On the efficiency properties of the Roy’s model under uncertainty and market incompleteness

We consider Roy’s economies with perfectly competitive labor markets and uncertainty. Firms choose their investments in physical capital before observing the characteristics of the workers that they will hire. 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 in human and physical capital and letting the other endogenous variables adjust to restore market clearing. We also provide a robust example of a class of economies where equilibria are constrained Pareto inefficient due to overinvestments in high skills.