In this paper we extend the dimensionality of the standard income taxation problem. Specifically, we allow agents to purchase at a price, from the government, discounts on their marginal tax rates. Consequently agents have two decision variables: the level of income they choose to earn and the...

We prove in the context of optimal taxation that the utility possibility frontier can be reached with step functions. This opens a possibility of existence of legitimate - with suitably chosen marginal social welfare weights - optimal taxation problems that admit solutions of a different form...