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From Marx's fundamental equalities to the solving of the transformation problem -- Coherence of the model

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  • Norbert Ankri
  • Paikan Marcaggi

Abstract

Recently, V. Laure van Bambeke used an original approach to solve the famous problem of transformation of values into production prices by considering that capital reallocation to each department (branch) was part of the problem. Here, we confirm the validity of this consideration in relation with the satisfaction of demand (social need which is able to pay for the given product). In contrast to V. Laure van Bambeke's method of solving an overdetermined system of equations (implying that compliance with Marx's fundamental equalities could only be approached), we show that the transformation problem is solvable from a determined (two-branch models) or an underdetermined system of equations enabling to obtain exact solutions through an algorithm we provide, with no approximation needed. For systems with three branches or more, the solution of the transformation problem belongs to an infinite ensemble, accounting for the observed high competition-driven market fluidity. Furthermore, we show that the transformation problem is solvable in the absence of fixed capital, supporting that dealing with the latter is not essential and cannot be seen as a potential flaw of the approach. Our algorithm enables simulations illustrating how the transient rise in the rate of profit predicted by the Okishio theorem is consistent with the tendency of the rate of profit to fall (TRPF) subsequent to capital reallocation, and how the TRPF is governed by the increase of organic composition, in value. We establish that the long-standing transformation problem is not such a problem since it is easily solved through our algorithm, whatever the number of branches considered. This emphasizes the high coherence of Marx's conception, and its impressive relevance regarding issues such as the TRPF, which have remained intensely debated.

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  • Norbert Ankri & Paikan Marcaggi, 2022. "From Marx's fundamental equalities to the solving of the transformation problem -- Coherence of the model," Papers 2210.09097, arXiv.org, revised Oct 2024.
    • Handle: RePEc:arx:papers:2210.09097
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    References listed on IDEAS

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    1. Vincent Laure Van Bambeke, 2006. "Des valeurs aux prix absolus. Essai de théorie économique rationnelle," Innovations, De Boeck Université, vol. 24(2), pages 171-198.
    2. Gilbert Abraham-Frois & Emeric Lendjel, 2001. "Une première application du théorème de Perron-Frobenius à l'économie : l'abbé Potron comme précurseur," Revue d'économie politique, Dalloz, vol. 111(4), pages 639-665.
    3. Serge Latouche, 1973. "A propos de la baisse tendancielle du taux de profit," Revue Économique, Programme National Persée, vol. 24(1), pages 163-175.
    4. Duncan K. Foley, 1982. "The Value of Money the Value of Labor Power and the Marxian Transformation Problem," Review of Radical Political Economics, Union for Radical Political Economics, vol. 14(2), pages 37-47, June.
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    Cited by:

    1. Norbert Ankri & Païkan Marcaggi, 2023. "Both invariant principles implied by Marx’s law of value are necessary and sufficient to solve the transformation problem through Morishima's formalism [Les deux principes invariants qu’implique la," Working Papers hal-03994960, HAL.
    2. Norbert Ankri & Paikan Marcaggi, 2023. "Both invariant principles implied by Marx's law of value are necessary and sufficient to solve the transformation problem through Morishima's formalism," Papers 2303.11471, arXiv.org, revised Oct 2024.

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