Transformation problem
A transformation problem for Marxist political economy was raised by the Polish neo-Ricardian theoretician Ladislaus Bortkiewicz in 1907, gaining currency in the post-war Western Marxian tradition after its translation and adoption by the influential Marxian economist and philosopher Paul Sweezy in 1942. It is in effect a formal restatement of the critique of Marxist value theory offered by the "Austrian" economist socially necessary labour time) with Ricardo's (based simply on labour).
The pivotal moment of transformation in Capital III, from values to an intermediary 'price of production', corresponds to the point at which Böhm-Bawerk's critique attacks Marx.
Significance
In one interpretation, if Bortkiewicz is correct, Marxian value categories will always fail to describe determinate economic relationships. Marxian value theory would thus be obsolete, and Marxism as a whole either discredited, or consigned to the category of what Marx himself would call 'cookshop recipes' - a utopian idealism, lacking any objective foundations.
A secondary significance lies in the various responses raised to the transformation problem critique by Marx supporters. Given the overlap with Böhm-Bawerk's criticism, a successful refutation of Bortkiewicz could be expected to amount to a refutation of Böhm-Bawerk. No such refutation is widely recognised, though certain Marxian political groups offer theirs.
Influence
The "transformation problem" critique has had more impact within Marxian circles than the related critique offered by Böhm-Bawerk, which itself found more favour with external critics of Marxism. It is taken very seriously in academic representations of Marxism, where both Marx sympathisers and Marx critics typically accept it as a true criticism of Marx's value theory.
On the whole, Marxist activists reject the critique. Contrary to Sweezy, and other Marx sympathisers who take the problem seriously, they dismiss the challenge entirely as a neo-Ricardian error. For them, the essential failure of the "corrected" transformation schemes offered by Sweezy or Piero Sraffa is that they mistake the social relation, value, for the stuff it is expressed in.
Further, there are alternative interpretations that totally reject Bortkewicz's mathematical framework as a way to understand the relationship between prices and values.
