Freeman, Alan (1998): A general refutation of Okishio’s theorem and a proof of the falling rate of profit. Published in: Bellofiore, R (ed) Marxian Economics: a Reappraisal, Volume 2, pp139162. Basingstoke: McMillan. ISBN 0 333 64411 5 (1998): pp. 139162.

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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 costreducing 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 costsaving technical changes, and since Kliman and McGlone demonstrate a particular case in which costsaving technical change leads to a fall in the profit rate, the KlimanMcGlone 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.