Competitive Equilibria in General Choice Spaces

This paper primarily demonstrates the existence of Arrow-Debreu equilibria in a general class of topological vector spaces of commodity bundles. Two conditions based on production possibilities, preferences, and the topological nature of bounded sets are shown to substitute, in any locally convex space, for the advantages of the Euclidean topology. Examples fulfilling these conditions are supplied. The approach is that of Bewley, demonstrating equilibria on kite-dimensional sub-economies, each of which is a copy of the classical Debreu economy, and establishing a net of these equilibria which converge to an equilibrium on the whole commodity space. Other results concern the existence and price support of efficient allocations and the relationship between equilibria and the core of the allocation game.