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Essentially the same material has been published in Journal of Mathematical Economics, 28 (1997) pp 481-501 the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by North Holland. This material may not be copied or reposted without explicit permission. (Copyright (C)1986 by North Holland, Inc.). North Holland is on the web at

Arbitrage, equilibrium and gains from trade: A counterexample

Paulo K Monteiro,
Frank H Page Jr
and Myrna Holtz Wooders


We present a counterexample to a theorem due to Chichilnisky (Bulletin of the American Mathematical Society, 1993, 29 189-207; American Economic Review, 1994, 84, 427-434), Chichilnisky's theorem states that her condition of limited arbitrage is necessary and sufficient for the existence of an equilibrium in an economy with unbounded short sales. Our counterexample shows that the condition defined by Chichilnisky is not sufficient for existence of equilibrium. We also discuss difficulties in Chichilnisky (Economic Theory, 1995, 5,79-107)

JEL Classification: C62, C71, D51, D61, G12

Key words: Arbitrage; General equilibrium; Necessary and sufficient conditions, Recession cones.