Choosing the tax rate in a linear income tax structure: an introduction

Abstract

This paper provides an introduction to modelling the choice of linearincome tax rate in both majority voting and social welfare maximisingcontexts. Although the basic problem in each case — of findingthe most preferred tax for the median voter and the welfare maximisingtax for an independent judge or decision-maker — can be simplystated, it is usually not possible to obtain explicit solutions even forsimple assumptions about preferences and population heterogeneity.The present paper instead gives special attention to a formulation ofthe required conditions in terms of easily interpreted magnitudes, theelasticity of average earnings with respect to the tax rate and a measureof inequality. The inequality measure takes the same basic formin each model (depending either on median earnings or a weightedaverage of earnings, where the weights depend on value judgementsregarding inequality aversion. The approach enables the comparativestatic effects of a range of parameter changes to be considered. Theresults are reinforced using numerical examples based on the constantelasticity of substitution utility function.