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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. 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.
    7. Partha Dasgupta & Geoffrey Heal, 1974. "The Optimal Depletion of Exhaustible Resources," Review of Economic Studies, Oxford University Press, vol. 41(5), pages 3-28.
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    Cited by:

    1. Hala Abu-Kalla & Ruslana Rachel Palatnik & Ofira Ayalon & Mordechai Shechter, 2020. "Hoard or Exploit? Intergenerational Allocation of Exhaustible Natural Resources," Energies, MDPI, Open Access Journal, vol. 13(24), pages 1-20, December.
    2. Ngo Long & Vincent Martinet, 2018. "Combining rights and welfarism: a new approach to intertemporal evaluation of social alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(1), pages 35-64, January.
    3. Cairns, Robert D. & Del Campo, Stellio & Martinet, Vincent, 2019. "Sustainability of an economy relying on two reproducible assets," Journal of Economic Dynamics and Control, Elsevier, vol. 101(C), pages 145-160.
    4. Bosi, Stefano & Desmarchelier, David, 2018. "An economic model of metapopulation dynamics," Ecological Modelling, Elsevier, vol. 387(C), pages 196-204.
    5. Kaniovski, Serguei, 2017. "The Optimal Use of Exhaustible Resources under Nonconstant Returns to Scale," VfS Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168079, Verein für Socialpolitik / German Economic Association.
    6. Antony, Jürgen & Klarl, Torben, 2019. "Non-renewable resources, subsistence consumption, and Hartwick's investment rule," Resource and Energy Economics, Elsevier, vol. 55(C), pages 124-142.
    7. 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.
    8. Smulders, Sjak & Withagen, Cees, 2012. "Green growth -- lessons from growth theory," Policy Research Working Paper Series 6230, The World Bank.
    9. Hooper, Emma, 2019. "Sustainable growth and financial markets in a natural resource-rich country," Structural Change and Economic Dynamics, Elsevier, vol. 51(C), pages 341-348.
    10. Cees A. Withagen, 2018. "The Social Cost of Carbon and the Ramsey Rule," CESifo Working Paper Series 7359, CESifo.
    11. Emma Hooper, 2015. "Sustainable Growth and Financial Markets in a Natural Resource Rich Country," Working Papers halshs-01119420, HAL.
    12. van der Meijden, Gerard & Smulders, Sjak, 2018. "Technological Change During The Energy Transition," Macroeconomic Dynamics, Cambridge University Press, vol. 22(4), pages 805-836, June.
    13. Antony, Jürgen & Klarl, Torben, 2019. "Resource depletion in a Ramsey economy with subsistence consumption, exogenous technical change and capital depreciation: A full characterization," VfS Annual Conference 2019 (Leipzig): 30 Years after the Fall of the Berlin Wall - Democracy and Market Economy 203640, Verein für Socialpolitik / German Economic Association.
    14. Emma Hooper, 2015. "Sustainable growth and financial markets in a natural resource rich country," AMSE Working Papers 1510, Aix-Marseille School of Economics, France.
    15. Kakeu, Johnson & Nguimkeu, Pierre, 2017. "Habit formation and exhaustible resource risk-pricing," Energy Economics, Elsevier, vol. 64(C), pages 1-12.
    16. Sjak Smulders & Michael Toman & Cees Withagen, 2014. "Growth Theory and “Green Growthâ€," OxCarre Working Papers 135, Oxford Centre for the Analysis of Resource Rich Economies, University of Oxford.
    17. 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.
    18. 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.
    19. Germain, Marc, 2019. "Georgescu-Roegen versus Solow/Stiglitz: Back to a controversy," Ecological Economics, Elsevier, vol. 160(C), pages 168-182.
    20. Robert D. Cairns, 2011. "Accounting for Sustainability: A Dissenting Opinion," Sustainability, MDPI, Open Access Journal, vol. 3(9), pages 1-16, August.
    21. Sergey Aseev & Konstantin Besov & Serguei Kaniovski, 2016. "The Optimal Use of Exhaustible Resources Under Non-constant Returns to Scale," WIFO Working Papers 525, WIFO.

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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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