Some Simplified Formulae for Optimal Income Taxation

This paper attempts a reinterpretation of some results on optimal income taxation by recasting the model in a framework which makes it possible to use the analytical tools of optimal commodity taxation. In the context of a linear income tax this leads to three alternative formulae for the optimal marginal tax rate which highlight the equity-efficiency tradeoff more readily than previous formulations. Given the general equilibrium practice of treating labor services as just another commodity, we should expect the treatment of optimal income taxation to parallel that of commodity taxation. In fact there seems to be very little contact between the literature on the two. This is often confusing to students. To remedy this we take the model of optimal linear income taxation, due to Sheshinski (1972), and recast it in a framework which allows us to use the analytical tools of optimal commodity taxation. We first show that this leads to a tax formula which is similar to one of optimal commodity taxes when individuals are unequal. Next, we reformulate the model so as to achieve a result which is very similar to Diamond's (1975) work on commodity taxation; this result can be given in two alternative versions, each of which has an interesting economic interpretation. All three formulae can be interpreted in a way that highlights the equity-efficiency conflict more readily than previous formulations. There are several reasons for the usual differences in the treatments of the two cases. First, a non-linear schedule (with varying marginal tax rates) is commonly sought for income taxation, while commodity taxes are usually restricted to be linear, i.e. proportional to revenue in the ad valorem case or quantity in the specific case. But recent work by Mirrlees (1976) and Seade