NationMaster - Encyclopedia: Transformation problem

In Karl Marx's economics the transformation problem is the problem of finding a general rule to transform the "values" of commodities (based on labour according to his labour theory of value) into the "competitive prices" of the marketplace. This problem was first introduced by Marx himself in Chapter 9 of Capital's draft Volume III, where he also tried to solve it. The essential difficulty was this: given that he derived profit ("surplus value") from direct labour inputs and that the amount of direct labour input varied widely between commodities, how could he explain the tendency to an average rate profit? Marxism refers to the philosophy and social theory based on Karl Marxs work on one hand, and to the political practice based on Marxist theory on the other hand (namely, parts of the First International during Marxs time, communist parties and later states). ... This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... In Marxs early writings, alienation (Entfremdung in German) refers to the separation of things that naturally belong together, or to antagonism between things that are properly in harmony. ... Bourgeoisie (RP [], GA []) refers to a group of people whose social and political opinions are determined primarily by concern for property values and personal appearance of wealth. ... Class consciousness is a category of Marxist theory, referring to the self-awareness of a social class, its capacity to act in its own rational interests, or measuring the extent to which an individual is conscious of the historical tasks their class (or class allegiance) sets for them. ... In Marxist theory, commodity fetishism is an inauthentic state of social relations, said to arise in complex capitalist market systems, where social relationships are confused with their medium, the commodity. ... This article is about communism as a form of society and as a political movement. ... Cultural hegemony is a concept coined by Marxist philosopher Antonio Gramsci. ... The term exploitation may carry two distinct meanings: The act of utilizing something for any purpose. ... Marxs theory of human nature occupies an important place in his critique of capitalism, his conception of communism, and his materialist conception of history. Marx has sometimes been held to deny the existence of any human nature, though this view is now generally accepted to be mistaken. ... An ideology is an organized collection of ideas. ... The proletariat (from Latin proles, offspring) is a term used to identify a lower social class; a member of such a class is proletarian. ... Reification (German: Verdinglichung, literally: ver-, over + ding: thing + -lichung: as english, -ify) is the consideration of an abstraction or an object as if it had human or living existence and abilities; at the same time it implies the thingification of social relations. ... Relations of production (German: Produktionsverhaltnisse) is a concept frequently used by Karl Marx in his theory of historical materialism and in Das Kapital. ... Socialism refers to a broad array of doctrines or political movements that envisage a socio-economic system in which property and the distribution of wealth are subject to social control. ... â€˜Young Marxâ€™ is one half of the concept in Marxology that Karl Marxâ€™s intellectual development can be broken into two board categories, the other being â€˜Mature Marxâ€™. There is disagreement though as to when Marx thought began to mature, Lenin claimed Marxs first mature work as â€œThe Poverty... Note: Marxian is not restricted to Marxian economics, as it includes those inspired by Marxs works who do not identify with Marxism as a political ideology. ... Note: Marxian is not restricted to Marxian economics, as it includes those inspired by Marxs works who do not identify with Marxism as a political ideology. ... Commodity is a term with distinct meanings in both business and in Marxian political economy. ... Labor power (in German: Arbeitskraft, or labor force) is a crucial concept used by Karl Marx in his critique of political economy. ... The law of value is a concept in Karl Marxs critique of political economy. ... Means of production (abbreviated MoP; German: Produktionsmittel), also called means of labour are the materials, tools and other instruments used by workers to make products. ... In the writings of Karl Marx and the Marxist theory of historical materialism, a mode of production (in German: Produktionsweise, meaning the way of producing) is a specific combination of: productive forces: these include human labor-power, tools, equipment, buildings and technologies, materials, and improved land social and technical relations... For the specific theoretical justifications behind the Great Leap Forward and the Five Year Plans, see Theory of Productive Forces. ... Surplus labour is a concept used by Karl Marx in his critique of political economy. ... Surplus value, according to Marxism, is unpaid labour that is extracted from the worker by the capitalist, and serves as the basis for capitalist accumulation. ... Wage labour is the socioeconomic relationship between a worker and an employer in which the worker sells their labour under a contract (employment), and the employer buys it, often in a labour market. ... The capitalist mode of production is a concept in Karl Marxâ€™s critique of political economy. ... Class struggle is class conflict looked at from a Marxist, libertarian socialist, or anarchist perspective. ... The