We consider an economy where production may use labor of two different skill levels. Workers are heterogeneous and, by investing in education, self-select into one of the two skills. Ex-ante, when firms choose their investments in physical capital, they do not know the level of human capital prevailing in the labor market they will be active in. We prove existence and constrained inefficiency of competitive equilibria, which are always characterized by overeducation. An increase in total expected surplus can be obtained by shrinking, at the margin, the set of workers investing in high skills. This can be implemented by imposing taxes on the cost of investing in high skills or by imposing a progressive labor earning tax.