On the efficiency properties of the Roy's model under asymmetric information

We consider Roy's economies with perfectly competitive labor markets and asymmetric information. Firms choose their investments in physical capital before observing the characteristics of the labor markets they will face. We provide conditions under which equilibrium allocations are constrained Pareto efficient, i.e., such that it is impossible to improve upon the equilibrium allocation by changing agents' investments and letting the other endogenous variables adjust to restore market clearing. We also provide a robust example of a class of economies where these conditions fail and where equilibria are characterized by overinvestments in high skills. Finally, we discuss some implications of our main results for the optimal taxation literature.