In this paper we attempt to show that, however being little from a topological point of view, the set of singular economies plays a considerable role in the development of the economies.

Our concern in this work is to obtain conditions for the uniqueness of equilibria, with commodity bundles as consumption patterns which depend on the state of the world.

The aim of this paper is to characterise the set of non regular economies, when there is a finite number of consumers with either finite or infinitely many goods. We prove that the structure of the equilibrium set is the same in both cases and that there exist bifurcations in some of these models.