Profits equal surplus value on average and the significance of this result for the Marxian theory of accumulation

Marx's justification of his theory of surplus value in the face of unequal compositions of capital, by interpreting total profits as a redistribution of surplus value, is not correct in general. However, it is shown here that the equality holds if the input matrices are random and the labour theory of value holds, in a sense to be specified, on average. Manuscripts recently published for the first time confirm that to the end Marx trusted his approach to the theory of value in that he continued to use the identity of the aggregates of capital and surplus in value and in price terms. His insistence was rooted in his philosophy. An attempt is made to clarify his use of a Hegelian methodology by comparing Hegel's and Marx's approaches to the foundation of the infinitesimal calculus. The article concludes with Marx's late reconsiderations of his theory of the falling rate of profit, which also continue to be based on the equality of profit and surplus value.