Optimal Redistributive Taxation with both Extensive and Intensive Responses

We derive a general optimal income tax formula when individuals respond along both the intensiveand extensive margins and when income effects can prevail. Individuals are heterogeneous across twodimensions: their skill and their disutility of participation. Preferences over consumption and workeffort can differ with respect to the level of skill, with only the Spence-Mirrlees condition beingimposed. Employing a new tax perturbation approach that integrates the nonlinearity of the taxfunction into the behavioral elasticities, we derive a fairly mild condition for optimal marginal taxrates to be nonnegative everywhere. Numerical simulations using U.S. data confirm the mildness ofour conditions. The extensive margin strongly reduces the level of optimal marginal tax rates