IDEAS home Printed from https://ideas.repec.org/p/mcl/mclwop/2010-01.html
   My bibliography  Save this paper

The Optimal Depletion Of Exhaustible Resources: A Complete Characterization

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mcgill.ca/files/economics/Benchekroun_Withagen.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(5), pages 29-45.
    5. repec:bla:scandj:v:96:y:1994:i:2:p:257-65 is not listed on IDEAS
    6. repec:bla:scandj:v:100:y:1998:i:2:p:513-27 is not listed on IDEAS
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hassan Benchekroun & Cees Withagen, 2008. "Global Dynamics In A Growth Model With An Exhaustible Resource," Departmental Working Papers 2008-01, McGill University, Department of Economics.
    2. Nick Hanley & Louis Dupuy & Eoin McLaughlin, 2015. "Genuine Savings And Sustainability," Journal of Economic Surveys, Wiley Blackwell, vol. 29(4), pages 779-806, September.
    3. Mitra, Tapan & Asheim, Geir B. & Buchholz, Wolfgang & Withagen, Cees, 2013. "Characterizing the sustainability problem in an exhaustible resource model," Journal of Economic Theory, Elsevier, vol. 148(5), pages 2164-2182.
    4. Antony, Jürgen & Klarl, Torben, 2022. "Poverty and sustainable development around the world during transition periods," Energy Economics, Elsevier, vol. 110(C).
    5. Antony, Jürgen & Klarl, Torben, 2023. "Subsistence consumption and natural resource depletion: Can resource-rich low-income countries realize sustainable consumption paths?," Journal of Macroeconomics, Elsevier, vol. 77(C).
    6. Adrian Boos, 2015. "Genuine Savings as an Indicator for “Weak” Sustainability: Critical Survey and Possible Ways forward in Practical Measuring," Sustainability, MDPI, vol. 7(4), pages 1-37, April.
    7. Smulders, Sjak & Withagen, Cees, 2012. "Green growth -- lessons from growth theory," Policy Research Working Paper Series 6230, The World Bank.
    8. 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.
    9. Jürgen Antony & Torben Klarl, 2019. "Non-Renewable Resources in a Ramsey Economy with Subsistence Consumption, Human and Physical Capital Accumulation: A full Characterization," Bremen Papers on Economics & Innovation 1904, University of Bremen, Faculty of Business Studies and Economics.
    10. Cairns, Robert D. & Martinet, Vincent, 2021. "Growth and long-run sustainability," Environment and Development Economics, Cambridge University Press, vol. 26(4), pages 381-402, August.
    11. Toman, Michael & Pezzey, John C., 2002. "The Economics of Sustainability: A Review of Journal Articles," RFF Working Paper Series dp-02-03, Resources for the Future.
    12. van der Ploeg, Frederick, 2010. "Why do many resource-rich countries have negative genuine saving?: Anticipation of better times or rapacious rent seeking," Resource and Energy Economics, Elsevier, vol. 32(1), pages 28-44, January.
    13. Growiec, Jakub & Schumacher, Ingmar, 2008. "On technical change in the elasticities of resource inputs," Resources Policy, Elsevier, vol. 33(4), pages 210-221, December.
    14. Geir B. Asheim, 2017. "Sustainable growth," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(3), pages 825-848, December.
    15. Daniele Schilirò, 2019. "Sustainability, Innovation, and Efficiency: A Key Relationship," Palgrave Studies in Impact Finance, in: Magdalena Ziolo & Bruno S. Sergi (ed.), Financing Sustainable Development, chapter 0, pages 83-102, Palgrave Macmillan.
    16. Pezzey, John C.V., 2001. "Exact Measures of Income in Two Capital-Resource Economies," 2001 Conference (45th), January 23-25, 2001, Adelaide, Australia 125834, Australian Agricultural and Resource Economics Society.
    17. Lucas Bretschger, 2013. "Population Growth and Natural-Resource Scarcity: Long-Run Development under Seemingly Unfavorable Conditions," Scandinavian Journal of Economics, Wiley Blackwell, vol. 115(3), pages 722-755, July.
    18. Simone Valente, 2005. "Sustainable Development, Renewable Resources and Technological Progress," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 30(1), pages 115-125, January.
    19. Dorothée Charlier & Florian Fizaine, 2020. "Does Becoming Richer Lead to a Reduction in Natural Resource Consumption? An Empirical Refutation of the Kuznets Material Curve," Working Papers 2020.05, FAERE - French Association of Environmental and Resource Economists.
    20. Mircea Sˇveanu, 2014. "Energy and the Economics of Sustainability. The Entropy Paradox," Management of Sustainable Development, Sciendo, vol. 6(1), pages 1-5, August.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mcl:mclwop:2010-01. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Shama Rangwala (email available below). General contact details of provider: https://edirc.repec.org/data/demcgca.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.