Queen's Economics Department Working Paper No. 1073
Using the Mirrlees optimal income tax model with a maxi-min social welfare function, we derive conditions for a decreasing marginal tax rate throughout the skill distribution, a strictly concave tax function in income and a single-peaked average tax schedule. With additive preferences and a constant labor supply elasticity, marginal tax rates are decreasing below the modal skill level, and will also decrease above the mode if aggregate skills are non-decreasing with the skill level. In this case and with a bounded skill distribution or with a constant hazard rate, the tax function is strictly concave in income and the average tax rate single-peaked. When quasilinear utility functions apply in either consumption or leisure, under fairly mild restrictions on the truncated or untruncated distribution function, marginal tax rates are decreasing in skill and the average tax profile is single-peaked. The distribution of skills has the same qualitative influence for either case of quasilinearity. These results continue to hold when there is bunching at the bottom due to a binding non-negativity constraint. We also illustrate how relaxing the assumption of constant elasticity of labor supply, generally used in the literature, modifies the results.