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

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  • Antoine d'Autume

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Katheline Schubert

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

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 which yields a generalization of Hartwick's rule. We characterize solutions in the Cobb-Douglas utility case, and analyse the influence of the intertemporal elasticity of substitution on the time profile of the optimal paths. We show that the ratio of the values of the resource and capital stocks remains constant along the optimal path, and is independent of the initial conditions.

Suggested Citation

  • Antoine d'Autume & Katheline Schubert, 2008. "Zero discounting and optimal paths of depletion of an exhaustible resource with an amenity value," PSE-Ecole d'économie de Paris (Postprint) halshs-00976395, HAL.
    • Handle: RePEc:hal:pseptp:halshs-00976395
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00976395
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    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," The Review of Economic Studies, Review of Economic Studies Ltd, 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," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(5), pages 3-28.
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    Cited by:

    1. 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, issue forthcomi.
    2. 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.
    3. 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.
    4. Cairns, Robert D. & Martinet, Vincent, 2014. "An environmental-economic measure of sustainable development," European Economic Review, Elsevier, vol. 69(C), pages 4-17.
    5. François Allisson & Antoine Missemer, 2020. "Some Historiographical Tools for the Study of Intellectual Legacies," Post-Print halshs-02931492, HAL.

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    More about this item

    Keywords

    undiscounted utilitarianism; maximin; Hartwick's rule;
    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

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