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Exact measures of income in two capital-resource-time economies

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  • John C. V. Pezzey

    ()
    (Centre for Resource and Environmental Studies, Australian National University)

Abstract

Exact optimal paths are calculated for two closed, continuous-time economies with explicit functional forms for utility from consumption, and for production from human-made capital and a non-renewable resource. Features of the first economy are non-linear utility, hyperbolic utility discounting and (possibly) hyperbolic technical progress. In it: (a) welfare-equivalent income > wealth-equivalent income > Sefton-Weale income > Net National Product, confirming that even if income is viewed only as a measure of prosperity, there is no point in trying to define it uniquely; (b) the Solow (1974) constant consumption path is a special case for a particular discount rate; (c) for a low enough discount rate, sustained growth is optimal even when technical progress is zero. The second economy has linear utility, a non-linear output split between consumption and investment, and exponential technical progress. In it, (a) Weitzman's (1997) technological progress premium works only if an upwards correction factor is first applied to the rate of progress in production, to convert it to a rate of progress in Net National Product; (b) Hartwick's rule has an unfamiliar form.

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Bibliographic Info

Paper provided by Australian National University, Centre for Resource and Environmental Studies, Ecological Economics Program in its series Working Papers in Ecological Economics with number 0102.

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Date of creation: Apr 2001
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Handle: RePEc:anu:wpieep:0102

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Web page: http://incres.anu.edu.au/EEP/wp.html

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  1. Norman Henderson & Ian Bateman, 1995. "Empirical and public choice evidence for hyperbolic social discount rates and the implications for intergenerational discounting," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 5(4), pages 413-423, June.
  2. William D. Nordhaus, 2000. "New Directions in National Economic Accounting," American Economic Review, American Economic Association, vol. 90(2), pages 259-263, May.
  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. Usher, Dan, 1994. "Income and the Hamiltonian," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 40(2), pages 123-41, June.
  5. Laibson, David, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, MIT Press, vol. 112(2), pages 443-77, May.
  6. M. L. Weitzman, 1974. "On the Welfare Significance of National Product in Dynamic Economy," Working papers 125, Massachusetts Institute of Technology (MIT), Department of Economics.
  7. Asheim, Geir B, 1997. " Adjusting Green NNP to Measure Sustainability," Scandinavian Journal of Economics, Wiley Blackwell, vol. 99(3), pages 355-70, September.
  8. R. M. Solow, 1973. "Intergenerational Equity and Exhaustable Resources," Working papers 103, Massachusetts Institute of Technology (MIT), Department of Economics.
  9. Asheim, G.B., 1998. "Green National Accounting: Why and How?," Memorandum 08/1998, Oslo University, Department of Economics.
  10. Weitzman, Martin L, 1997. " Sustainability and Technical Progress," Scandinavian Journal of Economics, Wiley Blackwell, vol. 99(1), pages 1-13, March.
  11. Sefton, J. A. & Weale, M. R., 1996. "The net national product and exhaustible resources: The effects of foreign trade," Journal of Public Economics, Elsevier, vol. 61(1), pages 21-47, July.
  12. 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.
  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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