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The Optimal Depletion of Exhaustible Resources : A Complete Characterization


  • WITHAGEN, Cees


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

    1. 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.
    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. R. M. Solow, 1974. "Intergenerational Equity and Exhaustible Resources," Review of Economic Studies, Oxford University Press, vol. 41(5), pages 29-45.
    4. Asheim, Geir B, 1994. " Net National Product as an Indicator of Sustainability," Scandinavian Journal of Economics, Wiley Blackwell, vol. 96(2), pages 257-265.
    5. 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.
    6. 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.
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    Cited by:

    1. Gerard van der Meijden & Sjak Smulders, 2014. "Technological Change during the Energy Transition," Tinbergen Institute Discussion Papers 14-108/VIII, Tinbergen Institute.
    2. Emma Hooper, 2015. "Sustainable growth and financial markets in a natural resource rich country," AMSE Working Papers 1510, Aix-Marseille School of Economics, Marseille, France.
    3. Kaniovski, Serguei, 2017. "The Optimal Use of Exhaustible Resources under Nonconstant Returns to Scale," Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168079, Verein für Socialpolitik / German Economic Association.
    4. repec:eee:eneeco:v:64:y:2017:i:c:p:1-12 is not listed on IDEAS
    5. Sjak Smulders & Michael Toman & Cees Withagen, 2014. "Growth theory and ‘green growth’," Oxford Review of Economic Policy, Oxford University Press, vol. 30(3), pages 423-446.
    6. Roy Cerqueti & Raffaella Coppier & Gustavo Piga, 2012. "Corruption, growth and ethnic fractionalization: a theoretical model," Journal of Economics, Springer, vol. 106(2), pages 153-181, June.
    7. repec:spr:sochwe:v:50:y:2018:i:1:d:10.1007_s00355-017-1073-5 is not listed on IDEAS
    8. André, Francisco J. & Smulders, Sjak, 2014. "Fueling growth when oil peaks: Directed technological change and the limits to efficiency," European Economic Review, Elsevier, vol. 69(C), pages 18-39.
    9. Ruiz-Tamarit, J.R. & Ventura-Marco, M., 2011. "Solution to nonlinear MHDS arising from optimal growth problems," Mathematical Social Sciences, Elsevier, vol. 61(2), pages 86-96, March.
    10. Robert D. Cairns, 2011. "Accounting for Sustainability: A Dissenting Opinion," Sustainability, MDPI, Open Access Journal, vol. 3(9), pages 1-16, August.
    11. Smulders, Sjak & Withagen, Cees, 2012. "Green growth -- lessons from growth theory," Policy Research Working Paper Series 6230, The World Bank.
    12. Sergey Aseev & Konstantin Besov & Serguei Kaniovski, 2016. "The Optimal Use of Exhaustible Resources Under Non-constant Returns to Scale," WIFO Working Papers 525, WIFO.
    13. Emma Hooper, 2015. "Sustainable Growth and Financial Markets in a Natural Resource Rich Country," Working Papers halshs-01119420, HAL.

    More about this item


    Exhaustible resources; Dasgupta-Heal-Solow-Stiglitz economy; exponential integral;

    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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