Arrow-Debreu and the classical and neoclassical economics

This article challenges the notion that the modern general equilibrium theory of Arrow-Debreu is a rigorous formulation of neoclassical economics and that, by contrast, Sraffian and Marxian economics are not compatible with it. It shows that the standard Arrow-Debreu assumptions regarding the production sets and profit maximization are sufficient to determine equilibrium prices, which then do not depend on consumers’ preferences. Arrow-Debreu equilibrium prices are similar to Marxian labor values since they are proportional to labor time and factor prices are variables that determine the distribution of income but not commodity prices. Instead of being related to the quantity of capital, profits are also proportional to the quantity of labor, causing capital to have different prices at the same point in time and at the same market, which is hardly compatible with the hypothesis of free competition. If the notion of equilibrium prices is modified as to make capital to be rewarded at the same rate in all sectors of the economy, the hypothesis of decreasing returns to scale ensures that competitive prices are an increasing function of demand and, as a consequence, they can be viewed as a product of the interaction between supply and demand. However, in any case there is no inverse relationship between the quantity of capital and its rate of rewards, as requires the neoclassical law of diminishing returns.