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Global Dynamics In A Growth Model With An Exhaustible Resource

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  • Hassan Benchekroun

    ()

  • Cees Withagen

    ()

Abstract

We revisit the seminal growth model with exhaustible resources, the so called Dasgupta-Heal-Stiglitz-Solow model (DHSS). For this optimal control problem with two state variables, we explicitly characterize the dynamics of all the variables in the model and from all possible initial values of the stocks. We determine the condition under which consumption is initially increasing with time and the condition under which initial investment is positive implying that overshooting of man-made capital occurs. We show that the initial consumption under a utilitarian criterion starts below the maximin rate of consumption if and only if the resource is abunduant 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 2008-01.

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Length: 28 pages
Date of creation: Jan 2008
Date of revision:
Handle: RePEc:mcl:mclwop:2008-01

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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. & 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. Raouf Boucekkine & B. Martínez & J. R. Ruiz-Tamarit, 2007. "A note on global dynamics and imbalance effects in the Lucas-Uzawa model," Working Papers 2007_26, Business School - Economics, University of Glasgow.
  5. BOUCEKKINE, Raouf & MARTINEZ, Blanca & RUIZ-TAMARIT, Jose R., 2007. "Global dynamics and imbalance effects in the Lucas-Uzawa model: further results," CORE Discussion Papers 2007025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. 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.
  7. Asheim, Geir B, 1994. " Net National Product as an Indicator of Sustainability," Scandinavian Journal of Economics, Wiley Blackwell, vol. 96(2), pages 257-65.
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  1. > Environmental and Natural Resource Economics > Resource Economics
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Cited by:
  1. Neustroev, Dmitry, 2013. "The Uzawa-Lucas Growth Model with Natural Resources," MPRA Paper 52937, University Library of Munich, Germany.
  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. Karolina Ryszka, 2013. "Resource Extraction in a Political Economy Framework," Tinbergen Institute Discussion Papers 13-094/VIII, Tinbergen Institute.
  4. 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.
  5. André, Francisco J. & Smulders, Sjak, 2014. "Fueling growth when oil peaks: Directed technological change and the limits to efficiency," European Economic Review, Elsevier, vol. 69(C), pages 18-39.
  6. Smulders, Sjak & Withagen, Cees, 2012. "Green growth -- lessons from growth theory," Policy Research Working Paper Series 6230, The World Bank.
  7. 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.
  8. Robert D. Cairns, 2011. "Accounting for Sustainability: A Dissenting Opinion," Sustainability, MDPI, Open Access Journal, vol. 3(9), pages 1341-1356, August.
  9. J. R. Ruiz-Tamarit & M. Ventura-Marco, . "Solution to Non-Linear MHDS arising from Optimal Growth Problems," Working Papers 2000-16, FEDEA.
  10. Bazhanov, Andrei, 2008. "Sustainable growth in a resource-based economy: the extraction-saving relationship," MPRA Paper 12350, University Library of Munich, Germany.

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