Optimal redistributive taxation with both extensive and intensive responses

This paper characterizes the optimal income taxation when individuals respond along both the intensive and extensive margins. Individuals are heterogeneous in two dimensions: their skills and their disutility of participation. Preferences over consumption and work effort can differ with the skill level, only the Spence-Mirrlees condition being imposed. We derive an optimal tax formula thanks to a tax perturbation approach. This formula 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. The relevance of this condition is discussed with analytical examples and numerical simulations on U.S. data