dictatorship of the proletariat is a term employed by Karl Marx in his 1875 Critique of the Gotha Program that refers to a transition period between capitalist and communist society in which the state can be nothing but the revolutionary dictatorship of the proletariat. The term refers to a... Primitive accumulation of capital is a concept introduced by Karl Marx in part 8 of the first volume of Das Kapital (in German: ursprungliche Akkumulation, literally original accumulation or primeval accumulation). Its purpose is to help explain how the capitalist mode of production can come into being. ... A communist revolution is a social revolution inspired by the ideas of Marxism that aims to replace capitalism with communism, normally with socialism (public ownership over the means of production) as an intermediate stage. ... International Socialism redirects here. ... World revolution is a Marxist concept of a violent overthrow of capitalism that would take place in all countries, although not necessarily simultaneously. ... See also Marxian economics Marxist philosophy or Marxist theory designs work in philosophy which is strongly influenced by Karl Marxs materialist approach to theory or which is written by Marxists. ... See also Marxian economics Marxist philosophy or Marxist theory designs work in philosophy which is strongly influenced by Karl Marxs materialist approach to theory or which is written by Marxists. ... Historical materialism is the methodological approach to the study of society, economics and history which was first articulated by Karl Marx (1818-1883), although Marx himself never used the term. ... It has been suggested that Marxist philosophy of nature be merged into this article or section. ... Analytical Marxism refers to a style of thinking about Marxism that was prominent amongst English-speaking philosophers and social scientists during the 1980s. ... For other meanings of autonomism, see autonomism (disambiguation) page Raised fist, stenciled protest symbol of Autonome at the Ernst-Kirchweger-Haus in Vienna, Austria Autonomism refers to a set of left-wing political and social movements and theories close to the socialist movement. ... Marxist feminism is a sub-type of feminist theory which focuses on the dismantling of capitalism as a way to liberate women and states that capitalism, which gives rise to economic inequality, dependence, political confusion and ultimately unhealthy social relations between men and women, is the root of womens... The term Marxist humanism has as its foundation Marxs conception of the alienation of the labourer as he advances it in his Economic and Philosophic Manuscripts of 1844--an alienation that is born of a capitalist system in which the worker no longer functions as (what Marx terms) a... Structural Marxism was an approach to Marxist philosophy primarily associated with the work of the French philosopher Louis Althusser, although the thought of Lucien Goldmann is sometimes seen as a precursor. ... Western Marxism is a term used to describe a wide variety of Marxist theoreticians based in Western and Central Europe (and more recently North America), in contrast with philosophy in the Soviet Union. ... Karl Heinrich Marx (May 5, 1818, Trier, Germany â€“ March 14, 1883, London) was a German philosopher, political economist, and revolutionary. ... Friedrich Engels (November 28, 1820, Wuppertal â€“ August 5, 1895, London), a 19th-century German political philosopher, developed communist theory alongside his better-known collaborator, Karl Marx, co-authoring The Communist Manifesto (1848). ... Karl Kautsky (October 18, 1854 - October 17, 1938) was a leading theoretician of social democracy. ... Lenin redirects here. ... Note: This page is very long. ... Rosa Luxemburg Rosa Luxemburg (March 5, 1870 or 1871 â€“ January 15, 1919, in Polish RÃ³Å¼a Luksemburg) was a Polish-born German Marxist political theorist, socialist philosopher, and revolutionary. ... This article does not cite its references or sources. ... Georg LukÃ¡cs (April 13, 1885 â€“ June 4, 1971) was a Hungarian Marxist philosopher and literary critic in the tradition of Western Marxism. ... Antonio Gramsci (IPA: ) (January 22, 1891 â€“ April 27, 1937) was an Italian writer, politician and political theorist. ... Karl Korsch (1886 - 1961) was born in Todstedt, near Hamburg, to the family of a middle-ranking bank official. ... Max Horkheimer (front left), Theodor Adorno (front right), and JÃ¼rgen Habermas in the background, right, in 1965 at Heidelberg The Frankfurt School is a school of neo-Marxist social theory (which is more akin to anarchism than communism), social research, and philosophy. ... Louis Pierre Althusser (Pronunciation: altuË¡seÊ) (October 16, 1918 - October 23, 1990) was a Marxist philosopher. ... This article is on criticisms of Marxism, a branch of socialism. ... Karl Heinrich Marx (May 5, 1818, Trier, Germany â€“ March 14, 1883, London) was a German philosopher, political economist, and revolutionary. ... Face-to-face trading interactions on the New York Stock Exchange trading floor Economics is the social science that studies the production, distribution, and consumption of valuable goods and services. ... The labor theory of value (LTV) is a theory in economics and political economy concerning a market-oriented society: the theory equates the value of an exchangeable good or service (i. ... Das Kapital (Capital, in the English translation) is a very lengthy treatise on political economy written by Karl Marx in German. ...

