Full and constrained Pareto optimality with incomplete financial markets

We study the efficiency properties of equilibria in a neighborhood of economies with Pareto optimal (PO) initial endowments, when the number of agents is finitely large. We provide conditions under which, for all the economies in some open neighborhood of the PO reference economy, all the equilibria are constrained PO (CPO). We also provide conditions under which each open neighborhood of these exceptional PO economies contains both open sets of economies with CPO equilibria and open sets of economies where CPO fails.