We derive a general optimal income tax formula when individuals respond along both the intensive and extensive margins and when income effects can prevail. Individuals are heterogeneous across two dimensions: their skill and their disutility of participation. Preferences over consumption and...

This paper characterizes optimal income taxation when individuals respond along both the intensive and extensive margins. Individuals are heterogeneous across two dimensions: specifically, their skill and disutility of participation. Preferences over consumption and work effort can differ with...

Half of the jobs in the U.S. feature pay-for-performance. We study nonlinear income taxation in a model where such contracts arise in private labor markets that are constrained by moral hazard frictions. We derive novel formulas for the incidence of arbitrarily nonlinear reforms of a given tax...