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A general refutation of Okishio’s theorem and a proof of the falling rate of profit

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  • Freeman, Alan

Abstract

This is the first published general refutation of the Okishio theorem. An earlier refutation based on a specific example was published by Kliman and McGlone in 1988. Okishio’s theorem, published in 1961, asserts that if real wages stay constant, the rate of profit necessarily rises in consequence of any cost-reducing technical change. It proves this within a simultaneous equation (general equlibrium) framework. This paper establishes that this proposition is false within a differential equation (temporal) approach. In such a framework the denominator of the rate of profit rises continuously, regardless of whether or not there is technical change, unless capitalist consumption exceeds profit, as occurs in a slump. Okishio himself asserts that his theorem is ‘contrary to Marx’s Gesetz des Tendentiellen Falls der Profitrate’ – contrary to Marx’s law of the tendency of the rate of profit to fall. This assertion is, within the literature, universally taken to be the substantive content of the ‘Okishio Theorem’. Thus, if Marx’s approach to value is in fact temporal, and not simultaneist, this assertion by Okishio is false, since it applies not to Marx’s own theory, but to the interpretation of that theory subsequently attributed to Marx by a specific school of thought represented principally by Bortkiewicz, Sweezy, Morishima, Seton, and Steedman. The subsequent accumulation of hermeneutic evidence strongly supports the thesis that Marx’s theory is temporalist and not simultaneist. Since the Okishio theorem makes the general assertion that the rate of profit must necessarily rise if there are cost-saving technical changes, and since Kliman and McGlone demonstrate a particular case in which cost-saving technical change leads to a fall in the profit rate, the Kliman-McGlone paper is the first published refutation of the Okishio theorem. The present paper is a generalisation of this refutation which establishes the precise conditions under which the profit rate rise or falls, and establishes the general result that the profit rate necessarily falls as a consequence of capitalist accumulation with a constant real wage, until and unless accumulation ceases in value terms. Consequently the mathematical findings set out in this paper, refute the Okishio Theorem.

Suggested Citation

  • Freeman, Alan, 1998. "A general refutation of Okishio’s theorem and a proof of the falling rate of profit," MPRA Paper 1998, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:1998
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    File URL: https://mpra.ub.uni-muenchen.de/1998/1/MPRA_paper_1998.pdf
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    References listed on IDEAS

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    1. Harcourt,G. C., 1972. "Some Cambridge Controversies in the Theory of Capital," Cambridge Books, Cambridge University Press, number 9780521096720.
    2. José Alberro & Joseph Persky & José Alberro & Joseph Persky, 1981. "The Dynamics of Fixed Capital Revaluation and Scrapping," Review of Radical Political Economics, Union for Radical Political Economics, vol. 13(2), pages 32-37, July.
    3. Mohun, Simon, 1994. "A Re(in)statement of the Labour Theory of Value," Cambridge Journal of Economics, Oxford University Press, vol. 18(4), pages 391-412, August.
    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. Mohun, Simon & Veneziani, Roberto, 2009. "The temporal single-system interpretation: underdetermination and inconsistency," MPRA Paper 30452, University Library of Munich, Germany.
    2. Kliman, Andrew & Freeman, Alan & Potts, Nick & Gusev, Alexey & Cooney, Brendan, 2013. "The Unmaking of Marx’s Capital: Heinrich’s Attempt to Eliminate Marx’s Crisis Theory," MPRA Paper 48535, University Library of Munich, Germany, revised 22 Jul 2013.

    More about this item

    JEL classification:

    • B50 - Schools of Economic Thought and Methodology - - Current Heterodox Approaches - - - General
    • O30 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - General
    • O10 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - General
    • B41 - Schools of Economic Thought and Methodology - - Economic Methodology - - - Economic Methodology
    • B24 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Socialist; Marxist; Scraffian
    • B51 - Schools of Economic Thought and Methodology - - Current Heterodox Approaches - - - Socialist; Marxian; Sraffian
    • O31 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Innovation and Invention: Processes and Incentives
    • B20 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - General

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