Gini and Optimal Income Taxation by Rank

We solve the nonlinear income tax program for rank-dependent social welfare functions, expressing trade-off between size and inequality using Gini related families of positional indices. Absent bunching, ranks in actual optimal allocations are invariant. Exploiting this feature, we provide new, simple, intuitive formulas both quasilinear additive cases new comparative static results. Our approach makes insights from taxation more widely accessible. In some our simulations US policy is close to being optimal—except at top, where rates much higher than actuality. (JEL D31, D63, H21, H24, K34)