As Easy as ABC? Multidimensional Screening in Public Finance

Abstract

We characterize the second-best allocation in a Mirrleesian optimal tax model where agents differ in multiple dimensions and the planner can tax multiple goods non-linearly. We develop a new method that allows us to solve the partial differential equations that describe the optimum regardless of the dimensionality of the problem. We derive four theoretical properties of the optimum. First, the optimal tax system is described by a multidimensional version of Diamond's (1998) and Saez' (2001) ABC-formula. Second, the Atkinson-Stiglitz theorem does not generalize to settings where the planner screens in multiple dimensions. Third, the optimal marginal tax rate on each good depends on the consumption level of multiple goods. Fourth, a no-distortion at the top/bottom result continues to hold. A calibrated simulation on taxation of couples shows a strong positive relationship between an individual's optimal marginal tax rate and the income earned by his spouse.

A general solution to the quasi linear screening problem

“…Similarly,Renes and Zoutman (2017) adopt a mechanism design approach and solve the relaxed problem (first order approach) where the second order conditions of individuals' optimization programs are neglected.…”