We characterize optimal policies in a multidimensional nonlinear taxation model with bunching. We develop an empirically relevant model with cognitive and manual skills, firm heterogeneity, and labor market sorting. The analysis of optimal policy is based on two main results. We first derive an optimality condition − a general ABC formula − that states that the entire schedule of benefits of taxes second order stochastically dominates the entire schedule of tax distortions. Second, we use Legendre transforms to represent our problem as a linear program. This linearization allows us to solve the model quantitatively and to precisely characterize the regions and patterns of bunching. At an optimum, 9.8 percent of workers is bunched both locally and nonlocally. We introduce two notions of bunching – blunt bunching and targeted bunching. Blunt bunching constitutes 30 percent of all bunching, occurs at the lowest regions of cognitive and manual skills, and lumps the allocations of these workers resulting in a significant distortion. Targeted bunching constitutes 70 percent of all bunching and recognizes the workers’ comparative advantage. The planner separates workers on their dominant skill and bunches them on their weaker skill, thus mitigating distortions along the dominant skill dimension. Tax wedges are particularly high for low skilled workers who are bluntly bunched and are also high along the dimension of comparative disadvantage for somewhat more skilled workers who are targetedly bunched.
We consider the problem of revenue-maximizing Bayesian auction design with several i.i.d. bidders and several items. We show that the auctiondesign problem can be reduced to the problem of continuous optimal transportation introduced by Beckmann (1952). We establish the strong duality between the two problems and demonstrate the existence of solutions. We then develop a new numerical approximation scheme that combines multi-tosingle-agent reduction and the majorization theory insights to characterize the solution.