Ladislaus von Bortkiewicz’s Errors and a Reliable Solution to the Marxian Problem of Transformation in Direct and Inverse Formulation

The paper argues that economists still regard the solution to the problem of the transformation of values into prices of production, got by L. von Bortkiewicz, as belonging to Marx himself. After all, it was allegedly “correctly corrected” by the said author in 1907. Bortkiewicz based his solution on several erroneous interpretations’ theory of Marx. Because of Bortkiewicz’s errors, the representatives of the mainstream see no connection between the “value system” and the “production price system”. They claim that the transformation problem itself results from impossibility and that Marxist value theory is, at best, irrelevant and irremediably inconsistent. The paper shows that the solution to the transformation issue exists in both the direct and inverse formulation. We used for this purpose the Tugan-Baranowsky—Bortkiewicz three-sector model. These results are consistent with the concept of Marx within the dualistic approach. They coincide with the results generated by the author in his previous work (see https://osf.io/tk43d/). In the present paper, we introduce methods and examples of transformation, including iterative and based on solving systems of simultaneous equations. We prove again with their help that at equilibrium prices, profit arises from surplus value, or more precisely, from the newly created value generated by workers’ labour and from no other source. We also show that a dualistic approach to transformation allows us to see the advantages of value prices, which, unlike production prices, do not limit the growth of the productive power of labour when enterprises introduce new machines. Value prices are in demand under socialism.