TAXING LEISURE COMPLEMENTS

I. INTRODUCTION Income taxation distorts labor effort downward. Accordingly, it tends to be optimal on second-best grounds to set other policy instruments so as to introduce additional distortions if (though only if) doing so helps to mitigate the excessive consumption of leisure. This principle has been considered most extensively with regard to differential commodity taxation. In a Ramsey setting, Corlett and Hague (1953) showed that it is optimal to tax complements to leisure and to subsidize substitutes--relatively speaking--which serves to offset the distorting effect of taxation on labor supply. Consider a simple example for concreteness. Begin with a labor income tax, which as is well known induces individuals to reduce labor effort, increasing leisure. (This is the substitution effect; even if the income effect is so large that uncompensated labor supply does not fall, it is the substitution effect that matters for efficiency.) Ideally, we would like to tax leisure directly or otherwise adjust the income tax to avoid this inefficiency, but this is assumed to be impossible because the government can only observe income and not the amount of labor effort that contributed to producing it. This preexisting inefficiency raises the possibility that other, more indirect, instruments may have a role to play, and indeed they do, specifically with regard to commodity taxation. To develop this possibility further, suppose that disposable income is spent on two goods, pizza and swimsuits. Think of pizza as a benchmark good that produces utility equally well in all settings, whether at work or at play, including at the beach or swimming pool. Swimsuits are classic leisure complements: having more swimsuits enhances utility to a greater extent the more time one has to swim, whereas swimsuits produce no additional value while at work. In this setting, the Corlett-Hague argument suggests the optimality of a relative tax on swimsuits. To be sure, this will impose an efficiency cost by distorting individuals' consumption (too few swimsuits, too much pizza) but that cost is second order as the tax is imposed starting at a level of 0. The other effect of the tax will be to make leisure less attractive, now that individuals consume fewer swimsuits. This, in turn, will raise labor effort. Since labor is distorted downward by the income tax, this effect entails a first-order efficiency gain. Therefore, it is indeed the case that imposing some positive relative tax on swimsuits, the leisure complement, is optimal. Analysis of these matters became more formal with Atkinson and Stiglitz's (1976) seminal examination of the simultaneous optimization of a nonlinear income tax and commodity taxes. The article is most famous for its uniformity result: if labor is weakly separable in the utility function, the optimum is characterized by no differential commodity taxation. (1) Although many Ramsey principles (e.g., the inverse elasticity rule) do not survive the introduction of an income tax, the Corlett-Hague result that it tends to be optimal to tax leisure complements and subsidize substitutes is widely understood to remain intact. (2) Surprisingly, this generally accepted understanding seems to be contradicted by Atkinson and Stiglitz (1976). Their central analytical contribution in the relevant part of the article is their derivation of an expression for optimal taxation of any given commodity (relative to the tax rate on commodity 1, arbitrarily set equal to 0 as a benchmark). First, they use their derivation to establish their uniformity result in the case of weak separability. When the utility function has the stated feature, one of the terms in their expression for the optimal commodity tax rate on good i equals 0 (and this is true for all i), so no commodity taxation is optimal. However, regarding the more general case, Atkinson and Stiglitz (1976) state: "From the results given above, it follows that goods which are complementary . …