The Lorenz curve of income after tax is known to dominate the one before tax for all given pre-tax income distributions, if, and only if, average tax liability is increasing with income (Jakobsson 1976; Eichhorn et al. 1984). It is shown in this note that the absolute inequality of incomes (Kolm 1976) is unambiguously reduced by taxation if, and only if, tax liability is increasing with income.
It is a pleasure to acknowledge the intellectual debt I owe to W. Eichhorn, H. Funke, and W. F. Richter whose result on progressive taxation and income inequality stimulated the present research. I am grateful to an anonymous referee whose comments on an earlier draft improved the paper.