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

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  • Asheim, Geir B.
  • Buchholz, Wolfgang
  • Hartwick, John M.
  • Mitra, Tapan
  • Withagen, Cees

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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Suggested Citation

  • 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.
  • Handle: RePEc:eee:jeeman:v:53:y:2007:i:2:p:213-229
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    References listed on IDEAS

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    1. Avinash Dixit & Peter Hammond & Michael Hoel, 1980. "On Hartwick's Rule for Regular Maximin Paths of Capital Accumulation and Resource Depletion," Review of Economic Studies, Oxford University Press, vol. 47(3), pages 551-556.
    2. Withagen, Cees & Asheim, Geir B. & Buchholz, Wolfgang, 2003. "On the sustainable program in Solow's model," Memorandum 33/2002, Oslo University, Department of Economics.
    3. Heal, Geoffrey M., 1993. "The optimal use of exhaustible resources," Handbook of Natural Resource and Energy Economics,in: A. V. Kneeseā€  & J. L. Sweeney (ed.), Handbook of Natural Resource and Energy Economics, edition 1, volume 3, chapter 18, pages 855-880 Elsevier.
    4. Geir Asheim & Wolfgang Buchholz & Cees Withagen, 2003. "The Hartwick Rule: Myths and Facts," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 25(2), pages 129-150, June.
    5. Pezzey, John C.V., 2004. "Exact measures of income in a hyperbolic economy," Environment and Development Economics, Cambridge University Press, vol. 9(04), pages 473-484, August.
    6. 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 155-168, February.
    7. R. M. Solow, 1974. "Intergenerational Equity and Exhaustible Resources," Review of Economic Studies, Oxford University Press, vol. 41(5), pages 29-45.
    8. Kirk Hamilton, 1995. "Sustainable development, the Hartwick rule and optimal growth," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 5(4), pages 393-411, June.
    9. 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.
    10. Geir B. Asheim & Wolfgang Buchholz, 2004. "A General Approach to Welfare Measurement through National Income Accounting," Scandinavian Journal of Economics, Wiley Blackwell, vol. 106(2), pages 361-384, June.
    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. T. W. Swan, 1956. "ECONOMIC GROWTH and CAPITAL ACCUMULATION," The Economic Record, The Economic Society of Australia, vol. 32(2), pages 334-361, November.
    13. Hartwick, John M, 1977. "Intergenerational Equity and the Investing of Rents from Exhaustible Resources," American Economic Review, American Economic Association, vol. 67(5), pages 972-974, December.
    14. 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, September.
    15. Dixit, A. K., 1976. "The Theory of Equilibrium Growth," OUP Catalogue, Oxford University Press, number 9780198770817.
    16. Mitra, Tapan, 2002. "Intertemporal Equity and Efficient Allocation of Resources," Journal of Economic Theory, Elsevier, vol. 107(2), pages 356-376, December.
    17. Hamilton, Kirk, 1994. "Green adjustments to GDP," Resources Policy, Elsevier, vol. 20(3), pages 155-168, September.
    18. Geir Asheim, 2004. "Green national accounting with a changing population," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(3), pages 601-619, March.
    19. 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.
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    More about this item

    JEL classification:

    • Q10 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Agriculture - - - General
    • Q32 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation - - - Exhaustible Resources and Economic Development

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