Optimally eating a stochastic cake: a recursive utility approach

• Published in: Resource and energy economics Vol. 25; no. 2; pp. 129 - 139
• Main Authors: Epaulard, Anne, Pommeret, Aude
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.05.2003; Elsevier; Elsevier Sequoia S.A
• Series: Resource and Energy Economics
• Subjects: Applied sciences; Economic data; Economic theory; Energy; Energy economics; Energy resources; Exact sciences and technology; General, economic and professional studies; Methodology. Modelling; Non-renewable resource; Optimization; Recursive utility; Renewable resources; Stochastic models; Studies; Uncertainty; Q11; Non-renewable resource; Uncertainty; Recursive utility; D81; Q30; Natural resources; Reserve; Technical progress; Energy economy; Econometric model; Recursive function; Stochastic process; Risk aversion; Brownian motion; Optimal strategy; Substitution; Price; Resource management; Ratio of economic flexibility
• ISSN: 0928-7655; 1873-0221
• DOI: 10.1016/S0928-7655(02)00022-2

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 representative 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.