Genericity Analysis on the Pseudo-Equilibrium Manifold

In this paper we study the size of the set of equilibria on the pseudo-equilibrium manifold. It is shown that, with incomplete real asset markets, the set of equilibria is an open and dense subset of the pseudo-equilibrium manifold, whose complement is the disjoint union of a finite number of lower dimensional smooth submanifolds. When markets are generically complete, the pseudo-equilibrium manifold with fixed real asset structures is identical to the equilibrium manifold in the Arrow–Debreu model and the above result is still persistent. In addition, it is shown that the complement of the set of equilibria is also a trivial vector bundle over a semi-algebraic set.Journal of Economic LiteratureClassification Number: D52.