Some Properties of the Optimal Income-Tax

Abstract

This paper explores the properties of optional income taxation when individuals differ in productive ability. Interest in this question can stem from either or both of two considerations. One is the fact that disparities in abilities will lead to inequalities in well-being among individuals. Tax policies can be developed to ameliorate such inequalities. This was the major concern of nineteenth century utilitarians and gave rise to minimum sacrifice theories of taxation. A second consideration arises from the fact that income taxation, for whatever purpose, will generally distort the allocation of resources in an economy. Because an individual's innate ability is difficult to measure objectively, taxes must be based upon the manifestation of this ability in the market place, i.e., earned income. As a consequence, individuals have incentives to alter their effective supply of labor, resulting in excess burden. Thus the policy-maker is confronted with the task of designing a tax structure which minimizes excess burden. This aspect of taxation has come under heavy scrutiny by economists in the past decade, giving rise to various optimal tax rules. With one major exception, however, the literature has restricted its attention to unit taxes on commodities or linear taxes upon income. In a seminal work, Mirrlees [8], examined the question of optimal income taxation without imposing the condition of linearity and within a framework which incorporated both equity and efficiency criteria. His numerical analysis seemed to suggest that an optimal income tax was apt to be far less progressive than utilitarian concepts would lead us to suspect. Indeed, in recent extensions, Phelps [10] and Sadka [11] demonstrated that the optimal marginal tax rate on the highest income bracket is zero!2 Despite the obvious policy significance of Mirrlees' work, it is reasonable to assert that his analysis is not widely understood by most economists. In part this reflects the complexity of the problem, but more importantly it owes to his use of variational techniques. The latter makes the analysis cumbersome and the findings difficult to interpret.