# The optimal depletion of exhaustible resources: A complete characterization

*Hassan Benchekroun* () and
*Cees Withagen*

*Resource and Energy Economics*, 2011, vol. 33, issue 3, 612-636

**Abstract:**
Abstract We provide the closed form solution to the Dasgupta-Heal-Solow-Stiglitz (DHSS) model. The DHSS model is based on the seminal articles (Dasgupta and Heal, 1974) and (Solow, 1974) and Stiglitz (1974) and describes an economy with two assets, man-made capital and a nonrenewable resource stock. We explicitly characterize, for such an economy, the dynamics along the optimal trajectory of all the variables in the model and from all possible initial values of the stocks. We use the analytical solution to prove several properties of the optimal consumption path. In particular, we show that the initial consumption under a utilitarian criterion starts below the maximin rate of consumption if and only the resource is abundant enough and that under a utilitarian criterion, it is not necessarily the present generation that benefits most from a windfall of resources.

**Keywords:** Special; functions; Exponential; integral; Exhaustible; resources; Dasgupta-Heal-Solow-Stiglitz; economy (search for similar items in EconPapers)

**Date:** 2011

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**Related works:**

Working Paper: THE OPTIMAL DEPLETION OF EXHAUSTIBLE RESOURCES: A COMPLETE CHARACTERIZATION (2010)

Working Paper: The Optimal Depletion of Exhaustible Resources: A Complete Characterization (2010)

Working Paper: GLOBAL DYNAMICS IN A GROWTH MODEL WITH AN EXHAUSTIBLE RESOURCE (2008)

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:resene:v:33:y:2011:i:3:p:612-636

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