Sraffa's Reproduction Prices versus Prices of Production: Probability and Convergence

Abstract

The article argues that the reproduction prices introduced in the first chapter of Sraffa's book are not necessarily compatible with the profit equalising prices that form the substance of the book. It uses probabilistic arguments about how probable it is that reproduction prices will approximate to profit equalising prices. By use of random matrix techniques, it shows that the solutions space associated with prices of production is similar to that associated with classical labour values. In the latter part of the article, a random sample of reproduction schemes is simulated over time, under assumptions of capital movement, to see whether such systems dynamically converge on profit equalising prices. It is found that some converge and some fail to converge.