From singularity theory to finiteness of Walrasian equilibria

• We establish that a “generic” critical economy has a finite number of equilibria.
• Debreu’s 1970 result extended from regular to both regular and critical economies.
• “Generically”, aggregate excess demand functions are of finite singularity type.

The main result of this paper states that there exists a residual subset of the set of critical economies whose associated equilibria are finite in number. We also show that this subset does not contain any open set and therefore the result is the best possible for our choice of topology (compact-open topology). The proof rests on results and concepts from singularity theory.