The Pareto-Frontier in a Simple Mirrleesian Model of Income Taxation

Abstract

We characterize the Pareto-frontier in a simple Mirrleesian model of income taxation. We show how the second-best frontier, which incorporates incentive constraints due to private information on productive abilities, relates to the first-best frontier, which takes only resource constraints into account. In particular, we argue that the second-best frontier can be interpreted as a Laffer-curve. We also use this second-best frontier for a comparative statics analysis of how optimal income tax rates vary with the degree of inequity aversion, and for a characterization of optimal public-good provision. We show that a more inequity-averse policy maker chooses tax schedules that are more redistributive and involve higher marginal tax rates, while simultaneously providing less public goods.* I. Introduction In this paper we characterize the set of Pareto-efficient allocations in a simple version of the MIRRLEES [1971] model of optimal nonlinear income taxation. We consider an economy where there are two types of individuals who differ in their productive abilities. Individuals have a linear effort cost, so that an individual’s marginal cost of contributing to the economy’s output is low if the individual is high-skilled and high if the individual is low-skilled. 1 We obtain the following results. First, we show how the second-best Pareto-frontier compares to the first-best Pareto-frontier in a model in which information about productive abilities is publicly observed. The first-best frontier is linear and there is neither a maximal, nor a minimal utility level for high-skilled or low-skilled individuals. With the second-best Pareto-frontier, by contrast, such maxima and minima exist. Moreover, we show that each point on the second-best Pareto-frontier is associated with a marginal income tax rate for low-skilled individuals, and a marginal income tax rate for high-skilled individuals. Both marginal tax rates are shown to be non-decreasing functions of the utility of the low-skilled individuals. The fact that there is a minimum of utility for the high-skilled individuals implies that the second-best frontier is similar to a Laffer-curve: 2 if the high-skilled individuals’ utility level fell below the minimal level, then an increase in their utility level would also make the low-skilled individuals better off. Moreover, the minimal utility level of the high-skilled individuals is