Equilibrium and Optimality in a Mean-Variance Model

This article reexamines an old debate over the optimality of market allocations in a symmetric mean-variance world, with production nonconvexities, imperfectly correlated outputs, and free entry. We show that Walrasian equilibrium does not exist: that non-Walrasian equilibrium under price-taking behavior allocates resources optimally between the risky and risk-free sectors, but spreads resources in the risky sector over an insufficient number of activities; and that non-Walrasian equilibrium under consistent conjectures allocates insufficient resources to the risky sector, and spreads them over an excessive number of activities. These results have analogues in the theory of product differentiation.