Existence of equilibria in economies with increasing returns and infinitely many commodities

Abstract

In this paper, we prove the existence of equilibria in a model with infinitely many commodities and where production sets exhibit increasing returns to scale or more general types of non-convexities. We distinguish two cases. In the first, producers follow loss free pricing rules like the average cost or the profit maximizing pricing rule. The second case is devoted to bounded loss pricing rules. In each case, we give an existence result under assumptions which extend those considered in the finite dimensional case. In particular, they are satisfied by a firm with a convex production set which maximizes its profits. We also give a new sufficient condition to have an economically meaningful equilibrium price.