The Optimal Income Tax: Restatement and Extensions

The paper presents an axiomatic restatement of the standard approach to nonlinear income taxation. It assumes a finite number of taxpayers rather than an uncountable infinity. Analytical tools are developed which facilitate proving the existence of tax schedules that are continuous, differentiable almost everywhere, and possess left-and right-derivatives at every point of non-differentiability. These tax schedules even become differentiable in the limit. Numerical examples are provided.