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 finite–dimensional sub-economies and establishing a net of these equilibria that converges to an equilibrium on the whole commodity space. An example of equilibrium with a storage technology is given. An auxiliary result concerns the price support of efficient allocations. This paper was distributed in draft in July 1983. A version appeared in a dissertation completed in the Engineering–Economic Systems Department at Stanford University. I am grateful for the comments of David Luenberger, David Kreps, Kenneth Arrow, Donald Brown, Andreu Mas–Colell, William Zame, and a referee.