Transformation problem

In Marxian Economics, and Classical Economics the Transformation Problem refers to the transformation of values into prices of production. It poses the question whether prices of production (or natural prices) can be found for each class of commodity that allows a redistribution of surplus value among producing enterprises to form an equal rate of profit among them. Proponents and opponents both typically understand this transformation problem as proving or disproving whether surplus labor alone is the source of total industrial profit. The profits of any particular industrial enterprise will differ from the surplus labor it appropriates in the form of surplus value. But the total industrial profits for all enterprises would need to equal the total surplus value appropriated if surplus labor were to account for the industrial profits.

The problem therefore arises in finding such a set of prices where: 1) the total value added during production remains proportional to the labor performed and; 2) the total profits realized by these enterprises equals the total surplus value apropriated by them. In other words can this transformation occur while still adhering to what Marx called the law of value. If the total value added when measured by the prices of commodities differs from the total value added by direct (living) labor in terms of the unit-value of these same commodities then this transformation would not be consistent with the law of value. An additional requirement is often imposed: that ths sum of values (the value of means of production or the value of constant capital plus value added) must equal the sum of prices of finished commodities for each turnover of capital.

In the 19th century Ricardo and later Marx attempted to demonstrate this compatibility through numeric examples: Marx's exposition, published posthumously through the careful editing of his lifelong friend and collaborator Friedrich Engels. In Engels preface to Capital volume 2, he called for what has since been referred to as an "essay competition" challenging readers to solve this quandary before he and Marx revealed the answer through the publication of Capital volume 3. Many credit (or blame depending on one's perspective) Engel's preface for the whirlwind of controversy that has since ensued surrounding the issue. Yet much of the controversy also stems from the worry of many defenders of capitalism and capitalist exploitation that just such a demonstration could undermine the rhetoric surrounding capitalist institutions. If this transformation demonstrated that the value distributed by capitalists to wage-labourers, to themselves and to others equals the value added by laborers, then this would lend support for the role ascribed to workers by Marx (and also Ricardo before him).

The debate has therefore raged for nearly two centuries with significant contributions from Ricardo, Malthus, Rodbertus, Marx, Bortkiewicz, Winternitz, Sraffa, Steedman, Foley, Roberts, Moseley, Duméneil, Lévy, Freeman, Kliman and others. Nineteenth century discourse typically involved numeric examples, while linear matrix algebra has increasingly dominated the discourse of the past century. The frontier of the debate therefore typically centers on the appropriate way to build the linear system of equations to reflect the ideas expressed in the text and numeric examples of Marxian or classical political economy. Or to put it another way: how does one render these often complex ideas (expressed in prose, logical argument, and numeric examples) in the simplified form of matrix algebra. The field has produced an impressive array of renditions both supporting and undermining the theories advanced by Marx and Ricardo.

References

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Anwar Shaikh papers: http://homepage.newschool.edu/~AShaikh/
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Fred Moseley papers: http://home.mtholyoke.edu/~fmoseley/
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Gerard Dumenil & Dominique Levy papers http://www.jourdan.ens.fr/~levy/
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Problem: A Reply." Cambridge Journal of Economics 15(3): 365-71.

Wolff, Richard D., Antonino Callari and Bruce B. Roberts (1984). "A Marxian Alternative to the Traditional "Transformation Problem."" Review of Radical Political Economics 16(2&3): 115-35.
Wolff, Richard D., Bruce B. Roberts and Antonino Callari (1984). "Unsnarling the Tangle: A Rejoinder [Marx's (Not Ricardo's) "Transformation Problem": A Radical Reconceptualization]." History of Political Economy 16(3): 431-36.
Wolff, Richard D., Bruce B. Roberts and Antonio Callari (1982). "Marx's (not Ricardo's) 'Transformation Problem': A Radical Reconceptualization." History of Political Economy 14(4): 564-82.

Transformation problem

References

See also