Choosing the tax rate in a linear income tax structure

This paper considers the choice of linear income tax rate in both majority voting and social welfare maximising contexts. Although the basic problem in each case - of finding the most preferred tax for the median voter and the welfare maximising tax for an independent judge or decision-maker - can be simply stated, it is usually not possible to obtain explicit solutions even for simple assumptions about preferences and population heterogeneity. The present paper instead gives special attention to a formulation of the required conditions in terms of easily interpreted magnitudes, the elasticity of average earnings with respect to the tax rate and a measure of inequality. The inequality measure takes the same basic form in each model, depending either on median earnings or a weighted average of earnings where the weights depend on value judgements regarding inequality aversion. The approach enables the comparative static effects of a range of parameter changes to be considered. The results are reinforced using numerical examples based on the constant elasticity of substitution utility function.