Existence of equilibrium with nonconvexities and finitely many agents

Many economic models in the fields of public finance, location theory, and choice under uncertainty involve characteristic nonconvexities in either preferences or production sets for some types of commodities. One useful way to attack such nonconvexities is to employ the convexifying effect of large numbers of agents on demand for a finite number of commodities. The alternative proposed here relies on the convexifying effect of large numbers of commodities rather than agents. Sufficient substitutability and a large number of commodities can be used to replace some convexity assumptions. Existence of an equilibrium and the first welfare theorem are proved using Zame's existence theorem and Lyapunov's theorem as the key tools.