I explore optimal education subsidies and progressivity of labour taxes in a model with stochastic human capital accumulation and incomplete markets, endogenous labour supply and an education choice modelled as a stopping time problem, where agents choose an optimal number of years to study before starting work. In a purely analytical
Baseline model with tight borrowing constraints on students, which leads to a no-trade equilibrium without savings, the government pays for education via transfers to students or – equivalently – via grants to universities. The social welfare-maximising policy features generous student transfers and highly progressive labour taxes, much more so
than currently seen in the US or Europe. This result is robust to myriad extensions, including a Quantitative model with relaxed financial frictions where students can borrow to finance their education, and where hence the equilibrium features extensive precautionary saving by workers.