The so-called transformation problem has to do with an apparent contradiction between Marx’s labor theory of value and the tendency of profit rates to equalize across industries. The labor theory of value, which assumes that labor is the source of both value and surplus value (or profit), seems to imply that “labor-intensive” industries would have a higher rate of profit than “capital-intensive” industries. Marx claimed to have resolved this apparent contradiction in Part 2 of Volume 3 of Capital with his theory of prices of production, which may be very briefly summarized as follows:
- The general rate of profit is determined by the ratio of the total surplus value to the total capital invested in the economy as a whole (R = S / [C + V ]) (in Volume 1 of Capital, the total surplus value is determined by the labor theory of value).
- The average profit in each industry is determined by the product of the general rate of profit and the capital invested in each industry (∏;i = R [Ci + Vi ]).
- The price of production for each industry is determined by the sum of the constant capital and variable capital in each industry and the average profit in each industry (PPi = Ci + Vi + ∏i ).
In this way, Marx claimed, each industry receives the same rate of profit in a way that is consistent with the labor theory of value.
A long-standing criticism of Marx’s theory of prices of production is that he “failed to transform the inputs” of constant capital and variable capital from values to prices of production. According to this interpretation, constant capital and variable capital are derived from given physical quantities of means of production and means of subsistence (they are first determined as the values of these groups of commodities in Volume 1, and then determined as their prices of production in Volume 3). The criticism is that Marx failed to make this transformation of constant capital and variable capital in Volume 3, but instead left these inputs in value terms. Marx’s theory is therefore logically incomplete and inconsistent: Output prices are prices of production, but input prices are values. It is further argued that Marx’s mistake can be corrected, using a method first suggested by Ladislaus von Bortkeiwicz in 1905 and popularized by Paul Sweezy in 1942, but this correction has damaging consequences for Marx’s theory. This is because Marx’s two aggregate equalities (total price of production = total value, and total profit = total surplus value) cannot both be true simultaneously, and because the rate of profit changes (so that the “value rate of profit” ≠ “price rate of profit”). These results mean that individual prices and profits are not merely the redistribution of aggregate amounts of value and surplus value, as Marx claimed. This alleged logical inconsistency has been the main reason for the rejection of Marx’s theory over the last century by mainstream economists and others. The Sraffian interpretation of Marx’s theory (Steedman 1977) has reinforced these criticisms.
Most Marxists have largely accepted these criticisms of Marx’s theory of prices of production (that he failed to transform the inputs, and that the two aggregate equalities cannot both be true at the same time), although they draw different conclusions. Marxists have generally argued that these are minor problems, requiring only minor modifications, and that they are not sufficient reason to reject Marx’s theory, especially when compared to mainstream theories of profit, which have much more serious logical problems and much less explanatory power.
Since the 1980s, there have been several new reinterpretations of the transformation problem that have provided stronger defenses of Marx’s theory. The best known and most influential of these new works on the transformation problem has been called the “new interpretation.” It was presented originally, and independently, by Duncan Foley in 1982 and Gerard Duménil in 1983 and 1984. The main innovation of the new interpretation is that it argues that variable capital is not derived from a given quantity of means of subsistence, but is instead taken as given, as the actual quantity of money capital advanced to purchase labor power in the real capitalist economy, and that this is equal to the price of production of the means of subsistence, not the value of the means of subsistence. Furthermore, this same quantity of variable capital is taken both in the theory of value and in the theory of prices of production. In other words, variable capital does not change in the transformation of values into prices of production. It follows from this interpretation of variable capital that total profit is always equal to total surplus value. The new interpretation also redefines the aggregate price equality in terms of the “net price” of commodities, rather than the “gross price,” and it assumes that this net-price equality is always true. Therefore, according to the new interpretation, both of Marx’s two aggregate equalities, redefined in this way, are always true simultaneously. However, the new interpretation continues to accept the standard interpretation of constant capital, so that constant capital changes in the transformation of values into prices of production, and Marx’s gross aggregate price equality is not satisfied (and the rate of profit also changes).
The “macro-monetary” interpretation presented by Fred Moseley in 2000 extends the new interpretation to constant capital as well as variable capital. Moseley argues that both variable capital and constant capital are taken as given, as the actual quantities of money capital advanced to purchase means of production and labor power in the real capitalist economy, and that these are equal to the price of production of the means of subsistence and the means of production, respectively. The crucial point is that these same quantities of constant capital and variable capital are taken as given in both the theory of value and the theory of prices of production. It follows from this interpretation of the initial givens in Marx’s theory that both of Marx’s two aggregate equalities are always true simultaneously, and also that the rate of profit does not change.
Similar interpretations have been presented by Richard Wolff, Antonio Callari, and Bruce Roberts (1984), and by Andrew Kliman and Ted McGlone (1988), although these interpretations are also different in some respects. It remains to be seen whether these recent reinterpretations will be accepted by the majority of Marxist economists and by the critics of Marx. But a new phase in the long debate has been opened up, which could lead to different conclusions concerning the logical consistency of Marx’s theory.
SEE ALSO Forces of Production; Labor Theory of Value; Value
Bortkiewicz, Ladislaus von.  1952. Value and Price in the Marxian System. International Economic Papers 2: 5–60.
Duménil, Gerard. 1983-1984. Beyond the Transformation Riddle: A Labor Theory of Value. Science and Society 47 (4):427–450.
Foley, Duncan. 1982. The Value of Money, the Value of Labor Power, and the Marxian Transformation Problem. Review of Radical Political Economics 14 (2): 37–49.
Kliman, Andrew, and Ted McGlone. 1988. The Transformation Non-Problem and the Non-Transformation Problem. Capital and Class 35.
Moseley, Fred. 2000. The “New Solution” to the Transformation Problem: A Sympathetic Critique. Review of Radical Political Economics 32 (2): 282–316.
Steedman, Ian. 1977. Marx after Sraffa. London: New Left Books.
Sweezy, Paul. 1942. Theory of Capitalist Development. Chapter 7. New York: Modern Reader Paperbacks.
Wolff, Richard, Antonio Callari, and Bruce Roberts. 1984. A Marxian Alternative to the Traditional “Transformation Problem.” Review of Radical Political Economics 16 (2–3): 115–135.