Discounting an uncertain future

We discuss the selection of the socially optimal discount rate for public investment projects that entail costs and benefits in the very long run. More specifically, we examine in an expected utility framework how the uncertainty on the growth rate of the GNP per head affects this rate. Under various conditions on preferences, as positive prudence, decreasing relative risk aversion or decreasing absolute risk aversion, we prove that (1) the fact that growth is uncertain reduces the optimal discount rate, and (2) that this discount rate should be smaller the longer the time horizon is. This rate could even become zero or negative if there is a positive probability that growth be negative. We also examine the case of Kreps-Porteus social welfare functions.