1996 Reports

Limited Arbitrage is Necessary and Sufficient for the Existence of an Equilibrium

Chichilnisky, Graciela

In 1991, in [1], [2] and in [8], I introduced the concept of global cone and used it to define a condition on endowments and preferences, "˜limited arbitrage', which I showed to be necessary and sufficient for the existence of a competitive equilibrium [8]. In response to a comment [19], I show here that the authors misunderstood my results by focusing on brief announcements which cover other areas, social choice [6] and algebraic topology [3], rather than on the publication which contains my proofs on equilibrium [8]. The comment's example is irrelevant to my results in [8] 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 [8].