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.