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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 Centre interuniversitaire de recherche en économie quantitative, CIREQ in its series Cahiers de recherche with number 23-2005.

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Length: 32 pages
Date of creation: 2005
Date of revision:
Handle: RePEc:mtl:montec:23-2005

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Keywords: nonrenewable natural resources; renewable natural resources; order of use; water resource; oil;

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References

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  1. Amigues, Jean-Pierre & Favard, Pascal & Gaudet, Gerard & Moreaux, Michel, 1998. "On the Optimal Order of Natural Resource Use When the Capacity of the Inexhaustible Substitute Is Limited," Journal of Economic Theory, Elsevier, vol. 80(1), pages 153-170, May.
  2. Lewis, Tracy R, 1982. "Sufficient Conditions for Extracting Least Cost Resource First," Econometrica, Econometric Society, vol. 50(4), pages 1081-83, July.
  3. Hartwick, John M. & Kemp, Murray C. & Van Long, Ngo, 1986. "Set-up costs and theory of exhaustible resources," Journal of Environmental Economics and Management, Elsevier, vol. 13(3), pages 212-224, September.
  4. Chakravorty, Ujjayant & Krulce, Darrell & Roumasset, James, 2005. "Specialization and non-renewable resources: Ricardo meets Ricardo," Journal of Economic Dynamics and Control, Elsevier, vol. 29(9), pages 1517-1545, September.
  5. 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.
  6. Léonard,Daniel & Long,Ngo van, 1992. "Optimal Control Theory and Static Optimization in Economics," Cambridge Books, Cambridge University Press, number 9780521337465, October.
  7. Chakravorty, Ujjayant & Krulce, Darrell L, 1994. "Heterogeneous Demand and Order of Resource Extraction," Econometrica, Econometric Society, vol. 62(6), pages 1445-52, November.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
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Citations

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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. Bazhanov, Andrei, 2011. "Investment and resource policy under a modified Hotelling rule," MPRA Paper 32428, University Library of Munich, Germany.
  3. Lafforgue, Gilles & Magné, Bertrand & Moreaux, Michel, 2008. "Energy substitutions, climate change and carbon sinks," Ecological Economics, Elsevier, vol. 67(4), pages 589-597, November.
  4. 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.
  5. Bazhanov, Andrei, 2011. "Investment and current utility change in dynamically inefficient economies," MPRA Paper 35487, University Library of Munich, Germany.
  6. Bazhanov, Andrei, 2013. "Inefficiency and Sustainability," MPRA Paper 51815, University Library of Munich, Germany.
  7. Bazhanov, Andrei, 2012. "Disregarded inefficiency may dominate sustainability policies," MPRA Paper 43621, University Library of Munich, Germany.
  8. Kuwayama, Yusuke & Olmstead, Sheila & Krupnick, Alan, 2013. "Water Resoures and Unconventional Fossil Fuel Development: Linking Physical Impacts to Social Costs," Discussion Papers dp-13-34, Resources For the Future.

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