We study the optimal design of student financial aid as a function of parental income. We derive optimal financial aid … formulas in a general model. For a simple model version, we derive mild conditions on primitives under which poorer students …, labor supply in college, and uncertain returns. Optimal financial aid is strongly declining in parental income even without …

We analyze optimal taxation of labor and capital income in a life-cycle framework with idiosyncratic income risk. We … provide a novel decomposition of labor income tax formulas into a redistribution and an insurance component. The latter is … independent of the social welfare function and determined by the degree of income risk and risk aversion. The optimal linear …