On the Optimal Rate Structure of an Individual Income Tax

Abstract

What is the optimal rate structure of a personal income tax? In the literature on optimal taxation this important question has been approached by introducing a linear income-tax formula into a revised Ramseyian model which takes into account both efficiency and equity objectives of taxation. The assumption of a linear tax enables us to examine the degree of tax progression through the behavior of the average rate, but it does not throw light on how the marginal rate should vary with income [1, Lecture 13]. A classic paper by Mirrlees [7], which was later expounded on by Atkinson and Stiglitz [1, 412-22], solves this problem by explicitly considering a general income tax schedule. However, both linear and general tax formulae provide little guide for policy making, since in practice the tax rates are graduated by a bracket system. That is, the income scale is divided into segments or brackets and rates are applied only to the income in each bracket. Rates increase (or decrease) by small percentage points from one bracket to the next, in order to avoid large and abrupt changes in tax burden as income rises. The present paper attempts to demonstrate how we can easily transform a segment-graduated tax system into a multiple linear system and then incorporate it into the standard optimum-taxation model. We then proceed to derive the conditions governing the optimal value of an upper (or lower) limit of a tax bracket and the marginal tax rate applied to the bracket. Combining these conditions together will enable us to infer what the optimal rate structure should be.