Price, value and profit – a continuous, general, treatment

This text comprises chapter 13 of Marx and non-equilibrium Economics[1].  It provides a general mathematical specification of a non-equilibrium interpretation of Marx’s theory of value. It refutes the Okishio theorem and solves the transformation problem. It is a foundation work of scholarship within the TSSI (temporal single-system interpretation) of Marx. It was the first specification of temporal values within a continuous-time framework as opposed to a discrete-time framework, and shows how to pass from discrete or serial time (difference equation, sequential) formalisations to continuous (differential equation, temporal) formalisations of the conservation of value. Nevertheless, a number of key ideas in it, in particular the integration of distribution in a continuous time framework, was not set upon a rigorous formulation. Instead the article advanced the hypothesis that this could be made rigorous. Therefore, although I derived the general continuous time formulation of the ‘laws of motion’ of capitalist society, in the last analysis the conclusion that the difference equation formulation would converge absolutely on the differential equation formulation eluded me for twenty years. I solved this problem to my own satisfaction in Freeman, A. 2020. ‘A General Theory of Value and Money: Foundations of an Axiomatic Theory.’ World Review of Political Economy, Vol. 11, No. 1 (spring 2020). pp28-75