On the Existence and the Structure Pseudo-Equilibrium Manifold

Abstract

A brief proof of the existence of an equilibrium in incomplete markets is given for regular economies (Theorem 1); a robust example of such economies is provided. Theorem 2 establishes that the manifold Q of global pseudo-equilibria is a fiber bundle with the topological structure of a one- or two-fold covering space of Gk,n, the space of k planes in Rn, where k is the number of assets in the economy and n the number of states of uncertainty. In particular, the pseudo-equilibrium manifold Q is not contractible with incomplete markets. This contrasts with the case of complete markets, where the equilibrium manifold is always contractible.