Abstract
We explore the optimal shape of the income tax and transfer schedule in an environment with distinct roles for public and private insurance. In a calibration to the United States, we find that the optimal system features marginal tax rates that increase in income. When we increase pressure on the government to raise revenue, the optimal marginal tax schedule becomes first flatter and then U-shaped, reconciling various findings in the literature. A power function parametric tax schedule outperforms an affine one, indicating that tax progressivity is more important than lump-sum transfers. We also explore various social welfare objectives and Pareto-improving reforms.