Data and Code for: Gini and Optimal Taxation by Rank

We solve the non-linear 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. The key idea is that absent bunching and when individuals optimize, ranks in the actual and optimal allocations are invariant. This allows us to provide new, simple and intuitive tax formulas, for both the quasi-linear and additive cases, and new comparative static results. This approach also serves a didactical role, making insights from optimal taxation more widely accessible. We provide an example in which the actual US tax policy is close to being optimal, except at the top where optimal rates are much higher than in actuality.