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The Alberta Dilemma: Optimal Sharing of a Water Resource by an Agricultural and an Oil Sector

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  • Gaudet, Gérard
  • Moreaux, Michel
  • Withagen, Cees

Abstract

The purpose of this paper is to characterize the optimal time paths of production and water usage by an agricultural and an oil sector that have to share a limited water resource. We show that for any given water stock, if the oil stock is sufficiently large, it will become optimal to have a phase during which the agricultural sector is inactive. This may mean having an initial phase during which the two sectors are active, then a phase during which the water is reserved for the oil sector and the agricultural sector is inactive, followed by a phase during which both sectors are active again. The agricultural sector will always be active in the end as the oil stock is depleted and the demand for water from the oil sector decreases. In the case where agriculture is not constrained by the given natural inflow of water once there is no more oil, we show that oil extraction will always end with a phase during which oil production follows a pure Hotelling path, with the implicit price of oil net of extraction cost growing at the rate of interest. If the natural inflow of water does constitute a constraint for agriculture, then oil production never follows a pure Hotelling path, because its full marginal cost must always reflect not only the imputed rent on the finite oil stock, but also the positive opportunity cost of water.

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Bibliographic Info

Paper provided by University of Toulouse 1 Capitole in its series Open Access publications from University of Toulouse 1 Capitole with number http://neeo.univ-tlse1.fr/1902/.

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Date of creation: Sep 2006
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Publication status: Published in Journal of Environmental Economics and Management (2006-09) v.52, p.548-566
Handle: RePEc:ner:toulou:http://neeo.univ-tlse1.fr/1902/

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Web page: http://www.univ-tlse1.fr/

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  1. L‚onard,Daniel & Long,Ngo van, 1992. "Optimal Control Theory and Static Optimization in Economics," Cambridge Books, Cambridge University Press, number 9780521337465.
  2. John Hartwick & Murray Kemp & Ngo van Long, 1980. "Set-up Costs and Theory of Exhaustible Resources," Working Papers 412, Queen's University, Department of Economics.
  3. Ujjayant Chakravorty & Darrell Krulce & James Roumasset, 2003. "Specialization and Nonrenewable Resources: Ricardo meets Ricardo," Emory Economics 0305, Department of Economics, Emory University (Atlanta).
  4. Swallow, Stephen K., 1990. "Depletion of the environmental basis for renewable resources: The economics of interdependent renewable and nonrenewable resources," Journal of Environmental Economics and Management, Elsevier, vol. 19(3), pages 281-296, November.
  5. Chakravorty, Ujjayant & Krulce, Darrell L, 1994. "Heterogeneous Demand and Order of Resource Extraction," Econometrica, Econometric Society, vol. 62(6), pages 1445-52, November.
  6. Amigues, J-P & Favard, P., Gaudet, G. & Moreaux, M, 1996. "On the Optimal Order of Natural Resource Use When the Capacity of the Inexhaustible Substitute is Limited," Cahiers de recherche 9628, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  7. Holland, Stephen P., 2003. "Extraction capacity and the optimal order of extraction," Journal of Environmental Economics and Management, Elsevier, vol. 45(3), pages 569-588, May.
  8. Lewis, Tracy R, 1982. "Sufficient Conditions for Extracting Least Cost Resource First," Econometrica, Econometric Society, vol. 50(4), pages 1081-83, July.
  9. Chakravorty, Ujjayant & Roumasset, James & Tse, Kinping, 1997. "Endogenous Substitution among Energy Resources and Global Warming," Journal of Political Economy, University of Chicago Press, vol. 105(6), pages 1201-34, December.
  10. Kemp, Murray C & Long, Ngo Van, 1980. "On Two Folk Theorems Concerning the Extraction of Exhaustible Resources," Econometrica, Econometric Society, vol. 48(3), pages 663-73, April.
  11. Favard, Pascal, 2002. "Does productive capital affect the order of resource exploitation?," Journal of Economic Dynamics and Control, Elsevier, vol. 26(6), pages 911-918, June.
  12. Gerard Gaudet & Michel Moreaux & Stephen W. Salant, 2001. "Intertemporal Depletion of Resource Sites by Spatially Distributed Users," American Economic Review, American Economic Association, vol. 91(4), pages 1149-1159, September.
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Cited by:
  1. Eric Bahel & Walid Marrouch & Gerard Gaudet, 2010. "The Economics of Oil, Biofuel and Food Commodities," Working Papers e07-26, Virginia Polytechnic Institute and State University, Department of Economics.
  2. Lafforgue, Gilles & Magné, Bertrand & Moreaux, Michel, 2007. "Energy Substitutions, Climate Change and Carbon Sinks," IDEI Working Papers 427, Institut d'Économie Industrielle (IDEI), Toulouse.
  3. Bazhanov, Andrei, 2011. "Investment and resource policy under a modified Hotelling rule," MPRA Paper 32428, University Library of Munich, Germany.
  4. Bazhanov, Andrei, 2011. "Investment and current utility change in dynamically inefficient economies," MPRA Paper 35487, University Library of Munich, Germany.
  5. Bazhanov, Andrei, 2012. "Disregarded inefficiency may dominate sustainability policies," MPRA Paper 43621, University Library of Munich, Germany.
  6. Andrei Bazhanov, 2012. "A Closed-Form Solution to Stollery’s Problem with Damage in Utility," Computational Economics, Society for Computational Economics, vol. 39(4), pages 365-386, April.

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