Editing Transformation problem (section)

== After Marx ==
=== Engels ===
[[Friedrich Engels]], the editor of volume 3 of ''Capital'', hinted since 1894 at an alternative way to look at the matter. His view was that the pure Marxian "law of value" of volume 1 and the "transformed" prices of volume 3 applied to different periods of economic history. In particular, the "law of value" would have prevailed in pre-capitalist exchange economies, from Babylon to the 15th century, while the "transformed" prices would have materialized under capitalism: see Engels's quotation by Morishima and Catephores (1975), p.&nbsp;310.

Engels's reasoning was later taken up by Meek (1956) and Nell (1973). These authors argued that, whatever one might say of his interpretation of capitalism, Marx's "value" theory retains 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 (and no more Marxian "values") at the beginning of the modern era. In this case, this true "historical transformation" could and should take the place of the mathematical transformation postulated by Marx in chapter 9 of volume 3.

=== Other Marxist views ===
There are several schools of thought among those who see themselves as upholding or furthering Marx on the question of transformation from values to prices, or modifying his theory in ways to make it more consistent.

According to the [[temporal single-system interpretation]] of ''Capital'' advanced by Alan Freeman, Andrew Kliman, and others, Marx's writings on the subject are most robustly interpreted in such a way as to remove any supposed inconsistencies.{{sfn|Choonara|2007}} Modern traditional Marxists argue that not only does the labour theory of value hold up today, but also that Marx's understanding of the transformation problem was in the main correct. Andrew Kliman claimed using the TSSI framework: "Simple reproduction and uniform profitability do require that supplies equal demands, but they can be equal even if the input and output prices of Period 1 are unequal. Since the outputs of one period are the inputs of the next, what is needed in order for supplies to equal demands is that the output prices of Period 1 equal the input prices of Period 2. But they are always equal; the end of one period is the start of the next, so the output prices of one period necessarily equal the input prices of the next period. Once this is recognized, Bortkiewicz’s proofs immediately fail, as was first demonstrated in Kliman and McGIone (1988)".<ref name=JG>Joseph Green (2010): [http://www.communistvoice.org/45cTransformation1.html On the non-naturalness of value: A defense of Marx and Engels on the transformation problem (part one)]</ref>

In the probabilistic interpretation of Marx advanced by Emmanuel Farjoun and Moshe Machover in ''Laws of Chaos'' (see references), they "''dis''solve" the transformation problem by reconceptualising the relevant quantities as random variables. In particular, they consider profit rates to reach an equilibrium ''distribution''. 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 (Economist)|Anwar Shaikh]], [[Makoto Itoh]], Gerard Dumenil and Dominique Levy, and Duncan Foley) who hold 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. 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&mdash;though not generally observed&mdash;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 they hold that the practical details of their workings are more complicated than Marx thought.