We develop a methodology to sign output distortions in the random participation framework. We apply our method to monopoly nonlinear pricing problem, to the regulatory monopoly problem and mainly to the optimal income tax problem. In the latter framework, individuals are heterogeneous across two...

This paper develops a general method to solve the optimal nonlinear income tax model with one action (individual pre-tax income) and multidimensional characteristics. Individuals differ in terms of skills and belong to different groups. A group is a subset of individuals with the same vector of...

We derive a general optimal income tax formula when individuals respond along both the intensive and extensive margins and when income effects can prevail. Individuals are heterogeneous across two dimensions: their skill and their disutility of participation. Preferences over consumption and...

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...