Income tax, subsidies to education, and investments in human capital in a two-sector economy

The paper studies a two-sector economy with investments in human and physical capital and imperfect labor markets. Workers and firms endogenously select the sector they are active in, and choose the amount of their investments. To enter the high-skill sector, workers must pay a fixed cost that we interpret as direct cost of education. The economy is characterized by two different pecuniary externalities. Given the distribution of the agents across sectors, at equilibrium, in each sector there is underinvestment in both human and physical capital, due to non-contractibility of investments. A second pecuniary externality is induced by the self-selection of the agents in the two sectors. When total factor productivities are sufficiently diverse, subsidies to labor income in the low skill sector and fixed taxes on the direct costs of education increase total surplus, while subsidies to labor income in the high skill sector can actually reduce it.