Overview

The production of any commodity generally requires both labour and some produced means of production (or capital goods), like tools and materials. The amount of labour so required is called the direct labour input into the commodity. But also the required capital goods have in their turn been produced (in the past) by labour and other capital goods; and so on for these other capital goods, and so on. The sum of all the amounts of labour, that were direct inputs into this backwards-stretching series of capital goods produced in the past, is called the indirect labour input into the commodity. Putting together the direct and indirect labour inputs, one finally gets the total labour input into the commodity, which may also be called the total amount of labour "embodied" in it, or its direct and indirect labour contents.

Now, according to Chapter I of Capital's Volume I, the Marxian "value" of a commodity is defined as its total amount of embodied labour. On the other hand, the (relative) "competitive price" of the same commodity is the ratio at which it is exchanged with other commodities in a competitive market system, and this ratio tends to be given by its relative cost of production. The transformation problem, studied by Marx in Chapter 9 of Capital's Volume III through a set of numerical examples, is hence the problem of finding a set of functions that transform the ratios between amounts of embodied labour into such relative prices.

However, it has been shown by mathematical economists that a similar set of functions does not generally exist, so that Chapter 9's transformation problem has formally no solution, outside two classes of very special cases. This was first pointed out long ago by, among others, Böhm-Bawerk (1896) and Bortkiewicz (1906). But it was only in the second half of the twentieth century that Leontief’s and Sraffa’s work on linear production models provided a framework within which to prove this result in a simple and general way. Eugen von BÃ¶hm-Bawerk Eugen von BÃ¶hm-Bawerk (February 12, 1851 â€“ August 27, 1914) made important contributions to the development of Austrian economics. ... Ladislaus Josephovich Bortkiewicz (August 7, 1868 - July 15, 1931) was a Russian economist and statistician of Polish descent. ... Wassily Leontief (August 5, 1905, Munich, Germany â€“ February 5, 1999, New York)[1], was an economist notable for his research on how changes in one economic sector may have an effect on other sectors. ... Piero Sraffa. ...

Although he never actually mentioned the transformation problem, Sraffa’s (1960) Chapter VI on the "reduction" of prices to "dated" amounts of current and past embodied labour gave implicitly the first general proof, showing that the competitive price

P i

of the

i - t h

produced good can be expressed as

where

n

is the time lag,

l i n

is the lagged-labour input coefficient,

w

is the wage and

r

is the "profit" (or net return) rate. Since total embodied labour is defined as

it follows from Sraffa’s result that there is generally no function from

E i

P i

, as was made explicit and elaborated upon by later writers.

The standard reference – with an extensive survey of this entire literature and a comprehensive bibliography – is now Samuelson's (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. Paul Anthony Samuelson Paul A. Samuelson (born May 15, 1915, in Gary, Indiana) is an American economist known for his work in many fields of economics. ...

