [1906–07]: 9,
Desai 1989, Dobb 1967: 532–3, Dumenil 1980: 8, 22–23, 51, Lipietz 1982: 64,
Sweezy 1949: xxiv and 1968 [1942]: 115, and de Vroey 1982: 47.
134 Capital & Class #63
Arthur, Chris (n.d.) The Subsumption of Labour Under Capital. Unpublished
Manuscript.
Bohm-Bawerk, Eugen von (1949 [1896]) ‘Karl Marx and the Close of His
System.’ In P.M. Sweezy (ed.) Karl Marx and the Close of His System. A.M.
Kelley, Clifton.
Bortkiewicz, Ladislaus von (1949 [1907]) ‘On the Correction of Marx’s
Fundamental Theoretical Construction on the Third Volume of Capital.’ In
P.M. Sweezy (ed.) Karl Marx and the Close of His System. A.M. Kelley,
Clifton.
__________ (1952 [1906–07]) ‘Values and Prices in the Marxian System.’
International Economic Papers 2: 5–60.
Burkett, Paul (1986) ‘A Note on Competition under Capitalism.’ Capital&Class 30,
Winter: 192–208.
Clarke, Simon (1994) Marx’s Theory of Crisis. Macmillan, London.
Desai, Meghnad (1989) ‘The Transformation Problem.’ Journal of Economic
Surveys 2 (4): 295–333.
Dobb, Maurice (1967) Marx’s ‘Capital’ and Its Place in Economic Thought.
Science & Society 31 (4): 527–540.
Dostaler, Gilles and Maurice Lagueux (1985) Un Echiquier Centenaire: Theorie
de la Valeur et Formation des Prix. La Decouverte, Paris.
Dumenil, Gerard (1980) De la Valeur aux Prix de Production. Economica, Paris.
Elson, Diane (1979) ‘The Value Theory of Labour’. In Value: The Representation
of Labour in Capitalism. CSE Books, London.
Fine, Ben (1980) Economic Theory and Ideology. Edward Arnold, London.
__________ (1983) ‘A Dissenting Note on the Transformation Problem.’
Economy & Society 12 (4): 520–525.
__________ (1992) ‘On the Falling Rate of Profit’. In G.A. Caravale (ed.) Marx
and Modern Economic Analysis 2 Vols. Edward Elgar, Aldershot.
Fine, Ben and Laurence Harris (1979) Rereading Capital. Macmillan, London.
Foley, Duncan (1982) ‘The Value of Money, the Value of Labour Power and the
Marxian Transformation Problem.’ Review of Radical Political Economics
14 (2): 37–47.
Freeman, Alan and Guglielmo Carchedi (eds.) (1996) Marx and Non-Equilibrium
Economics. Edward Elgar, Aldershot.
Kliman, A. and T. McGlone (1988) ‘The Transformation non- Problem and
the non-Transformation Problem.’ Capital&Class 35, Summer: 56–83.
Lipietz, Alain (1982) ‘The So-Called “Transformation Problem” Revisited.’
Journal of Economic Theory 26 (1), January: 59–88.
Marx, Karl (1969 [1959], 1972 [1962]) Theories of Surplus Value, Vols.II and III.
Lawrence & Wishart, London.
__________ (1976 [1867], 1981a [1894]) Capital, Vols.I and III. Penguin,
Harmondsworth.
__________ (1981b [1953]) Grundrisse. Penguin, Harmondsworth.
Mattick, Paul Jr. (1991–92) ‘Some Aspects of the Value-Price Problem.’
International Journal of Political Economy 21 (4), Winter: 9–66.
Mohun, Simon (1991) ‘The Context of the Transformation Problem’. In Paul
Dunne (ed.) Quantitative Marxism. Polity Press, Cambridge.
The Transformation ‘Problem’135
References
Moseley, Fred (ed.) (1993a) Marx’s Method in ‘Capital’: A Reexamination.
Humanities Press, Atlantic Highlands, N.J.
__________ (1993b)‘Marx’s Logical Method and the “Transformation
Problem” ’. Marx’s Method in ‘Capital’: A Reexamination. Humanities
Press, Atlantic Highlands, N.J.
Murray, Patrick (1988) Marx’s Theory of Scientific Knowledge. Humanities
Press, Atlantic Highlands, N.J.
__________ (1993) ‘The Necessity of Money: How Hegel Helped Marx Surpass
Ricardo’s Theory of Value’. In F. Moseley (ed.) Marx’s Method in ‘Capital’:
A Reexamination. Humanities Press, Atlantic Highlands, N.J.
Rosdolsky, Roman (1977 [1968]) The Making of Marx’s ‘Capital’. Pluto Press,
London.
Saad-Filho, Alfredo (1993a) ‘Labour, Money and “Labour-Money”: a Review of
Marx’s Critique of John Gray’s Monetary Analysis.’ History of Political
Economy 25 (1), Spring: 65–84.
__________ (1993b) A Note on Marx’s Analysis of the Composition of Capital.
Capital&Class 50 Summer: 127–46.
Samuelson, Paul M. (1957) ‘Wages and Interest: A Modern Dissection of
Marxian Economic Models.’ American Economic Review 47 (6), December:
884–912.
__________ (1971) ‘Understanding the Marxian Notion of Exploitation: A
Summary of the So-Called Transformation Problem Between Marxian
Values and Competitive Prices.’ Journal of Economic Literature 9 (2): 399–431.
Schefold, Bertram (1994) The Relation between the Rate of Profit and the Rate
of Interest. Unpublished manuscript.
Shamsavari, Ali (1991) Dialectic and Social Theory: The Logic of ‘Capital’.
Merlin Press, Braunton.
Smith, Tony (1990) The Logic of Marx’s ‘Capital’: Reply to Hegelian Criticisms.
State of New York Press, Albany.
Steedman, Ian (1977) Marx after Sraffa. New Left Books, London.
__________ (ed.) (1981) The Value Controversy. Verso, London.
Sweezy, Paul M. (ed.) (1949) ‘Editor’s Introduction.’ Karl Marx and the Close of
His System. A.M. Kelley, Clifton.
__________ (1968 [1942]) The Theory of Capitalist Development. Monthly
Review Press, New York.
Vroey, Michel de (1982) ‘On the Obsolescence of the Marxian Theory of Value:
a Critical Review.’ Capital&Class 17, Summer: 34–59.
Weeks, John (1981) Capital and Exploitation.Princeton University Press, Princeton.
Wolff, R., B. Roberts and A. Callari (1982) ‘Marx’s (not Ricardo’s) Transforma-
tion Problem: A Radical Reconceptualization.’ History of Political Economy
14 (4): 564–582.
__________ (1984) ‘A Marxian Alternative to the Traditional “Transformation
Problem”’. Review of Radical Political Economics 16 (2–3): 115–35.
Yaffe, David (1974) ‘Value and Price in Marx’s Capital.’ Revolutionary
Communist 1, May: 31–49.
______________________________
136 Capital & Class #63
