On the orientability of the asset equilibrium manifold

This paper addresses partly an open question raised in the Handbook of Mathematical Economics about the orientability of the pseudo-equilibrium manifold in the basic two-period General Equilibrium with Incomplete markets (GEI) model. For a broad class of explicit asset structures, it is proved that the asset equilibrium space is an orientable manifold if S-J is even, where S is the number of states of nature and J the number of assets. This implies, under the same conditions, the orientability of the pseudo-equilibrium manifold. By a standard homotopy argument, it also entails the index theorem for S-J even. A particular case is Momi's result, i.e the index theorem for generic endowments and real asset structures if S-J is even.