Bunching and Rank-Dependent Optimal Income Taxation

We consider optimal non-linear income tax problems when the social welfare function only depends on ranks as in Yaari (1987) and weights agree with the Lorenz quasi-ordering. Gini, S-Gini, and a class putting more emphasis on inequality in the upper part of the distribution belong to this set. Adopting a first-order approach, we establish marginal tax formula assuming a continuous population framework, and derive conditions on the primitives of the model for which the socially optimal allocation is either fully separating or involves some bunching. For all log-concave survival functions, bunching is precluded for the maximin, Gini, and "illfare-ranked single-series Ginis". We then turn to a discrete population setting, and provide "ABC" formulas for optimal marginal tax rates, which are related to those for a continuum of types but remain essentially distinct