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Constant Savings Rates and Quasi-Arithmetic Population Growth under Exhaustible Resource Constraints

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

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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Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 1573.

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Date of creation: 2005
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Handle: RePEc:ces:ceswps:_1573
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  1. Heal, G., 1990. "The Optimal Use Of Exhaustible Resources," Papers fb-_90-10, Columbia - Graduate School of Business.
  2. 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.
  3. Asheim, G.B. & Buchholz, W. & Withagen, C.A.A.M., 2002. "The Hartwick Rule : Myths and Facts," Discussion Paper 2002-52, Tilburg University, Center for Economic Research.
  4. Mitra, Tapan, 2002. "Intertemporal Equity and Efficient Allocation of Resources," Journal of Economic Theory, Elsevier, vol. 107(2), pages 356-376, December.
  5. Geir Asheim, 2004. "Green national accounting with a changing population," Economic Theory, Springer, vol. 23(3), pages 601-619, March.
  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 155-68, February.
  7. 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, 09.
  8. 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.
  9. R. M. Solow, 1973. "Intergenerational Equity and Exhaustable Resources," Working papers 103, Massachusetts Institute of Technology (MIT), Department of Economics.
  10. 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.
  11. 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, 06.
  12. Dixit, A. K., 1976. "The Theory of Equilibrium Growth," OUP Catalogue, Oxford University Press, number 9780198770817, March.
  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. 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.
  15. Withagen, Cees & Asheim, Geir B. & Buchholz, Wolfgang, 2003. "On the sustainable program in Solow's model," Memorandum 33/2002, Oslo University, Department of Economics.
  16. 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.
  17. 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.
  18. 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.
  19. Hamilton, Kirk, 1994. "Green adjustments to GDP," Resources Policy, Elsevier, vol. 20(3), pages 155-168, September.
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