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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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File URL: http://www.oxcarre.ox.ac.uk/images/stories/papers/ResearchPapers/oxcarrerp201283.pdf
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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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  1. 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.
  2. 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.
  3. 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.
  4. Dasgupta, Swapan & Mitra, Tapan, 2002. "Intertemporal Equity and Hartwick's Rules in an Exhaustible Resource Model," Working Papers 02-05, Cornell University, Center for Analytic Economics.
  5. Zuber, Stéphane & Asheim, Geir B., 2012. "Justifying social discounting: The rank-discounted utilitarian approach," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1572-1601.
  6. Geir B. Asheim & Tapan Mitra, 2009. "Sustainability and Discounted Utilitarianism in Models of Economic Growth," CESifo Working Paper Series 2521, CESifo Group Munich.
  7. Cass, David & Mitra, Tapan, 1991. "Indefinitely Sustained Consumption Despite Exhaustible Natural Resources," Economic Theory, Springer, vol. 1(2), pages 119-46, April.
  8. John Hartwick, 1976. "Intergenerational Equity and the Investing of Rents from Exhaustible Resources," Working Papers 220, Queen's University, Department of Economics.
  9. 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.
  10. Mitra, Tapan, 2002. "Intertemporal Equity and Efficient Allocation of Resources," Journal of Economic Theory, Elsevier, vol. 107(2), pages 356-376, December.
  11. 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.
  12. Martinet, V. & Doyen, L., 2007. "Sustainability of an economy with an exhaustible resource: A viable control approach," Resource and Energy Economics, Elsevier, vol. 29(1), pages 17-39, January.
  13. 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.
  14. 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.
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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, 2013. "An Environmental-Economic Measure of Sustainable Development," CESifo Working Paper Series 4327, CESifo Group Munich.

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