On the Welfare Improving Trade in Marginal Tax Rates

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 magnitude of discount they want to purchase at a given price. By rationally choosing to purchase discounts agents face lower effective marginal tax rates, which enhances efficiency. At the same time agents pay a price for the discounts, which can compensate for a shortfall in revenue resulting from lower eiquest;ective marginal tax rates. We show, in the case of the CRRA utility function, that for any tax function it is always possible to construct the corresponding discount price function that leads to a strict Pareto improvement through trade in discounts and that ensures that revenue collected is unaffected when trade in discounts is permitted. In addition, we show that a fat tax or a piece-wise linear tax function are never optimal in the Mirrlees's sense. Similarly, we argue that trade in discounts can lead to a Pareto improvement over the allocation induced by any tax function, including Mirrlees's solutions, that has an existing inverse and is differentiable. We also show that the standard asymptotic result of zero marginal tax rate at the top of income distribution can be extended to an open set. It is shown in the dynamic context that no tax function can be optimal unless it is conditioned on the entire income history