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

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  • d'Autume, Antoine
  • Hartwick, John M.
  • Schubert, Katheline

Abstract

Following Stollery (1998), we extend the Solow-Dasgupta-Heal model to analyze the effects of global warming. The rise in 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 in 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 and utility functions are Cobb-Douglas, and the temperature level is an exponential function of the remaining stock of resources. We show that a greater weight on temperature in intratemporal preferences and a larger intertemporal elasticity of substitution both lead to postponing resource use.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:matsoc:v:59:y:2010:i:2:p:193-207
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    References listed on IDEAS

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    1. Avinash Dixit & Peter Hammond & Michael Hoel, 1980. "On Hartwick's Rule for Regular Maximin Paths of Capital Accumulation and Resource Depletion," Review of Economic Studies, Oxford University Press, vol. 47(3), pages 551-556.
    2. Cairns, Robert D. & Long, Ngo Van, 2006. "Maximin: a direct approach to sustainability," Environment and Development Economics, Cambridge University Press, vol. 11(03), pages 275-300, June.
    3. 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.
    4. R. M. Solow, 1974. "Intergenerational Equity and Exhaustible Resources," Review of Economic Studies, Oxford University Press, vol. 41(5), pages 29-45.
    5. Hans-Werner Sinn, 2007. "Public Policies against Global Warming," NBER Working Papers 13454, National Bureau of Economic Research, Inc.
    6. 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.
    7. Kenneth Stollery, 1998. "Constant Utility Paths and Irreversible Global Warming," Canadian Journal of Economics, Canadian Economics Association, vol. 31(3), pages 730-742, August.
    8. Léonard,Daniel & Long,Ngo van, 1992. "Optimal Control Theory and Static Optimization in Economics," Cambridge Books, Cambridge University Press, number 9780521331586, April.
    9. 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.
    10. Mitra, Tapan, 1980. "On Optimal Depletion of Exhaustible Resources: Existence and Characterization Results," Econometrica, Econometric Society, vol. 48(6), pages 1431-1450, September.
    11. 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.
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    Cited by:

    1. 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.
    2. Robert D. Cairns & Stellio Del Campo & Vincent Martinet, 2016. "Sustainability of an economy relying on two reproducible assets," Working Papers 2016/03, INRA, Economie Publique.
    3. John M. Hartwick & Ngo Van Long, 2017. "Sustainability with endogenous discounting," CIRANO Working Papers 2017s-19, CIRANO.
    4. Bazhanov, Andrei V., 2015. "Inefficiency and sustainability," Resources Policy, Elsevier, vol. 45(C), pages 210-216.
    5. 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.

    More about this item

    Keywords

    Polluting exhaustible resources Global warming Maximin Zero discounting Sustainability;

    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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