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Constant savings rates and quasi-arithmetic population growth under exhaustible resource constraints

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Author Info

  • Asheim, Geir B.

    ()
    (Dept. of Economics, University of Oslo)

  • Buchholz, Wolfgang

    ()
    (Department of Economics, University of Regensburg)

  • Hartwick, John M.

    ()
    (Queen’s University, Kingston, Ontario)

  • Mitra, Tapan

    ()
    (Cornell University, Ithaca, New York)

  • Withagen, Cees

    ()
    (Free University, De Boelelaan, Nederland)

Abstract

In the Dasgupta-Heal-Solow-Stiglitz model of capital accumulation and resource depletion we show the following equivalence: If an efficient path has constant (gross and net of population growth) savings rates, then population growth must be quasi-arithmetic and the path is a maximin or a classical utilitarian optimum. Conversely, if a path is optimal according to maximin or classical utilitarianism (with constant elasticity of marginal utility) under quasiarithmetic population growth, then the (gross and net of population growth) savings rates converge asymptotically to constants.

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File URL: http://www.sv.uio.no/econ/english/research/unpublished-works/working-papers/pdf-files/2005/Memo-23-2005.pdf
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Bibliographic Info

Paper provided by Oslo University, Department of Economics in its series Memorandum with number 23/2005.

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Length: 30 pages
Date of creation: 10 Sep 2005
Date of revision:
Handle: RePEc:hhs:osloec:2005_023

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Postal: Department of Economics, University of Oslo, P.O Box 1095 Blindern, N-0317 Oslo, Norway
Phone: 22 85 51 27
Fax: 22 85 50 35
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Web page: http://www.oekonomi.uio.no/indexe.html
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Keywords: Constant savings rate; quasi-arithmetic population growth;

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References

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  1. Kirk Hamilton & John Hartwick, 2005. "Investing exhaustible resource rents and the path of consumption," Canadian Journal of Economics, Canadian Economics Association, vol. 38(2), pages 615-621, May.
  2. Geir Asheim, 2004. "Green national accounting with a changing population," Economic Theory, Springer, vol. 23(3), pages 601-619, March.
  3. Mitra, Tapan, 1983. "Limits on Population Growth under Exhaustible Resource Constraints," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(1), pages 155-68, February.
  4. John C. V. Pezzey, 2002. "Exact Measures of Income in a Hyperbolic Economy," Economics and Environment Network Working Papers 0203, Australian National University, Economics and Environment Network.
  5. Geir Asheim & Wolfgang Buchholz & Cees Withagen, 2003. "The Hartwick Rule: Myths and Facts," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 25(2), pages 129-150, June.
  6. Withagen, Cees & Asheim, Geir B. & Buchholz, Wolfgang, 2003. "On the sustainable program in Solow's model," Memorandum 33/2002, Oslo University, Department of Economics.
  7. 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.
  8. Hamilton, Kirk, 1994. "Green adjustments to GDP," Resources Policy, Elsevier, vol. 20(3), pages 155-168, September.
  9. Dixit, A. K., 1976. "The Theory of Equilibrium Growth," OUP Catalogue, Oxford University Press, number 9780198770817.
  10. Kirk Hamilton, 1995. "Sustainable development, the Hartwick rule and optimal growth," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 5(4), pages 393-411, June.
  11. Mitra, Tapan, 2000. "Intertemporal Equity and Efficient Allocation of Resources," Working Papers 00-12, Cornell University, Center for Analytic Economics.
  12. Asheim, Geir & Buchholz, Wolfgang, 2003. "A General Approach to Welfare Measurement through National Income Accounting," Memorandum 32/2002, Oslo University, Department of Economics.
  13. T. W. Swan, 1956. "ECONOMIC GROWTH and CAPITAL ACCUMULATION," The Economic Record, The Economic Society of Australia, vol. 32(2), pages 334-361, November.
  14. Heal, Geoffrey M., 1993. "The optimal use of exhaustible resources," Handbook of Natural Resource and Energy Economics, in: A. V. Kneese† & J. L. Sweeney (ed.), Handbook of Natural Resource and Energy Economics, edition 1, volume 3, chapter 18, pages 855-880 Elsevier.
  15. 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.
  16. R. M. Solow, 1973. "Intergenerational Equity and Exhaustable Resources," Working papers 103, Massachusetts Institute of Technology (MIT), Department of Economics.
  17. Kirk Hamilton & Cees Withagen, 2007. "Savings growth and the path of utility," Canadian Journal of Economics, Canadian Economics Association, vol. 40(2), pages 703-713, May.
  18. 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.
  19. 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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