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The Optimal Depletion Of Exhaustible Resources: A Complete Characterization

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  • Hassan Benchekroun
  • Cees Withagen

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

  • Hassan Benchekroun & Cees Withagen, 2010. "The Optimal Depletion Of Exhaustible Resources: A Complete Characterization," Departmental Working Papers 2010-01, McGill University, Department of Economics.
    • Handle: RePEc:mcl:mclwop:2010-01
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. R. M. Solow, 1974. "Intergenerational Equity and Exhaustible Resources," Review of Economic Studies, Oxford University Press, vol. 41(5), pages 29-45.
    5. Asheim, Geir B, 1994. " Net National Product as an Indicator of Sustainability," Scandinavian Journal of Economics, Wiley Blackwell, vol. 96(2), pages 257-265.
    6. Pezzey, John C V & Withagen, Cees A, 1998. " The Rise, Fall and Sustainability of Capital-Resource Economies," Scandinavian Journal of Economics, Wiley Blackwell, vol. 100(2), pages 513-527, June.
    7. 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.
    8. 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.
    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.
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    More about this item

    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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