A re-examination of constrained Pareto inefficiency in economies with incomplete markets

We establish that, when the number of agents is sufficiently large, but finite, there are open sets of economies with constrained Pareto inefficient equilibria and provide a simple sufficient condition for constrained inefficiency. We also show that there are open sets of economies with constrained efficient equilibria. Hence, for these economies, neither constrained efficiency, nor its lack, are generic properties. However, constrained inefficiency is a pervasive feature: for each economy with preferences satisfying a mild restriction, there are open sets of endowments such that their equilibrium allocations are constrained inefficient.