The lack of any function from Marx's "values" to competitive prices may have important implications for Marx's theory of labour exploitation and economic dynamics. While the modern mathematical proof that Marx's transformation problem has no general solution has never been formally questioned (though some of its interpretive assumptions have been debated [1]), some Marxist authors have refused to accept it, for reasons that will be surveyed below. Others accept the proof, but reject its relevance for some key elements of Marxian political economy. Still others reject Marxian economics outright, and emphasise the politics of the assumed relations of production instead. To such an extent, the transformation problem—or rather its implications—is still today a controversial question. The term exploitation may carry two distinct meanings: The act of utilizing something for any purpose. ... Most generally, the accumulation of capital refers simply to the gathering or amassment of objects of value; the increase in wealth; or the creation of wealth. ... Relations of production (German: Produktionsverhaltnisse) is a concept frequently used by Karl Marx in his theory of historical materialism and in Das Kapital. ...

This article uses a very simplified linear production model to survey Marx's labour theory of value, starting from its precursors in British classical economics. It then offers a simple proof of the general lack of solution for the transformation problem, highlighting Marx's formal error in his attempt to find one. Finally, it summarizes some possible implications of this result, as Marxists and non-Marxists see them. The labor theory of value (LTV) is a theory in economics and political economy concerning a market-oriented society: the theory equates the value of an exchangeable good or service (i. ... Face-to-face trading interactions on the New York Stock Exchange trading floor Economics is the social science that studies the production, distribution, and consumption of valuable goods and services. ...

British classical labour theory of value

Marx's value theory was developed from the labour theory of value discussed by Adam Smith and used by many British classical economists. It became central to his economics. The labor theory of value (LTV) is a theory in economics and political economy concerning a market-oriented society: the theory equates the value of an exchangeable good or service (i. ... For other persons named Adam Smith, see Adam Smith (disambiguation). ... Classical economics is a school of economic thought whose major developers include William Petty, Adam Smith, David Ricardo, and John Stuart Mill. ...

Simplest case: labour costs only

Consider the very simple example used by Adam Smith to introduce the subject. Assume a hunters’ economy with free land, no slavery and no significant current production of tools, where beavers

(B)

and deer

(D)

are hunted. In the language of modern linear production models, call the unit labour-input requirement for the production of each good

l i

, where

i

may be

B

D

(i.e.,

l i

is the number of hours of uniform labour normally required to catch either a beaver or a deer; notice that we need to assume labour as uniform in order to be able, later on, to use a uniform wage rate).

Then—Smith noticed—each hunter will be willing to exchange one deer (which costs him

l D

hours) for ${l_D over l_B}$ beavers. The ratio ${l_D over l_B}$ —i.e. the relative amount of labour embodied in (unit) deer production with respect to beaver—gives thus the exchange ratio between deer and beavers, the "relative price" of deer in units of beavers. Moreover, since the only costs are here labour costs, that ratio is also the "relative unit cost" of deer for any given competitive uniform wage rate

w

. Hence the relative amount of labour embodied in deer production coincides with the competitive relative price of deer in units of beavers, which can be written as ${P_D over P_B}$ (where the

P

stands for absolute competitive prices in some arbitrary unit of account, and are defined as

P i = w l i

Capital costs

Things get less simple if production uses some scarce capital good as well. Suppose that hunting requires also some arrows

(A)

, with input coefficients equal to

a i

, meaning that to catch for instance one beaver you need to use

a B

arrows, besides

l B

hours of labour. Now the unit total cost (or absolute competitive price) of beavers and deer becomes: Capital goods, in contrast to consumer goods, are goods used in the production of (physical) capital. ...

Now, this capital cost is made up of two parts. First, there is the replacement cost of substituting the arrow when it is lost in production. This is

P A

, or the competitive price of the arrows, times the proportion $h le 1$ of arrows lost after each shot. Second, there is the net rental or return required by the arrows' owner (who might or might not be the same person as the hunter using it). This can be expressed as the product

r P A

, where

r

is the (uniform) net rate of return of the system.

Summing up, and assuming a uniform replacement rate

h

, the absolute competitive prices of beavers and deer may be written as:

Yet, we still have to determine the arrows' competitive price

P A

. Assuming arrows are produced by labour only, with

l A

man-hours per arrow, we have:

Assuming further for simplicity

h = 1

(all arrows are lost after just one shot, so that they are circulating capital), the absolute competitive prices of beavers and deer become: Circulating capital is a term used by classical economists such as David Ricardo and others such as Karl Marx. ...

