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Efficient and Optimal Capital Accumulation under a Non Renewable Resource Constraint

  • Amigues, Jean-Pierre
  • Moreaux, Michel

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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Paper provided by Institut d'Économie Industrielle (IDEI), Toulouse in its series IDEI Working Papers with number 51.

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Date of creation: Nov 2008
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Publication status: Published in Revue d'Économie Politique, vol.�119, n°6, novembre 2008, p.�791-825.
Handle: RePEc:ide:wpaper:10018
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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. 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.
  3. Michel, Philippe, 1990. "Some Clarifications on the Transversality Condition," Econometrica, Econometric Society, vol. 58(3), pages 705-23, May.
  4. 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.
  5. 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.
  6. Michel, Philippe, 1982. "On the Transversality Condition in Infinite Horizon Optimal Problems," Econometrica, Econometric Society, vol. 50(4), pages 975-85, July.
  7. Cass, David & Mitra, Tapan, 1991. "Indefinitely Sustained Consumption Despite Exhaustible Natural Resources," Economic Theory, Springer, vol. 1(2), pages 119-46, April.
  8. 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.
  9. Mitra, Tapan, 2000. "Intertemporal Equity and Efficient Allocation of Resources," Working Papers 00-12, Cornell University, Center for Analytic Economics.
  10. John M. Hartwick, 2000. "National Accounting and Capital," Books, Edward Elgar, number 1885, March.
  11. John Hartwick, 1977. "Intergenerational Equity and the Investment of Rents from Exhaustible Resources in a Two Sector Model," Working Papers 281, Queen's University, Department of Economics.
  12. 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.
  13. 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.
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