Optimal nonlinear income tax and nonlinear pricing: optimality conditions and comparative static properties

Using the Mirrlees optimal income tax model, with no income effects on labour supply, this article shows that the discrete population approach provides new insights into the characterization of the optimal tax system, which complements the previous findings. The analysis is based on the “Spence-Mirrlees wedge” which corresponds, at each observed gross income level, to a ratio between the marginal tax rate of the individual for whom the bundle is designed and that of his nearest more productive neighbour if he chooses to mimic. Using this wedge, a necessary and sufficient condition for bunching to be optimal is obtained in terms of the primitives of the model, separating optima are characterized geometrically, and comparative statics properties derived, notably with respect to skill levels and individual social weights. It is then shown that the analysis extends to adverse-selection problems where participation constraints replace the tax revenue constraint.