The set of regular equilibria

Debreu has shown that the set of regular economies is open dense. This paper investigates the closely related issue of the size of the set of regular equilibria. It is shown that this set is an open dense subset of the equilibrium manifold. The proof exploits the real algebraic nature of the set of critical equilibria belonging to any given fiber of the equilibrium manifold. This proof yields as by-product an alternative proof of Debreu's theorem, a proof that does not hinge on Sard's theorem.