The social discount rate: some implications of the budget-constrained opportunity cost approach

Abstract

The social discount rate is an important issue in the cost-benefit analysis for selecting public projects. However, there has been no general consensus as to the appropriate value of the social rate of discount for public investment. In 1987, Quirk and Terasawa proposed using the opportunity cost rate of return as an alternative approach to the choosing of the social discount rate in a fixed-budget scenario. Essentially, the appropriate value of the government rate of discount is the highest rate of return available from the portfolio of the unfunded government projects. In this study, the characteristics of the discount rates is explored in the context of choosing an efficient portfolio of government projects under a fixed budget condition. The costs and benefits of the projects are treated as variables and are to be endogenously determined by optimizing the overall discounted benefits. It is assumed that the costs and benefits of projects are known and continuous functions of force size, unit system maintenance and operational support. A mathematical model is used to represent the relationship between the benefit and cost of various projects. The Karesh-Kuhn-Tucker (KKT) convexity conditions are assumed for these so-called diminishing-return projects. In addition, two-year constant-returns-to-scale projects with fixed rates of return are introduced as reference projects such that their rates of return can be used directly as the discount rates under the concept of the opportunity cost rate of return. The discounted present values (DPV) of the net benefits of both the optimal and the non-optimal portfolios are found to be in agreement with those expected under the concept of the opportunity cost rate of return.