A Characterization of Optimal Feasible Tax Mechanism

This paper is motivated by a practical income (or wealth) taxation problem: For a public good economy where the provision of public goods is to be financed by income taxes collected from individuals, what is the optimal feasible tax mechanism when a social planner is relatively uninformed of the incomes or endowments of the individuals? This kind of problem, the optimal private provision of public goods, is a typical Bayesian mechanism design question for a small economy such as a club. In this case, the social planner has to take into account not only the individuals' incentive to report their income truthfully, but also the (individual) feasibility of the designed tax mechanism in the sense that each individual's tax payment should be consistent with their ability to pay. We employ the feasible implementation model used in Hurwicz, Maskin, and Postlewaite [1995] to study such an optimal taxation problem. It has been assumed in the standard model of optimal labor income taxation literature, pioneered by Mirrlees [1971], that there is a continuum of individuals and the (labor) income is observable to avoid the feasibility problem. Also, the literature on private provision of public goods has paid little attention to the continuous provision of public goods and the constrained efficiency under incomplete information. This paper considers a finite economy where public goods are provided continuously. Using a simple Bayesian model, we provide the full characterization of the two-agent, two-type optimal feasible tax mechanism and its properties. We find that (i) when the total endowment of the economy is relatively low enough or high enough, the first best feasible taxation can be obtained; (ii) the second best feasible tax mechanism requires a poor agent to pay relatively more than a rich agent, that is, it is regressive; and (iii) the tax mechanism is increasing in the sense that the agent's tax payment increases with his endowment. We also provide a comparative statics analysis. For the case of more than two agents, under certain mild assumptions we give some partial results similar to (i) and (ii) above. In addition, we find the optimal feasible tax mechanism for the corresponding infinitely large economy