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.