IDEAS home Printed from https://ideas.repec.org/p/mse/cesdoc/09012.html
   My bibliography  Save this paper

Zero discounting and optimal paths of depletion of an exhaustible resource with an amenity value

Author

Abstract

This paper studies the undiscounted utilitarian optimal paths of the canonical Dasgupta-Heal-Solow model when the stock of natural capital is a direct argument of well-being, besides consumption. We use a Keynes-Ramsey rule wich yields a generalization of Hartwick's rule: if society has a zero discount rate but is ready to accept intertemporal substitution, net investment should not be zero as in the maximin case but should be positive, its level depending on the distance between the current and the long run bliss level of utility. We characterize solutions in the Cobb-Douglas utility and production case, and analyse the influence of the intertemporal elasticity of substitution on the time profile of the optimal paths. We show that, in the Cobb-Douglas case, the ratio of the values of the resource and capital stocks remains constant along the optimal path, and is independent of initial conditions

Suggested Citation

  • Antoine d'Autume & Katheline Schubert, 2009. "Zero discounting and optimal paths of depletion of an exhaustible resource with an amenity value," Documents de travail du Centre d'Economie de la Sorbonne 09012, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  • Handle: RePEc:mse:cesdoc:09012
    as

    Download full text from publisher

    File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2009/09012.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. John Hartwick, 1977. "Intergenerational Equity and the Investment of Rents from Exhaustible Resources in a Two Sector Model," Working Paper 281, Economics Department, Queen's University.
    2. Mitra, Tapan, 1980. "On Optimal Depletion of Exhaustible Resources: Existence and Characterization Results," Econometrica, Econometric Society, vol. 48(6), pages 1431-1450, September.
    3. Jeffrey A. Krautkraemer, 1985. "Optimal Growth, Resource Amenities and the Preservation of Natural Environments," Review of Economic Studies, Oxford University Press, vol. 52(1), pages 153-169.
    4. Roger Guesnerie, 2007. "Commentaires sur le rapport Stern : Quelques mots d'introduction," Revue d'économie politique, Dalloz, vol. 117(4), pages 457-462.
    5. d'Autume, Antoine & Schubert, Katheline, 2008. "Hartwick's rule and maximin paths when the exhaustible resource has an amenity value," Journal of Environmental Economics and Management, Elsevier, vol. 56(3), pages 260-274, November.
    6. R. M. Solow, 1974. "Intergenerational Equity and Exhaustible Resources," Review of Economic Studies, Oxford University Press, vol. 41(5), pages 29-45.
    7. Hartwick, John M, 1977. "Intergenerational Equity and the Investing of Rents from Exhaustible Resources," American Economic Review, American Economic Association, vol. 67(5), pages 972-974, December.
    8. Stern,Nicholas, 2007. "The Economics of Climate Change," Cambridge Books, Cambridge University Press, number 9780521700801.
    9. Partha Dasgupta & Geoffrey Heal, 1974. "The Optimal Depletion of Exhaustible Resources," Review of Economic Studies, Oxford University Press, vol. 41(5), pages 3-28.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. d'Autume, Antoine & Hartwick, John M. & Schubert, Katheline, 2010. "The zero discounting and maximin optimal paths in a simple model of global warming," Mathematical Social Sciences, Elsevier, vol. 59(2), pages 193-207, March.
    3. Cairns, Robert D. & Martinet, Vincent, 2014. "An environmental-economic measure of sustainable development," European Economic Review, Elsevier, vol. 69(C), pages 4-17.
    4. Martinet, Vincent & Del Campo, Stellio & Cairns, Robert D., 2022. "Intragenerational inequality aversion and intergenerational equity," European Economic Review, Elsevier, vol. 144(C).
    5. François Allisson & Antoine Missemer, 2020. "Some Historiographical Tools for the Study of Intellectual Legacies," Post-Print halshs-02931492, HAL.

