Endogenous restricted participation in general financial equilibrium

We consider an incomplete market model with numeraire assets. Each household faces an individual constraint on its participation in the asset market. In related literature, the constraint is described by a function whose sole argument is the asset portfolio. On the contrary, in our analysis the constraint depends not only on the asset portfolio, but also on asset and good prices—hence the reference to endogenous (in contrast to exogenous) in the title. Economies are described by endowments of commodities, utility functions, asset yield matrices, and restriction functions. We study two specifications of the constraint function. The first one is homogeneous of degree zero with respect to spot prices. The second one does not exhibit that property. We then consistently distinguish between homogeneous and nonhomogeneous economies. After having established existence of equilibria for both types of economies, we study indeterminacy for each of them and show the following results. For an open and dense subset of the set of homogeneous economies, equilibria are finite and regular, up to innocuous price normalizations. There exists an open and nonempty set of nonhomogeneous economies, whose associated equilibria exhibit real indeterminacy.