Income Inequality and Tax Progression

Asuming that the population size is fixed, this paper attempts to develop necessary and sufficiant conditions for a tax function to be unambiguously inequality reducing. I. IntroductionThe relationship between tax progressivity and income inequality has been studied by many authors in recent times.Kakwani ( 1977) showed that average progression, that is, increasing average tax liability will make the post-tax distribution more equitable than the pre-tax distribution according to the Lorenz criterion.Jakobsson ( 1976) and later on Eichhorn, Funke and Richter ( 1984) and Thon (1987) showed that the implication is, in fact, an equivalence.Precisely it is proved that the Lorenz curve of income after tax will dominate the one before tax if and only if the tax function is average progressive and weekly incentive preserving, where weak incentive preservation (IP) means that the post-tax income is a non-decreasing function of the pre-tax income [see Eichhorn, Funke and Richter (1984)]l.This result is based on a particular concept of distributive justice which demands invariance of inequality under equiproportionate changes in all incomes.Inequality indices satisfying this property are called relative indices.Another possibility is to assume that inequality incices are of absolute type-they should remain unaltered under equal absolute changes in all incomes.The problem of choice between these two approaches is essentially a matter of value judgement and a discussion on their relative merits and demerits could be endless [see Kolm (1976) and Blackorby and Donaldson ( 1980)] .The absolute counterpart to the Eichhorn-Funke-Richter (EFR) result is due to Moyes ( 1988).He showed that minimal progressivity (that is, increasingness of the tax liability) along with IP is necessary and sufficient for the tax function to be uniformly equalizing according to ' We wish to thank to W. Bossert and P.J. Lambert for helpful comments.We are also grateful to a referee for suggestions on an earlier draft.l For demonstrating that an average progressive tax function reduces mequality.Kakwani (1977) implicitly assumed that it is weakly incentive preserving.In fact, in almost all such distributional compansons, the preservation property is taken as an assumption.See, for example.Jakobsson (1976), Lambert (1989) and Chakravarty (1990).