On Optimal Taxation and Public Production

Abstract

In a perfectly competitive economy where lump sum transfers between individuals are not feasible one would like to see the government using taxation and public investment as a means of improving the distribution of income. When commodities that enter into individual utilities are taxed, the conditions for Pareto Optimality are violated. That is to say, in the absence of the possibility of lump sum transfers between individuals, maximizing social welfare might well entail the economy operating inside the utility possibility set. The question, nevertheless, remains as to whether one would like to achieve over-all production efficiency at the optimum. Put another way, one would like to know if social welfare can be increased by the government setting different prices to different producers of the same commodity. In a recent paper [1], Diamond and Mirrlees have addressed themselves to this question, among others, and have established the result that under various circumstances (e.g. that there are no restrictions on commodity taxation), one would require production efficiency at the social optimum. In their paper Diamond and Mirrlees assume that private producers face constant-returns-to-scale production schedules, so that individual utilities depend solely on consumer prices and the supply of public goods. In this and an earlier paper [3], we have been concerned with establishing exactly how robust that result is. In the earlier study, we showed that when there are restrictions on the set of taxes which the government can impose, e.g. when there is a maximum rate (less than 100 per cent) at which pure profits and rents may be taxed, or when two commodities must betaxed at the same rate, or when a tax cannot be imposed on the output of some industry, or when there is an over-all budget constraint facing the government then, even when all individuals are identical, production efficiency will not be optimal. In this paper, we show that if there are enough instruments, in particular, if the government can set different percentage profit (rent) taxes to different producers up to and including 100 per cent (but lump sum taxes are still not allowed), production efficiency is desirable even with non-constant returns to scale in the private sector. In a section of our earlier paper [3], we addressed ourselves to this question in the context of a single consumer economy. There we established the result that if government losses exceed the total of all rents (profits) from the private sector, then at the optimum one would want to tax all profits away (i.e. set 100 per cent profit tax on all private producers) and use distortionary commodity taxes to balance the government budget. In