When a Price is Enough: Implementation in Optimal Tax Design

This paper studies the design of tax systems that implement a planner's second-best 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 second-best 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.