ON THE EXISTENCE OF A CONTINUUM OF CONSTRAINED EQUILIBRIA

In this paper a general equilibrium model of an economy with price rig idities and quantity rationing is considered. The equilibria in such a model are called constrained equilibria. It is well-known that there exist two so-called trivial constrained equilibria at which every cons umer keeps his initial endowments. In this paper it is shown that ther e exists a connected set of constrained equilibria containing both the se trivial constrained equilibria, hence, there exists a continuum of constrained equilibria. Moreover, it is shown that all known equilibri um existence results for the model discussed follow as easy corollarie s from this result. The proof of the result combines theorems in the a reas of mathematical programming with those in topology. The result is shown without using differentiability assumptions and is also extende d to the case with upper semicontinuous demand correspondences. (C) 19 98 Elsevier Science S.A. All rights reserved.