Discount Rates and Public Investment: A Post-Scriptum

Abstract

1. Shortly after the publication of the paper by Sandmo and myself on Rates for Public Investment in Closed and Open Economies (Economica, November 1971), my attention has been drawn to a manuscript on the same subject by Mr. John Kay entitled Social Discount Rates.2 Kay reproduces and extends arguments introduced by K. J. Arrow in a paper Sandmo and I had unfortunately overlooked (Discounting and Public Investment Criteria, in Water Research, Kneese and Smith, Editors, Baltimore, Resources for the Future, 1966). The conclusions reached by Arrow and Kay seem to be at variance with those reached by Sandmo and myself. For the case of a closed economy, we conclude the public sector's discount rate should be a weighted average of the rate facing consumers and the tax-distorted rate used by firms, (loc. cit. p. 401). Arrow, on the other hand, argues that the optimal policy for taxation and public capital formation will be which equates the marginal productivity of public investment to the consumption rate of interest (loc. cit. p. 26). The divergence of conclusions has both logical and practical relevance.3 Since both analyses are formally correct (at least to my satisfaction), the divergence in the conclusions stems from diverging assumptions. The purpose of this post-scriptum is to acquaint those economists who read Economica, but do not keep up with water research, with Arrow's line of analysis; to explain where the divergences between the two approaches originate and how they can be reconciled; and to comment briefly on the policy recommendations implied by this comparison. This exercise may also serve as a useful illustration of some pitfalls connected with alternative approaches to intertemporal allocation problems. My purpose requires an extension of the SandmoDreze analysis to n periods; the technical development of this extension is