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The Zero discounting and maximin optimal paths in a simple model of global warming

Author

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  • Antoine d'Autume

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, 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)

  • John M. Hartwick

    (Queen's University - Queen's University [Kingston, Canada])

  • Katheline Schubert

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, 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)

Abstract

Following Stollery [1998], we extend the Solow, Dasgupta-Heal model to analyze the effects of global warning. The rise of temperature is caused by the use of fossil resources so that the temperature level can be linked to the remaining stock of these resources. The rise of temperature affects both productivity and utility. We characterize optimal solutions for the maximin and zero-discounting cases and present closed form solutions for the case where the production function and utility function are Cobb-Douglas, and the temperature level is an exponential function of the remaining stock of resources. We show that a greater weight of temperature in the preferences or a larger intertemporal elasticity of substitution both lead to postpone resource use.

Suggested Citation

  • Antoine d'Autume & John M. Hartwick & Katheline Schubert, 2009. "The Zero discounting and maximin optimal paths in a simple model of global warming," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00367917, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00367917
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00367917
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    References listed on IDEAS

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    1. Antoine d’Autume & Katheline Schubert, 2008. "Zero discounting and optimal paths of depletion of an exhaustible resource with an amenity value," Revue d'économie politique, Dalloz, vol. 118(6), pages 827-845.
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    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. Antoine d'Autume & Katheline Schubert, 2008. "Zero discounting and optimal paths of depletion of an exhaustible resource with an amenity value," Post-Print halshs-00424045, HAL.
    7. Hans-Werner Sinn, 2008. "Public policies against global warming: a supply side approach," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 15(4), pages 360-394, August.
    8. Cairns, Robert D. & Long, Ngo Van, 2006. "Maximin: a direct approach to sustainability," Environment and Development Economics, Cambridge University Press, vol. 11(3), pages 275-300, June.
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    11. Farzin, Y H & Tahvonen, O, 1996. "Global Carbon Cycle and the Optimal Time Path of a Carbon Tax," Oxford Economic Papers, Oxford University Press, vol. 48(4), pages 515-536, October.
    12. Antoine d’Autume & Katheline Schubert, 2008. "Zero discounting and optimal paths of depletion of an exhaustible resource with an amenity value," Revue d'économie politique, Dalloz, vol. 118(6), pages 827-845.
    13. 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.
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    Cited by:

    1. Daniel Grainger, 2023. "Sustainability criterion implied externality pricing for resource extraction," Papers 2306.04065, arXiv.org.
    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. 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.
    5. John M. Hartwick & Ngo Van Long, 2020. "Sustainability with endogenous discounting," International Journal of Economic Theory, The International Society for Economic Theory, vol. 16(2), pages 216-221, June.
    6. Bazhanov, Andrei V., 2015. "Inefficiency and sustainability," Resources Policy, Elsevier, vol. 45(C), pages 210-216.
    7. Grainger, Daniel, 2024. "Sustainability criterion implied externality pricing for resource extraction," Economics Letters, Elsevier, vol. 234(C).
    8. Van Long, Ngo, 2016. "The Impacts of Other-Regarding Preferences and Ethical Choice on Environmental Outcomes: A Review of the Literature," Strategic Behavior and the Environment, now publishers, vol. 6(1-2), pages 1-35, December.
    9. 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.
    10. Ngo Van Long & Vincent Martinet, 2016. "How to Take Rights Seriously: A New Approach to the Intertemporal Evaluation of Social Alternatives," CIRANO Working Papers 2016s-60, CIRANO.

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    More about this item

    Keywords

    Maximin; zero discounting; global warming; critère utilitariste non escompté; changement climatique;
    All these keywords.

    JEL classification:

    • Q32 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation - - - Exhaustible Resources and Economic Development

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