When a Price is Enough: Implementation in Optimal Tax Design

Abstract

This paper studies the design of tax systems that implement a planner's secondbest allocation in a market economy. An example shows that the widely used Mirrleesian (1976) tax system cannot implement all incentive-compatible allocations. Hammond's (1979) "principle of taxation" proves that any incentive-compatible allocation can be implemented through at least one tax system. However, this tax system is often undesirable since it severely restricts the choice space of agents in the economy. In this paper we derive necessary and sufficient conditions to verify whether a given tax system can implement a given incentive-compatible allocation. We show that when an incentive-compatible allocation is on the Pareto frontier, and/or surjective onto the choice space, a tax system that equates the marginal tax rates to the optimal wedges can implement the second best, without restricting the choice space of the agents. It follows that the Mirrleesian tax system can successfully implement the second best in the identified classes. Since the secondbest allocation of welfarist planners is always on the Pareto frontier, our results (ex post) validate most tax systems proposed in the literature. Outside of the identified classes, the planner may need to restrict the choice space of agents to implement its second best in the market. This sheds new light on rules, quotas and prohibitions used in real-world tax and benefit systems.

As Easy as ABC? Multidimensional Screening in Public Finance

“…The simulations reported in this paper show that such simulations are feasible, even though the multidimensional heterogeneity does set strong requirements on the optimization algorithm. In addition, the problem of implementation, which is discussed in Renes and Zoutman (2014), might add further difficulties. Implementation can proof especially difficult if there is bunching as well as separation.…”

“…Then additional constraints may need to be imposed on the tax function to ensure it implements the allocation in the market. However, proposition 1 of Renes and Zoutman (2014) shows that conditions the conditions in (32) are locally sufficient, provided the allocation {x (n) , y (n)} is optimal to a welfarist planner. Since the social planner in our model is indeed welfarist, this proposition applies here.…”

“…In our derivation we do not explicitly consider the optimal-tax system that implements the allocation in a market economy, nor do we address second-order constraints. In our simulations we ensure that second-order incentive constraints are not binding, while we know from Renes and Zoutman (2014) that a direct relation between the taxes and wedges exists. For technical convenience we discuss both issues separately in subsections 4.5 and 4.6.…”

Pareto-Efficient Tax Deductions

“…However, the open question is whether each individual bundle constitutes a global individual optimum. A theoretical analysis of this question is generally rather difficult (e.g., Renes and Zoutman, 2016). Therefore, our approach is to analyze the individual choice problem numerically.…”

Optimal Taxation of Capital Income with Heterogeneous Rates of Return

“…Renes and Zoutman (2014) show that separable tax schedules are sufficient to implement the full second-best optimum if there are no market failures, the government has a welfarist objective, and the population is characterized by onedimensional heterogeneity. These assumptions are fulfilled in our first microfoundation with type-dependent returns.…”