A Characterization of the Singular Economies of the Infinite Dimensional Models in General Equilibrium Theory.

Abstract

The aim of this paper is to characterize the set of singular economies, when there are a finite set of consumers with infinitely many goods in the sense that goods differ in the time which they are consumed or in the state of the world in which they become available. There exist l available goods in each time or in each state of the world. Employing well know results of the “ Singularity Theory” on differentiable maps, we characterize the structure of the equilibrium set from the so called singular economies. In the last section we introduce a continuous time economy and -although in a limited waywe study the dynamics along the equilibrium path. We show that if there exist singularities then the equilibrium set isn’t a finite set, moreover it may be a continuous set of equilibria. It is important to notice that we will not describe our models in terms of the tˆatonnement. The process of endowments move the price system, we don’t need the demand law to characterize the equilibrium manifold.