Limited Arbitrage is Necessary and Sufficient for the Existence of an Equilibrium
In 1991, in ,  and in , 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 . In response to a comment , I show here that the authors misunderstood my results by focusing on brief announcements which cover other areas, social choice  and algebraic topology , rather than on the publication which contains my proofs on equilibrium . The comment's example is irrelevant to my results in  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 .
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