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The optimal depletion of exhaustible resources: A complete characterization

  • 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, 1974) and (Solow, 1974) and Stiglitz (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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Article provided by Elsevier in its journal Resource and Energy Economics.

Volume (Year): 33 (2011)
Issue (Month): 3 (September)
Pages: 612-636

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Handle: RePEc:eee:resene:v:33:y:2011:i:3:p:612-636
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505569

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  1. 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.
  2. BOUCEKKINE, Raouf & RUIZ-TAMARIT, José Ramon, . "Special functions for the study of economic dynamics: The case of the Lucas-Uzawa model," CORE Discussion Papers RP 2003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Raouf Boucekkine & Blanca Martínez & José Ramón Ruiz-Tamarit, 2008. "Note on global dynamics and imbalance effects in the Lucas-Uzawa model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(4), pages 503-518.
  4. Rauf, BOUCEKKINE & Blanca, MARTINEZ & Jose R., RUIZ-TAMARIT, 2007. "Global dynamics and imbalance effects in the Lucas Uzawa model : further results," Discussion Papers (ECON - Département des Sciences Economiques) 2007018, Université catholique de Louvain, Département des Sciences Economiques.
  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.
  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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