Gini and Optimal Income Taxation by Rank

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