A Note on Nonlinear Income Taxes and the Utility Possibility Set

This note analyzes constrained Pareto efficient nonlinear income tax schedules that are monotonic chains to the left. The main result demonstrates that if all individuals have a positive consumption at the tax schedule that maximizes the utility of the worst-off individual, then the constrained utility possibility set is convex. As a consequence, all constrained Pareto efficient nonlinear income tax schedules that are monotonic chains to the left can be identified by maximizing a weighted summation of net utilities.