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Characterizing the Sustainability Problem in an Exhaustible Resource Model

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  • Tapan Mitra
  • Geir B Asheim
  • Wolfgang Buchholz
  • Cees Withagen

Abstract

The Dasgupta-Heal-Solow-Stiglitz model of capital accumulation and resource depletion poses the following sustainability problem: is it feasible to sustain inde nitely a level of consumption that is bounded away from zero? We provide a complete technological characterization of the sustainability problem in this model without reference to the time path. As a byproduct we show general existence of a maximin optimal path under weaker conditions that those employed in previous work. Our proofs yield new insights into the meaning and signi cance of Hartwick's reinvestment rule.

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Bibliographic Info

Paper provided by Oxford Centre for the Analysis of Resource Rich Economies, University of Oxford in its series OxCarre Working Papers with number 083.

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Date of creation: 2012
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Handle: RePEc:oxf:oxcrwp:083

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Keywords: sustainability; Maximin;

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References

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  1. Asheim, Geir B. & Mitra, Tapan, 2010. "Sustainability and discounted utilitarianism in models of economic growth," Mathematical Social Sciences, Elsevier, vol. 59(2), pages 148-169, March.
  2. Mitra, Tapan, 2002. "Intertemporal Equity and Efficient Allocation of Resources," Journal of Economic Theory, Elsevier, vol. 107(2), pages 356-376, December.
  3. Hartwick, John M, 1977. "Intergenerational Equity and the Investing of Rents from Exhaustible Resources," American Economic Review, American Economic Association, vol. 67(5), pages 972-74, December.
  4. Vincent Martinet & Luc Doyen, 2007. "Sustainability of an economy with an exhaustible resource: A viable control approach," Working Papers 22177, Institut National de la Recherche Agronomique, France.
  5. Tapan Mitra & Geir B Asheim & Wolfgang Buchholz & Cees Withagen, 2012. "Characterizing the Sustainability Problem in an Exhaustible Resource Model," OxCarre Working Papers 083, Oxford Centre for the Analysis of Resource Rich Economies, University of Oxford.
  6. Dixit, Avinash & Hammond, Peter & Hoel, Michael, 1980. "On Hartwick's Rule for Regular Maximin Paths of Capital Accumulation and Resource Depletion," Review of Economic Studies, Wiley Blackwell, vol. 47(3), pages 551-56, April.
  7. Wolfgang Buchholz & Swapan Dasgupta & Tapan Mitra, 2005. "Intertemporal Equity and Hartwick's Rule in an Exhaustible Resource Model," Scandinavian Journal of Economics, Wiley Blackwell, vol. 107(3), pages 547-561, 09.
  8. Stéphane Zuber & Geir B. Asheim, 2010. "Justifying Social Discounting: The Rank-Discounted Utilitarian Approach," CESifo Working Paper Series 3192, CESifo Group Munich.
  9. Asheim, Geir B. & Buchholz, Wolfgang & Hartwick, John M. & Mitra, Tapan & Withagen, Cees, 2005. "Constant savings rates and quasi-arithmetic population growth under exhaustible resource constraints," Memorandum 23/2005, Oslo University, Department of Economics.
  10. Dasgupta, Swapan & Mitra, Tapan, 1983. "Intergenerational Equity and Efficient Allocation of Exhaustible Resources," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(1), pages 133-53, February.
  11. Withagen, Cees & B. Asheim, Geir, 1998. "Characterizing sustainability: The converse of Hartwick's rule," Journal of Economic Dynamics and Control, Elsevier, vol. 23(1), pages 159-165, September.
  12. Cairns, Robert D. & Long, Ngo Van, 2006. "Maximin: a direct approach to sustainability," Environment and Development Economics, Cambridge University Press, vol. 11(03), pages 275-300, June.
  13. Burmeister, Edwin & Hammond, P J, 1977. "Maximin Paths of Heterogeneous Capital Accumulation and the Instability of Paradoxical Steady States," Econometrica, Econometric Society, vol. 45(4), pages 853-70, May.
  14. Cass, David, 1990. "Indefinitely sustained consumption despite exhaustible natural resources," CEPREMAP Working Papers (Couverture Orange) 9027, CEPREMAP.
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Cited by:
  1. Tapan Mitra & Geir B. Asheim & Wolfgang Buchholz & Cees A. Withagen, 2012. "Characterizing the Sustainability Problem in an Exhaustible Resource Model," CESifo Working Paper Series 3758, CESifo Group Munich.
  2. Robert D. Cairns & Vincent Martinet, 2012. "An Environmental-Economic Measure of Sustainable Development," EconomiX Working Papers 2012-2, University of Paris West - Nanterre la Défense, EconomiX.

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