In this paper we characterize quantitatively the optimal mix of progressive income taxes and education subsidies in a model with endogenous human capital formation, borrowing constraints, income risk and incomplete fi…nancial markets. Progressive labor income taxes provide social insurance...

We model the optimal reaction of a public PAYG pension system to demographic shocks. We compare the ex-ante first best and second best solution of a Ramsey planner with full commitment to the outcome under simple third best rules that mimic the pension systems observed in the real world. The...