Here

l i

is the amount of labour directly embodied in beaver and deer unit production, while

l A a i

is the labour indirectly thus embodied, through previous arrow production. The sum of the two,

It is now obvious that the relative competitive price of deer ${P_D over P_B}$ can no longer be generally expressed as the ratio between total amounts of labour embodied. With

a i > 0

the ratio ${E_D over E_B}$ will correspond to ${P_D over P_B}$ only in two very special cases: if either

r = 0

; or, if ${l_B over l_D} = {a_B over a_D}$ . In general the two ratios will not only differ: ${P_D over P_B}$ may change for any given ${E_D over E_B}$ , if the net rate of return or the wages vary.

As it will now be seen, this general lack of any functional relationship from ${E_D over E_B}$ to ${P_D over P_B}$ —of which Ricardo had been particularly well aware—is at the heart of Marx's transformation problem.

Marx’s labour theory of value

Labour as the "value-creating substance"

Marx defined the "value" of commodities as the total amount of socially necessary labour embodied in their production. He developed this special brand of the labour theory of value in the first Chapter of Capital's Volume I. Due to the influence of Marx's particular definition of value on the transformation problem, he is quoted at length where he argues as follows: The word commodity has a different meaning in business than in Marxian political economy. ...

However, contrary to popular belief, Marx did not deny the role of supply and demand influencing price:

It may be incidentally noticed that the uniform-labour assumption of modern linear production models makes their labour inputs quantitatively equivalent to amounts of Marx's "human labour in the abstract". The quantitative aspects of Marx's value and price theories—which include the transformation problem—can thus be expressed in the mathematical language of such models: see Samuelson (1971).

Surplus value and exploitation

Within the quantitative relationships relevant to the transformation problem, labour plays a twofold role according to Marx. First, labour is itself a commodity which is produced, exchanged and used as a means of production—labour is thus a kind of capital. The "labour value" of each unit of labour is the amount of labour embodied in the goods that make up the real subsistence wages rate. This amount of labour will be denoted here as

l W

(with

0 < l W < 1

in any viable system). In our previous example, the Marxian value of the direct-labour input required by unit beaver and deer production is thus

l W l i

. Like that of any other means of production (or capital), this value is entirely transmitted to the product. It has been suggested that this article or section be merged with Subsistence theory of wages. ...

However, this is not all. Being the "substance" of value, direct (or "living") current labour has for Marx the further property of creating and transmitting to the product a further amount of value, over and above its own. Formally, this property derives from the definition of value and the above assumption that

0 < l W < 1

: less than one unit of labour is embodied in the wage goods that pay for (or "produce", so to speak) one unit of labour. This extra value is called surplus value and denoted by

s

. The amount of surplus value created in unit beaver and deer production will be denoted here as

s i

. Surplus value, according to Marxism, is unpaid labour that is extracted from the worker by the capitalist, and serves as the basis for capitalist accumulation. ...

If the actual real wage is the subsistence wage used to calculate

l W

, all this surplus value created by labour will be received by the owners of the capital goods, called "capitalists". This is what Marx denoted as exploitation of labour. The term exploitation may carry two distinct meanings: The act of utilizing something for any purpose. ...

Variable and constant capital

As labour produces in this sense more than its own value, the direct-labour input is called variable capital and denoted as

v

. The amount of value which labour transmits to the deer in our previous example, varies according to the intensity of the exploitation. In our previous example one has

v i = l W l i

. Constant capital, or c, in Marxian political economy is one of the two forms that capital adopts in the workplace, in contrast to variable capital (v). ...

By contrast, the value of other inputs—in our example the indirect (or “dead”) past labour embodied in used up arrows—is transmitted to the product as it stands, without additions. It is hence called constant capital and denoted as c. The value transmitted by the arrow to the deer can never be greater than the value of the arrow itself. In our previous example one has

c i = l A a i

. Constant capital (c), is a concept created by Karl Marx and used in Marxian political economy. ...

