Resource and Energy Economics 25 (2003) 129–139 Optimally eating a stochastic cake: a recursive utility approach  Anne Epaulard a,1 , Aude Pommeret b,∗ a IMF Institute, Washington, DC 20431, USA b DEEP-HEC, Lausanne University, BFSH1, 1015 Lausanne, Switzerland Received 27 April 2001; received in revised form 29 April 2002; accepted 25 June 2002 Abstract In this short paper, uncertainties on resource stock and on technical progress are introduced into an intertemporal equilibrium model of optimal extraction of a non-renewable resource. The represen- tative consumer maximizes a recursive utility function which disentangles between intertemporal elasticity of substitution and risk aversion. A closed-form solution is derived for both the optimal extraction and price paths. The value of the intertemporal elasticity of substitution relative to unity is then crucial in understanding extraction. Moreover, this model leads to a non-renewable resource price following a geometric Brownian motion. © 2002 Elsevier Science B.V. All rights reserved. JEL classification: Q30; D81; Q11 Keywords: Non-renewable resource; Recursive utility; Uncertainty 1. Introduction How much of a non-renewable resource should we consume today if there exists a lack of precise knowledge about its available stock? Since 1970s, this general problem of optimal use has received considerable attention in the literature (see Gilbert, 1978; Kemp, 1976; Loury, 1978). Only recently have models been developed that explore the effects of un- certainty by allowing information to arrive over time: in 1980, Pindyck proposed a partial  The authors began this paper while Ms. Epaulard was professor of economics at the ´ Ecole Nationale de Statistique et d’Administration ´ Economique (ENSAE) in Paris and while Ms. Pommeret was a doctoral candidate at the Universit´ e Paris-I. ∗ Corresponding author. Tel.: +41-692-34-51; fax: +41-692-33-65. E-mail addresses: aepaulard@imf.org (A. Epaulard), aude.pommeret@hec.unil.ch (A. Pommeret). 1 Tel.: +1-202-623-43-69; fax: +1-202-623-60-71. 0928-7655/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII:S0928-7655(02)00022-2