LIMITED ARBITRAGE IS NECESSARY AND SUFFICIENT FOR THE EXISTENCE OF ANEQUILIBRIUM

In Chichilnisky (Working Paper No. 586, 1991), Chichilnisky (Working P aper 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 c ondition on endowments and preferences, 'limited arbitrage', which I s howed to be necessary and sufficient for the existence of a competitiv e equilibrium. In response to a comment (Monteiro et al., Journal of M athematical Economics, 1997, 26, 000-000), I show here that the author s misunderstood my results by focussing on brief announcements which c over other areas, social choice (Chichilnisky, American Economic Revie w, 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 ex ample is irrelevant to my results in Chichilnisky (Economic Theory, 19 95, 5, 79-108) because it starts from different conditions. Limited ar bitrage is always necessary and sufficient for the existence of a comp etitive equilibrium, with or without short sales, with the global cone s as I defined them, and exactly as proved in Chichilnisky (Economic T heory, 1995, 5, 79-108).