Reducing the dimensionality of a selfishly optimal nonlinear income tax problem

Abstract

Roell (Voting over nonlinear income tax schedules, unpublished manuscript, 2012) considers a political economy version of the finite-type Mirrlees (Rev Econ Stud 38:175–208, 1971) nonlinear income tax problem in which each type proposes its selfishly optimal tax schedule with majority rule used to select among them. We show that it is possible to solve a selfishly optimal nonlinear income tax problem by first solving for the optimal consumptions using a reduced-form problem that only involves these variables and then using the optimal consumptions in two recursion formulae to compute the optimal incomes. The analysis extends the methodology introduced in Weymark (J Publ Econ 30:199–217, 1986b) so as to handle problems in which not all of the adjacent incentive constraints bind in the same direction.