Limited Arbitrage is Necessary and Sufficient for the Existence of a Competitive Equilibrium

Abstract

In Chichilnisky (Working Paper N0. 586, 1991), Chichilnisky (Working Paper No. 650, 1992) and Chichilnisky (Economic Theory, 1995, 5, 79-108), I introduced the concept of a global cone and used it to define a condition on endowments and preferences, 'limited arbitrage', which I showed to be necessary and sufhcient for the existence of a competitive equilibrium. In response to a comment (Monteiro et al., Journal of Mathematical Economics, 1997. 26, 000-000), I show here that the authors misunderstood my results by focussing on brief announcements which cover other areas, social choice (Chichilnisky, American Economic Review, 1994, 427-434 and algebraic topology (Chichilnisky, Bulletin of the American Mathematical Society, 1993, 29, 189-207), rather than on the publication which contains my proofs on equilibrium. The comment's example is irrelevant to my results in Chichilnisky (Economic Theory. 1995, 5, 79- 108) because it starts from different conditions. Limited arbitrage is always necessary and sufficient for the existence of a competitive equilibrium, with or without short sales, with the global cones as I defined them. and exactly as proved in Chichilnisky (Economic Theory, 1995, 5, 79-108).