    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. Toman, Michael & Pezzey, John C., 2002. "The Economics of Sustainability: A Review of Journal Articles," Discussion Papers dp-02-03, Resources For the Future.
    2. Koji Tokimatsu & Louis Dupuy & Nick Hanley, 2019. "Using Genuine Savings for Climate Policy Evaluation with an Integrated Assessment Model," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 72(1), pages 281-307, January.
    3. d'Autume, Antoine & Schubert, Katheline, 2008. "Hartwick's rule and maximin paths when the exhaustible resource has an amenity value," Journal of Environmental Economics and Management, Elsevier, vol. 56(3), pages 260-274, November.
    4. Nick Hanley & Louis Dupuy & Eoin McLaughlin, 2015. "Genuine Savings And Sustainability," Journal of Economic Surveys, Wiley Blackwell, vol. 29(4), pages 779-806, September.
    5. d'Autume, Antoine & Hartwick, John M. & Schubert, Katheline, 2010. "The zero discounting and maximin optimal paths in a simple model of global warming," Mathematical Social Sciences, Elsevier, vol. 59(2), pages 193-207, March.
    6. Bazhanov, Andrei, 2010. "A closed form solution to Stollery's global warming problem with temperature in utility," MPRA Paper 22406, University Library of Munich, Germany.
    7. Andrei Bazhanov, 2012. "A Closed-Form Solution to Stollery’s Problem with Damage in Utility," Computational Economics, Springer;Society for Computational Economics, vol. 39(4), pages 365-386, April.
    8. Martinet, Vincent & Del Campo, Stellio & Cairns, Robert D., 2022. "Intragenerational inequality aversion and intergenerational equity," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics.
    9. Asheim, Geir B. & Hartwick, John M. & Mitra, Tapan, 2021. "Investment rules and time invariance under population growth," Journal of Economic Dynamics and Control, Elsevier, vol. 123(C).
    10. Sachverständigenrat zur Begutachtung der gesamtwirtschaftlichen Entwicklung & Conseil d'Analyse Économique, 2010. "Monitoring economic performance, quality of life and sustainability. Joint report as requested by the Franco-German Ministerial Council," Occasional Reports / Expertisen, German Council of Economic Experts / Sachverständigenrat zur Begutachtung der gesamtwirtschaftlichen Entwicklung, number 75366.
    11. Parks, Sarah & Gowdy, John, 2013. "What have economists learned about valuing nature? A review essay," Ecosystem Services, Elsevier, vol. 3(C), pages 1-10.
    12. Bromley, Daniel W., 1998. "Searching for sustainability: The poverty of spontaneous order," Ecological Economics, Elsevier, vol. 24(2-3), pages 231-240, February.
    13. Bazhanov, Andrei V., 2015. "Inefficiency and sustainability," Resources Policy, Elsevier, vol. 45(C), pages 210-216.
    14. Martinet, Vincent, 2011. "A characterization of sustainability with indicators," Journal of Environmental Economics and Management, Elsevier, vol. 61(2), pages 183-197, March.
    15. Andrei V. Bazhanov, 2009. "A constant-utility criterion linked to an imperfect economy affected by irreversible global warming," EERI Research Paper Series EERI_RP_2009_03, Economics and Econometrics Research Institute (EERI), Brussels.
    16. Hoberg, Nikolai & Baumgärtner, Stefan, 2017. "Irreversibility and uncertainty cause an intergenerational equity-efficiency trade-off," Ecological Economics, Elsevier, vol. 131(C), pages 75-86.
    17. Hartwick, John M. & Long, Ngo Van, 2018. "Sustainability with endogenous discounting when utility depends on consumption and amenities," Mathematical Social Sciences, Elsevier, vol. 95(C), pages 31-36.
    18. Seyhan, Demet & Weikard, Hans-Peter & van Ierland, Ekko, 2012. "An economic model of long-term phosphorus extraction and recycling," Resources, Conservation & Recycling, Elsevier, vol. 61(C), pages 103-108.
    19. 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.
    20. Bazhanov, Andrei, 2011. "Investment and current utility change in dynamically inefficient economies," MPRA Paper 35487, University Library of Munich, Germany.

    More about this item

    Keywords

    Exhaustible resources; Hartwick's rule; intertemporal substitution;
    All these keywords.

    JEL classification:

    • D9 - Microeconomics - - Micro-Based Behavioral Economics
    • Q01 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - General - - - Sustainable Development
    • Q3 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation

    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:mse:cesdoc:09012. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/cenp1fr.html .

    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: Lucie Label (email available below). General contact details of provider: https://edirc.repec.org/data/cenp1fr.html .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.