On the undesirability of commodity taxation even when income taxation is not optimal

An important result due to Atkinson and Stiglitz (1976) [Atkinson, A.B., Stiglitz, J.E., 1976. The design of tax structure: Direct versus indirect taxation. Journal of Public Economics 6, 55–75.] is that differential commodity taxation is not optimal in the presence of an optimal nonlinear income tax (given weak separability of utility between labor and all consumption goods). This article demonstrates that this conclusion holds regardless of whether the income tax is optimal. In particular, given any commodity tax and income tax system, differential commodity taxation can be eliminated in a manner that results in a Pareto improvement. Also, differential commodity taxation can be proportionally reduced so as to generate a Pareto improvement. In addition, for commodity tax reforms that neither eliminate nor proportionally reduce differential taxation, a simple efficiency condition is offered for determining whether a Pareto improvement is possible.