Existence of Marginal Cost Pricing Equilibria: The Nonsmooth Case
证明了一个存在性定理：在允许规模报酬递增或更一般非凸性的经济中，即使生产集不光滑，边际成本定价均衡仍然存在。模型包含任意数量的企业，消费者最大化效用，凸企业最大化利润，非凸企业遵循边际定价规则。
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)