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

Alan Freeman

MPRA Paper from University Library of Munich, Germany

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.

JEL-codes: B20 B24 B41 B50 B51 O10 O30 O31 (search for similar items in EconPapers)
Date: 1998
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in Bellofiore, R (ed) Marxian Economics: a Reappraisal, Volume 2, pp139-162. Basingstoke: McMillan. ISBN 0 333 64411 5 (1998): pp. 139-162

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/1998/1/MPRA_paper_1998.pdf original version (application/pdf)

Related works:
Chapter: A General Refutation of Okishio’s Theorem and a Proof of the Falling Rate of Profit (1998)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:1998

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter ().