Discount Rates for Public Investment in Closed and Open Economies

Abstract

Let us imagine a perfectly competitive economy operating under the usual neo-classical assumptions of decreasing returns, convexity of preferences, etc. To make our discussion simple we further limit ourselves to a one-good two-period framework, in which initial resources can be allocated to immediate consumption or to investment, and in which investment produces the goods available for future consumption. With a perfect loan market consumers will equate their marginal rates of time preference to the rate of interest, while private firms will carry investment to the point where the marginal productivity of private capital is equal to the interest rate. Suppose now thatfor reasons that we shall take as given-part of the total investment of the economy takes place in publicly-owned It is then obvious that the optimal amount of public investment is found by equating the marginal productivity of public investment to the market rate of interest; the marginal conditions for efficiency or Pareto-optimality will then be satisfied all around. Suppose now that are distortions in the economy, e.g. in the form of taxes, which prevent the equalization of marginal rates of substitution and transformation in the private sector. Then it is not any longer so easy to identify the correct rate of discount to use in the public sector. In a recent paper, Baumol [1]2 has argued that, under certain assumptions, the corporate income tax drives a wedge between the marginal rate of time preference of consumers and the marginal rate of transformation in private firms. Baumol concludes that in such a case there remains an inescapable indeterminacy in the choice of a discount rate on government projects, since this discount rate cannot simultaneously be equal to the marginal rate of time preference of consumers and the marginal productivity of private capital. Baumol further remarks that he can find no theoretical grounds for accepting either of these rates (or presumably any third alternative) as the appropriate discount rate to use in the public sector, and,that any choice of such a rate will to some extent be arbitrary. Our objective in this paper is to determine the rate of discount for public investment which is optimal on efficiency grounds, given that 1 We are indebted to Giorgio Basevi and Henry Tulkens for reading the manuscript of this paper and making useful suggestions. We also thank Maurice Mar