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The Optimal Depletion of Exhaustible Resources : A Complete Characterization

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  • BENCHEKROUN, Hassan
  • WITHAGEN, Cees

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 (Rev. Econ. Stud.,1974), Solow (Rev. Econ. Stud.,1974) and Stiglitz (Rev. Econ. Stud.,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.

Suggested Citation

  • BENCHEKROUN, Hassan & WITHAGEN, Cees, 2010. "The Optimal Depletion of Exhaustible Resources : A Complete Characterization," Cahiers de recherche 04-2010, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    • Handle: RePEc:mtl:montec:04-2010
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    References listed on IDEAS

    as
    1. R. M. Solow, 1974. "Intergenerational Equity and Exhaustible Resources," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(5), pages 29-45.
    2. Boucekkine, R. & Ruiz-Tamarit, J.R., 2008. "Special functions for the study of economic dynamics: The case of the Lucas-Uzawa model," Journal of Mathematical Economics, Elsevier, vol. 44(1), pages 33-54, January.
    3. repec:bla:scandj:v:100:y:1998:i:2:p:513-27 is not listed on IDEAS
    4. Joseph Stiglitz, 1974. "Growth with Exhaustible Natural Resources: Efficient and Optimal Growth Paths," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(5), pages 123-137.
    5. John Hartwick & Ngo Van Long & Huilan Tian, 2003. "On the Peaking of Consumption with Exhaustible Resources and Zero Net Investment," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 24(3), pages 235-244, March.
    6. Robert M. Solow, 1974. "The Economics of Resources or the Resources of Economics," Palgrave Macmillan Books, in: Chennat Gopalakrishnan (ed.), Classic Papers in Natural Resource Economics, chapter 12, pages 257-276, Palgrave Macmillan.
    7. Asheim, Geir B. & Buchholz, Wolfgang & Hartwick, John M. & Mitra, Tapan & Withagen, Cees, 2007. "Constant savings rates and quasi-arithmetic population growth under exhaustible resource constraints," Journal of Environmental Economics and Management, Elsevier, vol. 53(2), pages 213-229, March.
    8. repec:bla:scandj:v:96:y:1994:i:2:p:257-65 is not listed on IDEAS
    9. Partha Dasgupta & Geoffrey Heal, 1974. "The Optimal Depletion of Exhaustible Resources," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(5), pages 3-28.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Exhaustible resources; Dasgupta-Heal-Solow-Stiglitz economy; exponential integral;
    All these keywords.

    JEL classification:

    • E20 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - General (includes Measurement and Data)
    • Q30 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation - - - General
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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