Existence of Marginal Cost Pricing Equilibria: The Nonsmooth Case

Abstract

In this article we report a general existence theorem of a marginal (cost) pricing equilibrium for an economy which may exhibit increasing returns to scale or more general types of in the production sector. Our model considers an arbitrary number of firms and no smoothness assumption is made on their production sets or on the aggregate production set. In this article we report a general existence theorem of marginal (cost) pricing equilibria for an economy, which may exhibit increasing returns to scale or more general types of nonconvexities in the production sector. In our model, which considers a positive finite numbers 1 of commodities, m, of consumers, and, n, of firms, (a) consumers maximize their preferences subject to their budget constraints, (b) convex producers maximize profits, while nonconvex producers are instructed to follow the marginal pricing rule, i.e., they fulfill the first-order necessary condition for profit maximization in a precise mathematical sense, formalized with Clarke's normal cone. Our treatment of convex and nonconvex producers will in fact be symmetric. The technological possibilities of the jth producer (j = 1, ..., n)