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The transformation problem: a mathematical approach of its solution within Marx’s original framework

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  • Zhongren Zhang

    (The University of Shimane)

Abstract

This study demonstrates that the transformation problem concerns whether a contradiction exists between Marx’s concept of labor value and that of production price. In a narrow sense, this is just a mathematical problem. It can be boiled down to the construction of a mathematical model that can simulate the conversion from value to production price to conclude whether the constructed model meets certain constraints (so-called “the double invariance”). However, models of most researchers so far met only one of the two constraints, some of them couldn’t satisfy any one of them. So, they tried to explain this problem by modifying Marx’s conditions or conclusions, and hence doubted or even denied Marx’s conclusions. This was actually an act of self-deception. In contrast to related attempts that tampered with Marx’s transformation conditions or conclusions, this study is based on the solution of the transformation problem within Marx’s original framework. It extends Bortkiewicz (Third volume of Capital, Sweezy, 1907) and Samuelson (Am Econ Rev 47:884–912, 1957, Proc Natl Acad Sci 67:423–425, 1970, J Econ Lit 9:399–431, 1971) to overcome their shortcomings. This study provides the model of static transformation and that of dynamic transformation and illustrates them with examples of mathematical simulation: the static transformation is the result of the dynamic transformation and its end point. Both the general dynamic transformation model and the general static transformation model satisfy two constraints of Marx simultaneously. So, this study offers a new mathematical approach to the transformation problem. The author obtained a solution to the transformation problem in 2000 (a static version in line with Marx’s original intention), continued to conduct research, and published several research results. However, so far, the author’s publication was mainly in Chinese and Japanese and did not receive due attention in international academia. As I received the invitation to the Marx special feature of from this journal (*This plan was not realized. Some of contributed papers to this plan were published in this journal’s special feature “Promenade in the history of economic thought” (vol. 18–1). [Associate Editor]), I endeavored to describe my research in this topic deeper.

Suggested Citation

  • Zhongren Zhang, 2022. "The transformation problem: a mathematical approach of its solution within Marx’s original framework," Evolutionary and Institutional Economics Review, Springer, vol. 19(2), pages 701-728, September.
    • Handle: RePEc:spr:eaiere:v:19:y:2022:i:2:d:10.1007_s40844-022-00237-5
    DOI: 10.1007/s40844-022-00237-5
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    References listed on IDEAS

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    1. Samuelson, Paul, 2012. "Understanding the Marxian Notion of Exploitation: A Summary of the So-CalledTransformation Problem Between Marxian Values and Competitive Prices," Ekonomicheskaya Politika / Economic Policy, Russian Presidential Academy of National Economy and Public Administration, pages 182-202, August.
    2. R. M. Goodwin, 1983. "Essays in Linear Economic Structures," Palgrave Macmillan Books, Palgrave Macmillan, number 978-1-349-05507-4, December.
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    More about this item

    Keywords

    Transformation problem; Dynamic transformation; Inverse transformation; Static transformation; Production price; Marx’s double invariances;
    All these keywords.

    JEL classification:

    • B0 - Schools of Economic Thought and Methodology - - General
    • B51 - Schools of Economic Thought and Methodology - - Current Heterodox Approaches - - - Socialist; Marxian; Sraffian
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other

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