Optimal income taxation without single-crossing

In this paper we set up a simple two-type optimal nonlinear income tax model where the single-crossing condition is violated, and we characterize the properties of a second-best optimum by considering the entire second-best Pareto frontier. The violation of single-crossing is generated by the assumption that agents dier both in terms of market abilities and in terms of their needs for a work-related good. Our analysis highlights several non-standard features of a second-best optimum. In particular, we show that a nonlinear income tax may allow the government to convert a pooling laissez-faire equilibrium into a separating equilibrium, that the second-best Pareto frontier may be discontinuous, and that a second-best optimum may not preserve the income ranking prevailing under laissez-faire. Finally, we also show that at a second-best optimum the labor supply of some agents might be distorted even though no self-selection constraint is (locally) binding in equilibrium.