Value formulas

The total value of each produced good is obtained as the sum of the above three elements: constant capital plus variable capital plus surplus value. In our previous example:

However, from the definition of Marxian value as total labour embodied it must also be true that:

This necessarily uniform ratio ${s_i over v_i} = sigma$ is called by Marx the rate of surplus value, and it allows to re-write Marx's value equations as:

Transformation of values into prices

Like Ricardo, Marx knew that relative labour values— ${p_D over p_B}$ in the above example—do not generally tally with relative competitive prices— ${P_D over P_B}$ in the same example. However, in the third volume of Capital he argued that competitive prices were obtained from his values through a transformation process, whereby capitalists redistributed among themselves the given aggregate surplus value of the system, in such a way as to bring about a uniform rate of return

r

on the capital goods they owned in all production lines. This happened because of the capitalists' tendency to shift their capital towards the sectors where it earned higher returns. Marx's attempt to give a detailed account of this process is found in chapter 9 of Volume III.

Marx's reasoning

The two following tables adapt the deer-beaver-arrow example already seen above (which, of course, is not found in Marx, and is only a useful simplification), to illustrate Marx's approach. In both cases it is assumed that the total quantities of beavers and deer captured are

Q B

and

Q D

respectively. It is also supposed that the subsistence real wage is one beaver per unit of labour, so that the amount of labour embodied in it is

l W = E B = l A a B + l B < 1

Table 1 shows how the total amount of surplus value of the system—in the last row—is determined.

Table 2 then illustrates how Marx thought that this total would be redistributed between the two industries, as “profit” at a uniform return rate r over constant capital. First, the condition that total “profit” must equal total surplus value – in the last row of table 2 – is used to determine r. The result is then multiplied by the value of the constant capital of each industry, to get its “profit”. Finally, each (absolute) competitive price in labour units is obtained, as the sum of constant capital, variable capital and “profit” per unit of output, in the last column of Table 2.

Marx's "error" and its correction

It was however soon pointed out that Marx's formulas for competitive prices were mistaken.

First, competitive equilibrium requires a uniform rate of return over constant capital valued at its price, not its Marxian value, contrary to what is done in Table 2 above. Secondly, competitive prices result from the sum of costs valued at the prices of things, not as amounts of embodied labour. Thus, both Marx's calculation of

r

and the sums of his price formulas do not add up in all the normal cases, where—as in the above example—relative competitive prices differ from relative Marxian values.

Indeed, the formally correct way to compute competitive (relative) prices is today very well known. In the greatly simplified model of Tables 1 and 2, where by assumption the wages rate is given and equal to the price of beavers, the most convenient way is to express such prices in units of beavers, which means normalising

w = P B = 1

. This immediately yields the (relative) price of arrows as

As the reader can check, this latter result, which gives the correct competitive price of deer in units of beavers for the overly simplified model used here, is generally inconsistent with Marx's price formulas of Table 2.

This discrepancy has, however, been alternatively explained as due to the time frame of production rather than a logical error, i.e. in this simplified model, capital goods are purchased at a labour value price but final products are sold under prices which reflect redistributed surplus value. On this view, price levels are set by a dynamic equilibrium which cannot be captured by a static mathematical formula.[2]

The non-transformation problem

Moreover, it is now easy to show that deer's relative embodied labour defined as $e_D={E_D over E_B}$ can vary, while at the same time the correctly defined relative price

P D

remains constant. This follows from the fact that in our simple model

e D

varies with

l A

while—as long as the real wage is given—

P D

does not. Thus any change in the labour input required by arrow production will affect the Marxian value of deer relative to beavers, but will leave the economic value of deer (i.e., its exchange rate with beavers) totally unaffected.

The diagram on the right shows this through a numerical example. All the input coefficients, bar

l A

, have been given arbitrary numerical values. The two curves show the numerical corresponding values of

P D

and

e D

(on the vertical axis), calculated as

l A

varies along the horizontal axis. As one can see,

P D

is a horizontal line, showing constancy, while

e D

is a falling curve. Image File history File links Diagram illustrating Marxian transformation problem File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...

This appears to prove that the competitive exchange ratio between deer and beavers has actually nothing to do with relative total embodied labour, contrary to the above-quoted claim by Marx in Capital's Volume I.

