Income taxes, subsidies to education, and investments in human capital

We study a two-sector economy with investments in human and physical capital and imperfect labor markets. Investments are irreversible and noncontractible, due to random matching between …rms and workers. Income is allocated according to the Nash bargaining mechanism. At equilibrium, given the distribution of the agents across sectors, there is underinvestment in both human and physical capital, due to the hold-up problem generated by bargaining and contractibility. Self-selection of the agents into the two sectors typically induces too many workers to invest in high skills. Compared to the constrained e¢ cient allocation, at each equilibrium, there are too many people investing too little e¤ort in the high-skill sector. We also study the e¤ects of several tax policies on total expected surplus.