ARBITRAGE, EQUILIBRIUM, AND GAINS FROM TRADE - A COUNTEREXAMPLE

We present a counterexample to a theorem due to Chichilnisky (Bulletin of the American Mathematical Society, 1993, 29, 189-207; American Eco nomic Review: 1994, 84, 427-334). Chichilnisky's theorem states that h er condition of limited arbitrage is necessary and sufficient for tile existence of an equilibrium in an economy with unbounded short sales. Our counterexample shows that the condition defined by Chichilnisky i s not sufficient for existence of equilibrium. We also discuss difficu lties in Chichilnisky (Economic Theory, 1995, 5, 79-107).