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The Optimal Depletion Of Exhaustible Resources: A Complete Characterization

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  • Hassan Benchekroun

    ()

  • Cees Withagen

    ()

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 McGill University, Department of Economics in its series Departmental Working Papers with number 2010-01.

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Length: 28 pages
Date of creation: Jan 2010
Date of revision:
Handle: RePEc:mcl:mclwop:2010-01

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References

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  1. 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).
  2. Asheim, Geir B, 1994. " Net National Product as an Indicator of Sustainability," Scandinavian Journal of Economics, Wiley Blackwell, vol. 96(2), pages 257-65.
  3. 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.
  4. Geir B. Asheim & Wolfgang Buchholz & John M. Hartwick & Tapan Mitra & Cees A. Withagen, 2005. "Constant Savings Rates and Quasi-Arithmetic Population Growth under Exhaustible Resource Constraints," CESifo Working Paper Series 1573, CESifo Group Munich.
  5. 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.
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RePEc Biblio mentions

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. Karolina Ryszka, 2013. "Resource Extraction in a Political Economy Framework," Tinbergen Institute Discussion Papers 13-094/VIII, Tinbergen Institute.
  2. Neustroev, Dmitry, 2013. "The Uzawa-Lucas Growth Model with Natural Resources," MPRA Paper 52937, University Library of Munich, Germany.
  3. 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.
  4. Robert D. Cairns, 2011. "Accounting for Sustainability: A Dissenting Opinion," Sustainability, MDPI, Open Access Journal, vol. 3(9), pages 1341-1356, August.
  5. Bormotov, Michael, 2010. "Modern Knowledge Based Economy: all-factors endogenous growth model and total investment allocation," MPRA Paper 19932, University Library of Munich, Germany.
  6. 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.
  7. Bazhanov, Andrei, 2008. "Sustainable growth in a resource-based economy: the extraction-saving relationship," MPRA Paper 12350, University Library of Munich, Germany.
  8. 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.
  9. Smulders, Sjak & Withagen, Cees, 2012. "Green growth -- lessons from growth theory," Policy Research Working Paper Series 6230, The World Bank.
  10. 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.

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