Real Indeterminacy in Incomplete Financial Market Economies without Aggregate Risk

We analyze an exchange economy with incomplete financial markets and assets whose returns are fixed in units of account. Moreover, we assume absence of aggregate risk, i.e., that individual preferences and total resources are constrained to be invariant across different states of the world. In this framework we show that the set of (commodity) price-endowment equilibria is diffeomorphic to a Euclidean space. We then exploit this global parameterization to prove that the set of equilibrium allocations associated with each endowment in a generic set contains a smooth manifold, whose dimension is equal to the number of "missing" assets.