Optimal redistributive taxation with both extensive and intensive responses

We study optimal income taxation when labor supply reacts along the intensive and extensive margins. Individuals are heterogeneous across two unobserved dimensions: their skill and disutility of participation. We develop a new method to analytically derive conditions under which optimal marginal tax rates are non-negative everywhere. It is typically optimal to provide a distinct level of transfer to the non-employed and to workers with negligible earnings. Numerical simulations illustrate these properties for the US. We also apply our method to sign output distortions in other adverse selection frameworks with random participation, namely the monopoly nonlinear pricing and the regulatory monopoly problems.