We quantitatively characterize the optimal capital and labor income tax in an overlapping generations model with idiosyncratic, uninsurable income shocks and permanent productivity differences of households. The optimal capital income tax rate is significantly positive at 36 percent. The optimal progressive labor income tax is, roughly, a flat tax of 23 percent with a deduction of $7,200 (relative to average household income of $42,000). The high optimal capital income tax is mainly driven by the life-cycle structure of the model, whereas the optimal progressivity of the labor income tax is attributable to the insurance and redistribution role of the tax system. (JEL E13, H21, H24, H25).