Optimal income taxation with discrete skill distribution

This paper studies the pattern of the optimal marginal income tax rates in a discrete model allowing all forms of individual skill distribution. It derives an explicit solution to the optimal marginal income tax rates in terms of the parameters of the model, and then rigorously shows the optimal marginal tax rate can be U-shaped, inverse U-shaped, strictly increasing, or strictly decreasing in the interior of skill levels, depending crucially on skill distribution. The numerical examples indicate that the optimal marginal tax rates can be W-shaped and inverse W-shaped in the interior of skill levels. The explicit solution to the optimal marginal income tax rate derived in this discrete model can be used to find optimal marginal income tax rates for an economy with any empirical skill distribution, without the need to estimate the density function of skill.