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Optimal Use of a Polluting non Renewable Ressource Generating Both Manageable and Catastrophic Damages


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  • Jean-Pierre AMIGUES
  • Michel MOREAUX
  • Katheline SCHUBERT


We consider a model with two energy sources, a non-renewable one, cheap but polluting, and a renewable one, expensive but clean, let’s say coal and solar. The aim of environmental policy is to maintain atmospheric carbon concentration under a given ceiling, chosen to prevent an excessive rise of the temperature and catastrophic damages. Before the ceiling damages exist but remain small, hence manageable. We show first that costs matter a lot. Whatever abundant or rare, if solar is more expensive than coal at the ceiling, it will never be used before the end of the phase at the ceiling, when coal becomes so scarce that the ceiling will never be reached again. On the contrary, if solar is less expensive than coal at the ceiling, it may even be sufficiently cheap to be exploited before the ceiling, in which case first coal is exploited alone, next both resources are used together before, at and after the ceiling, and finally solar is exploited alone, after the exhaustion of coal. Second, the carbon shadow value is first increasing until the ceiling is reached, next decreasing during the phase at the ceiling, and finally is stabilized at a constant level after the ceiling. The initial carbon shadow cost is an increasing function of the value of the marginal damage, and a decreasing function of the ceiling. Lastly, contrary to intuition, higher marginal damages and/or a lower ceiling induce a delay in the penetration of solar and also a delay in the transition towards a totally clean energy.

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Article provided by ENSAE in its journal Annals of Economics and Statistics.

Volume (Year): (2011)
Issue (Month): 103-104 ()
Pages: 107-142

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Handle: RePEc:adr:anecst:y:2011:i:103-104:p:07

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  1. Ujjayant Chakravorty & Bertrand Magne & Michel Moreaux, 2003. "A Hotelling Model with a Ceiling on the Stock of Pollution," Emory Economics, Department of Economics, Emory University (Atlanta) 0321, Department of Economics, Emory University (Atlanta).
  2. Ulph, Alistair & Ulph, David, 1994. "The Optimal Time Path of a Carbon Tax," Oxford Economic Papers, Oxford University Press, vol. 46(0), pages 857-68, Supplemen.
  3. Sinn, Hans-Werner, 2008. "Public policies against global warming: A supply side approach," Munich Reprints in Economics, University of Munich, Department of Economics 19638, University of Munich, Department of Economics.
  4. Toman, Michael & Withagen, Cees, 1998. "Accumulative Pollution, "Clean Technology," and Policy Design," Discussion Papers, Resources For the Future dp-98-43, Resources For the Future.
  5. Hoel, Michael & Kverndokk, Snorre, 1996. "Depletion of fossil fuels and the impacts of global warming," Resource and Energy Economics, Elsevier, Elsevier, vol. 18(2), pages 115-136, June.
  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 515-36, October.
  7. Ujjayant CHAKRAVORTY & Bertrand MAGNE & Michel MOREAUX, 2006. "Plafond de concentration en carbone et substitutions entre ressources énergétiques," Annales d'Economie et de Statistique, ENSAE, ENSAE, issue 81, pages 141-168.
  8. Olli Tahvonen, 1997. "Fossil Fuels, Stock Externalities, and Backstop Technology," Canadian Journal of Economics, Canadian Economics Association, Canadian Economics Association, vol. 30(4), pages 855-74, November.
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Cited by:
  1. Amigues, Jean-Pierre & Moreaux, Michel, 2011. "The atmospheric carbon resilience problem : A theoretical analysis," LERNA Working Papers, LERNA, University of Toulouse 11.08.342, LERNA, University of Toulouse.
  2. Amigues, Jean-Pierre & Lafforgue, Gilles & Moreaux, Michel, 2012. "Optimal timing of CCS policies with heterogeneous energy consumption sectors," TSE Working Papers, Toulouse School of Economics (TSE) 12-326, Toulouse School of Economics (TSE), revised 03 Apr 2013.
  3. Amigues, Jean-Pierre & Moreaux, Michel, 2013. "Optimal growth under a climate constraint," IDEI Working Papers, Institut d'Économie Industrielle (IDEI), Toulouse 798, Institut d'Économie Industrielle (IDEI), Toulouse.
  4. Amigues, Jean-Pierre & Lafforgue, Gilles & Moreaux, Michel, 2012. "Optimal Timing of Carbon Capture Policies Under Alternative CCS Cost Functions," TSE Working Papers, Toulouse School of Economics (TSE) 12-318, Toulouse School of Economics (TSE).


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