Formal conclusions

Samuelson's eraser algorithm

As it has been shown in the literature, the above result holds true in general, including the more complicated models that Marx actually used. In Samuelson’s (1971) words, this means that the "transformation" of Marxian values into competitive prices must generally take the form of an eraser algorithm, described as follows:

Special cases

The are just two very special cases where this is not true. The first and best known one is when no "transformation" is actually needed, because competitive prices and Marxian values happen to coincide to begin with. As already noticed, that is the case with either

r = 0

or (in the previous example) ${l_B over a_B} = {l_D over a_D}$ . In Marxian parlance, the latter condition is described as a uniform organic composition of capital in all production lines.

But there is also a second and less trivial case, unnoticed until relatively recent times. This is a development of Sraffa’s (1960) notion of "standard commodity", and has been called by Samuelson (1971) the case of "equal internal composition of (constant) capitals". It takes place when every production line happens to use all the various produced means of production (including the goods entering the real wage) in the same proportions among themselves. When this is so, the same proportions apply to both value and cost calculations. Marx's transformation procedure—based on value proportions—can then be rescued, as it produces the correct relative costs and competitive prices.

Yet, even when such very special conditions are met, prices can still be computed in the generally correct way, just based on information about input coefficients, with no need for any detour through Marxian values. Moreover, once prices have been thus directly determined, one can formally set up an inverse transformation process, whereby Marxian values are obtained from prices, rather than the other way round.

Implications and interpretations

The literature summarised above relates to the logical (mathematical) aspects of the transformation problem, as discussed by the numerical examples of Chapter 9 of Capital's Volume III. All the above formal conclusions have ceased to be controversial since more than a generation ago. To many, their upshot appears to be that – since under competitive capitalism prices are generally unrelated to the direct and indirect labour contents of individual commodities – Marx's "value" of Capital's Volume I, and its attendant notions of surplus value, surplus labour and exploitation, are a purely fictional construct, of no theoretical or practical usefulness.

Yet, some controversy still remains, as some Marxist theorists have tried in various ways to rescue Marx's system, or at least some parts of it, from this apparent logical failure.

Mathematical vs historical transformation

Frederick Engels – the editor of Capital's Volume III – hinted since 1894 at a possibly alternative way to look at the whole matter. His view was that the pure Marxian "law of value" of Volume I and the "transformed" prices of Volume III applied to different periods of economic history. In particular, the "law of value" would have prevailed in the pre-capitalist exchange economies – from Babylon to the fifteenth century of the common era – while the "transformed" prices would have materialized under capitalism: see Engels' quotation by Morishima and Catephores (1975) p. 310.

Although Engels was reasoning on the mistaken presumption that Marx's transformation was formally correct, his basic idea does not depend on this, and was later taken up by Meek (1956) and Nell (1973). These authors argued that – whatever one must say of his interpretation of capitalism – Marx's "value" theory keeps its usefulness as a tool to interpret pre-capitalist societies, because – they maintained – in pre-capitalist exchange economies there were no "prices of production" with a uniform rate of return (or "profit") on capital. It hence follows that Marx's transformation must have had a historical dimension, given by the actual transition to capitalist production (an no more Marxian "values") at the beginning of the modern era. Then this true "historical transformation" could and should take the place of the failed mathematical transformation attempted by Marx in Chapter 9 of Volume III.

As Althusser and Balibar (1970) and others have pointed out, this proposal runs counter Marx's own ideas, as expressed in Marx (1859), where one reads:

Moreover, the available quantitative research by economic historians has not generally endorsed Engels' view of antiquity and the Middle Ages as a "value epoch" in the Marxian sense: see for instance Hicks (1969) and Godelier (1973).

However, be that as it may, the proposed "historical" dimension of the transformation problem does not seem to affect in any way the (non-) applicability of Marx's notion of exploitation to contemporary capitalist societies.

Other Marxist views

Most interpretations of Marx's value theory consider it as an attempt to explain capitalist distribution as the result of labour exploitation, defined through the notion of surplus value. Yet, particularly if the wage is given, distribution is in itself determined by prices. Thus the transformation problem is central to the usefulness of Marx's economics in explaining exploitation, via a linkage from values (and hence surplus value) to prices. Indeed, no positive Marxian theory of labour exploitation through distribution could ever be built without some at least implicit reference to such linkage. Marx's reference was very explicit, and this is precisely why the transformation problem worried him so much.

