Bunching in rank-dependent optimal income tax schedules

Considering optimal non-linear income tax problems when the social welfare function only depends on ranks as in Yaari (Econometrica 55(1):95–115, 1987) and weights agreeing with Lorenz quasi-ordering, we extend analysis of Simula Trannoy (Am Econ J Policy, 2021) two directions. First, establish conditions under which bunching does not occur optimum. We find a sufficient condition individual preferences, appears reinforcement Spence-Mirrlees condition. In particular, marginal dis-utility gross should be convex, but less convex higher productivity. also show that, for all productivity distributions log-concave survival function, is precluded maximin, Gini, “illfare-ranked single-series Ginis”. Second, turn to discrete population setting, provide an “ABC” formula rates, related those continuum types found (2021), remain essentially distinct.