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The Zero Discounting and Maximin Optimal Paths in a Simple Model of Global Warming

  • Antoine D'Autume

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics)

  • John Hartwick

    (Department of Economics - Queen's University)

  • Katheline Schubert


    (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics)

Following Stollery (1998), we extend the Solow-- Dasgupta--Heal model to analyze the effects of global warming 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 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 of temperature in intratemporal preferences or a larger intertemporal elasticity of substitution both lead to postpone resource use.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00547282.

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Date of creation: Mar 2010
Date of revision:
Publication status: Published in Mathematical Social Sciences, Elsevier, 2010, 59 (2), pp.193-207. <10.1016/j.mathsocsci.2009.10.002>
Handle: RePEc:hal:cesptp:halshs-00547282
DOI: 10.1016/j.mathsocsci.2009.10.002
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  1. Kenneth Stollery, 1998. "Constant Utility Paths and Irreversible Global Warming," Canadian Journal of Economics, Canadian Economics Association, vol. 31(3), pages 730-742, August.
  2. Mitra, Tapan, 1980. "On Optimal Depletion of Exhaustible Resources: Existence and Characterization Results," Econometrica, Econometric Society, vol. 48(6), pages 1431-50, September.
  3. 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.
  4. Antoine D'Autume & Katheline Schubert, 2008. "Hartwick's rule and maximin paths when the exhaustible resource has an amenity value," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00275765, HAL.
  5. Léonard,Daniel & Long,Ngo van, 1992. "Optimal Control Theory and Static Optimization in Economics," Cambridge Books, Cambridge University Press, number 9780521331586.
  6. 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.
  7. 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.
  8. Hartwick, John M, 1977. "Intergenerational Equity and the Investing of Rents from Exhaustible Resources," American Economic Review, American Economic Association, vol. 67(5), pages 972-74, December.
  9. Hans-Werner Sinn, 2007. "Public Policies against Global Warming," NBER Working Papers 13454, National Bureau of Economic Research, Inc.
  10. Sinn, Hans-Werner, 2008. "Public policies against global warming: A supply side approach," Munich Reprints in Economics 19638, University of Munich, Department of Economics.
  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 515-36, October.
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