However, there are also political-economic readings of Capital, such as Harry Cleaver's Reading Capital Politically, that re-define exploitation as a direct control of worked time, unrelated as such to distribution. These readings are usually associated with the autonomist strand of Marxism, which focuses on production as the key economic site within society. These readings of Capital are typically hostile to economics as such, and seek to side-step issues like the transformation problem by claiming that all social arrangements in capitalism (in particular, profit and distribution) are politically determined as contests between classes. Harry Cleaver is best known as the author of Reading Capital Politically, an autonomist reading of Karl Marxs Capital. ... Autonomism, or Autonomist Marxism is a left-wing political movement and theory. ...

Notice should also be taken of the probabilistic interpretation of Marx advanced by Emmanuel Farjoun and Moshe Machover in Laws of Chaos (see references). They "dissolve" the transformation problem by reconceptualising the relevant quantities as random variables. In particular, they drop the assumption of strict equalisation of profit rates and instead consider an equilibrium distribution of firm profit rates. A heuristic analogy with the statistical mechanics of an ideal gas leads them to the hypothesis that this equilibrium distribution should be a gamma distribution.

Finally, there are Marxist scholars (e.g. Anwar Shaikh, Fred Moseley, Alan Freeman, Makoto Itoh, Gerard Dumenil & Dominique Levy, Duncan Foley) who accept that there exists no incontestable logical procedure by which to derive price magnitudes from value magnitudes, but still think that it has no lethal consequences on his system as a whole, for the following reasons.

As it has just been seen, in a few very special cases, Marx's idea of labour as the "substance" of (exchangeable) value would not be openly at odds with the facts of market competitive equilibrium. These authors have argued that such cases—though admittedly not generally observed—throw light on the "hidden" or "pure" nature of capitalist society. Thus Marx's related notions of surplus value and unpaid labour can still be treated as basically true, although the practical details of their workings are admittedly much more complicated than Marx thought.

In particular, some (e.g. Anwar Shaikh) have suggested, following the explicit remarks by Marx and Engels, that—since aggregate surplus value will generally differ from aggregate "profit"—the former should be in fact treated as a mere pre-condition for the latter, rather than a full explanation of it. Using input-output data and empirical proxies for labour-values, Shaikh & Ochoa have provided some statistical evidence to show that, although there may be no incontestable logical deduction possible of specific price magnitudes from specific value magnitudes even within a complex model (in contrast to a probabilistic prediction), even a "93% Ricardian theory" of labour-value appears to be a better empirical predictor of price than its rivals. Real capitalism just seems to function much more like ordinary people, businessmen and accountants understand it, and much less like neo-classical economists insist on portraying it, whatever the beavers and deer happen to be doing. That is probably one reason why, rightly or wrongly, Marx's theory retains its plausibility for many people.

Mainstream views

Mainstream scholars question the assumption that the basic nature of capitalist production and distribution can be gleaned from unrealistic special cases. Moreover, from the fact that in all such special cases Marx's reasoning can be easily turned upside down, through an inverse transformation process, they argue that Marx's inference:

To further clarify this point, it may be noticed that the special cases in question are also precisely those where J.B. Clark’s old model of aggregate marginal productivity holds strictly true, leading to equality between the equilibrium levels of the real wage rate and labour's aggregate marginal product: see the neo-Ricardian disputes of the Sixties and Seventies. One would thus have a "pure" state of capitalist society where Marx's exploitation theory and its main supposed confutation were somehow both true. John Bates Clark John Bates Clark (26 January 1847 â€“ 21 March 1938) was an American neo-classical economist. ...

This remarkable result, it is maintained, leads straight to the heart of the matter. Like Clark’s contention about the "fairness" of marginal-productivity wages, so Marx's basic argument—from the "substance" of value to the concept of exploitation—is a set of non-analytical and non-empirical propositions. That is why, being non-falsifiable, both theories may be found to apply to the same formal and/or empirical object, though they are supposed to negate each other, as Karl Popper and many others had argued. Sir Karl Raimund Popper, CH, MA, Ph. ...

References

Encyclopedia > Transformation problem

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