Optimal redistributive taxation with both extensive and intensive responses

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 respect to the level of skill, with only the Spence-Mirrlees condition imposed. Employing a tax perturbation approach, we derive an optimal tax formula that generalizes previous results by allowing for income effects and extensive margin responses. We provide a sufficient condition for optimal marginal tax rates to be nonnegative everywhere. We discuss the relevance of this condition with analytical examples and numerical simulations using U.S. data. -- Optimal tax formula ; tax perturbation ; random participation