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Efficient and Optimal Capital Accumulation under a Non Renewable Resource Constraint

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  • Michel Moreaux
  • Jean-Pierre Amigues

Abstract

Usual resource models with capital accumulation focus upon simple one to one process transforming output either into some consumption good or into some capitalgood. We consider a bisectoral model where the capital good, labor and a non renewable resource are used to produce the consumption good and the capital good. Capitalaccumulation is an irreversible process and capital is depreciating over time. In thisframework we reconsider the usual results of the efficient and optimal growth theoryunder an exhaustible resource constraint. We show that the efficiency conditions relatesto an investment function including the properties of the production functions of theboth sectors what cannot be shown neither in the monosectoral canonical model ofDasgupta and Heal nor in the fully disaggregated model of Dixit, Hammond and Heolwhich is disolving the sectoral structure of the economy. We show then that the standard Hotelling rule relating the growth rate of the consumption good to the growth rateof the marginal productivity of the resource in the consumption good sector remainsvalid independently of the multisectoral specification of the model. Last we exploredifferent forms of the Hartwick rule in the context of efficient paths and optimal paths.

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Bibliographic Info

Article provided by Dalloz in its journal Revue d'économie politique.

Volume (Year): Volume 118 (2008)
Issue (Month): 6 ()
Pages: 791-825

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Handle: RePEc:cai:repdal:redp_186_0791

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Web page: http://www.cairn.info/revue-d-economie-politique.htm

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Keywords: Efficient and optimal growth; non renewable resource; Hartwick rule;

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  1. Mitra, Tapan, 2002. "Intertemporal Equity and Efficient Allocation of Resources," Journal of Economic Theory, Elsevier, vol. 107(2), pages 356-376, December.
  2. John Hartwick, 1976. "Intergenerational Equity and the Investing of Rents from Exhaustible Resources," Working Papers 220, Queen's University, Department of Economics.
  3. Michel, Philippe, 1982. "On the Transversality Condition in Infinite Horizon Optimal Problems," Econometrica, Econometric Society, vol. 50(4), pages 975-85, July.
  4. Heal, G., 1990. "The Optimal Use Of Exhaustible Resources," Papers fb-_90-10, Columbia - Graduate School of Business.
  5. Cass, David, 1990. "Indefinitely sustained consumption despite exhaustible natural resources," CEPREMAP Working Papers (Couverture Orange) 9027, CEPREMAP.
  6. 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.
  7. 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.
  8. Mitra, Tapan, 1978. "Efficient growth with exhaustible resources in a neoclassical model," Journal of Economic Theory, Elsevier, vol. 17(1), pages 114-129, February.
  9. R. M. Solow, 1973. "Intergenerational Equity and Exhaustable Resources," Working papers 103, Massachusetts Institute of Technology (MIT), Department of Economics.
  10. 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.
  11. Michel, Philippe, 1990. "Some Clarifications on the Transversality Condition," Econometrica, Econometric Society, vol. 58(3), pages 705-23, May.
  12. 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.
  13. 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.
  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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