A foundation of location theory: Existence of equilibrium, the welfare theorems, and core

An exchange economy with land and a finite number of traders is examined. Land is modeled as a sigma algebra of subsets of a Euclidean space. Since this commodity space has no natural convex or linear structure, standard existence results cannot be applied. The contribution of this paper is the introduction of continuity, convexity, and "nonwasteful partition" assumptions (the latter joint on the land supply and consumer preferences) for such a situation. Examples are provided where no equilibrium exists when each of these assumptions is violated. Under these assumptions, equilibrium is shown to exist, the core is shown to be nonempty, and the welfare theorems are proved. Examples satisfying all the assumptions are provided.