Conditions that guarantee the uniqueness of equilibrium in models of economic competition are crucial to applications of these models in exercises of comparative statics. Until now, most of the attention given to the uniqueness question has been focused on pure exchange economies. In this paper we use a topological index theorem to derive necessary and sufficient conditions for the uniqueness of equilibrium in economies with production. Unfortunately, conditions that imply uniqueness appear to be too restrictive to have much applicability. We argue, for example, that the only economically interpretable restrictions that imply uniqueness are either that the demand side of an economy behaves like a single consumer or that the supply side is an input-output system. Our results suggest a need for reformulation of the comparative statics method. © President and Fellows of Harvard College.