A note on the finiteness of the set of equilibria in an exchange economy with constrained endowments

Debreu, G. (1970) proved that for smooth finite exchange economies, the set of endowment assignments which result in a finite number of price equilibria is ''large'' in the sense that it has null closed complement. We show that if the individual endowment space of each agent does not include all the commodities, then this conclusion need not hold. In particular, we consider the case where each agent's endowment space includes only one good. We construct a class of examples in which every economy in an open subset of the constrained endowment space gives rise to a continuum of equilibria. (C) 1997 Elsevier Science B.V.