On the existence of a continuum of constrained equilibria

In this paper a general equilibrium model of an economy with price rigidities 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 consumer keeps his initial endowments. In this paper it is shown that there exists a connected set of constrained equilibria containing both these trivial constrained equilibria, hence, there exists a continuum of constrained equilibria. Moreover, it is shown that all known equilibrium existence results for the model discussed follow as easy corollaries from this result. The proof of the result combines theorems in the areas of mathematical programming with those in topology. The result is shown without using differentiability assumptions and is also extended to the case with upper semicontinuou