What Is Wrong with the Flat Tax?

The simplest flat tax proposals envisage a single marginal tax rate applying on all income. In the context of a simple model where agents vary in ability to earn, we demonstrate (a) that everyone is better off in the long run with an income-tax exemption for investment, than without it, and (b) that, in a static context, the optimal two-rate income tax is Pareto-superior to the optimal single-rate tax, under both Utilitarian and Rawlsian welfare functions.