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The Optimal Depletion of Exhaustible Resources : A Complete Characterization

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  • BENCHEKROUN, Hassan
  • WITHAGEN, Cees

Abstract

We provide the closed form solution to the Dasgupta-Heal-Solow-Stiglitz (DHSS) model. The DHSS model is based on the seminal articles Dasgupta and Heal (Rev. Econ. Stud.,1974), Solow (Rev. Econ. Stud.,1974) and Stiglitz (Rev. Econ. Stud.,1974) and describes an economy with two assets, man-made capital and a nonrenewable resource stock. We explicitly characterize, for such an economy, the dynamics along the optimal trajectory of all the variables in the model and from all possible initial values of the stocks. We use the analytical solution to prove several properties of the optimal consumption path. In particular, we show that the initial consumption under a utilitarian criterion starts below the maximin rate of consumption if and only the resource is abundant enough and that under a utilitarian criterion, it is not necessarily the present generation that benefits most from a windfall of resources.

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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 04-2010.

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Length: 28 pages
Date of creation: 2010
Date of revision:
Handle: RePEc:mtl:montec:04-2010

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Keywords: Exhaustible resources; Dasgupta-Heal-Solow-Stiglitz economy; exponential integral;

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References

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  1. Asheim, Geir B, 1994. " Net National Product as an Indicator of Sustainability," Scandinavian Journal of Economics, Wiley Blackwell, vol. 96(2), pages 257-65.
  2. Asheim, Geir B. & Buchholz, Wolfgang & Hartwick, John M. & Mitra, Tapan & Withagen, Cees, 2007. "Constant savings rates and quasi-arithmetic population growth under exhaustible resource constraints," Journal of Environmental Economics and Management, Elsevier, vol. 53(2), pages 213-229, March.
  3. John Hartwick & Ngo Van Long & Huilan Tian, 2003. "On the Peaking of Consumption with Exhaustible Resources and Zero Net Investment," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 24(3), pages 235-244, March.
  4. Pezzey, John C V & Withagen, Cees A, 1998. " The Rise, Fall and Sustainability of Capital-Resource Economies," Scandinavian Journal of Economics, Wiley Blackwell, vol. 100(2), pages 513-27, June.
  5. Raouf, BOUCEKKINE & José R. , RUIZ-TAMARIT, 2004. "Special functions for the study of economic dynamics : The case of the Lucas-Uzawa model," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2004026, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
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As found on the RePEc Biblio, the curated bibliography for Economics:
  1. > Environmental and Natural Resource Economics > Resource Economics
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Cited by:
  1. Roy Cerqueti & Raffaella Coppier & Gustavo Piga, 2011. "Corruption, Growth and Ethnic Fractionalization: a Theoretical Model," CEIS Research Paper 216, Tor Vergata University, CEIS, revised 08 Nov 2011.
  2. Bormotov, Michael, 2010. "Modern Knowledge Based Economy: all-factors endogenous growth model and total investment allocation," MPRA Paper 19932, University Library of Munich, Germany.
  3. Neustroev, Dmitry, 2013. "The Uzawa-Lucas Growth Model with Natural Resources," MPRA Paper 52937, University Library of Munich, Germany.
  4. Bazhanov, Andrei, 2008. "Sustainable growth in a resource-based economy: the extraction-saving relationship," MPRA Paper 12350, University Library of Munich, Germany.
  5. Ruiz-Tamarit, J.R. & Ventura-Marco, M., 2011. "Solution to nonlinear MHDS arising from optimal growth problems," Mathematical Social Sciences, Elsevier, vol. 61(2), pages 86-96, March.
  6. Francisco J. André & Sjak Smulders, 2012. "Fueling Growth when Oil Peaks: Directed Technological Change and the Limits to Efficiency," CESifo Working Paper Series 3977, CESifo Group Munich.
  7. Robert D. Cairns, 2011. "Accounting for Sustainability: A Dissenting Opinion," Sustainability, MDPI, Open Access Journal, vol. 3(9), pages 1341-1356, August.
  8. Sjak Smulders & Michael Toman & Cees Withagen, 2014. "Growth Theory and "Green Growth"," OxCarre Working Papers 135, Oxford Centre for the Analysis of Resource Rich Economies, University of Oxford.
  9. Smulders, Sjak & Withagen, Cees, 2012. "Green growth -- lessons from growth theory," Policy Research Working Paper Series 6230, The World Bank.
  10. Karolina Ryszka, 2013. "Resource Extraction in a Political Economy Framework," Tinbergen Institute Discussion Papers 13-094/VIII, Tinbergen Institute.

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