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Exact Measures of Income in a Hyperbolic Economy

  • John C. V. Pezzey

    ()

    (Australian National University, Centre for Resource and Environmental Studies
    University of Bath, Department of Economics)

Exact optimal paths are calculated for a closed economy with human-made capital, non-renewable resource depletion and exogenous technical progress in production, hyperbolic utility discounting, and (possibly) hyperbolic technical progress. On its optimal path, generally, welfare-equivalent income > wealth-equivalent income > Sefton-Weale income > NNP, with possibly dramatic differences among these measures; and sustainable income can be greater, equal or less than NNP. This supports the view that there can be no best, exact definition of income. For low enough discounting, growth is optimal even when technical progress is zero. A particular discount rate makes all income measures and consumption constant and (except NNP) equal; and zero technical progress then gives the Solow (1974) maximin as a special case. General problems with calculating sustainable income when there is technical progress are discussed, and the optimal path is time-consistent if the discount rate can depend on the economy's stocks and absolute time.

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File URL: http://een.anu.edu.au/download_files/een0203.pdf
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Paper provided by Australian National University, Economics and Environment Network in its series Economics and Environment Network Working Papers with number 0203.

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Length: 27 pages
Date of creation: Jan 2002
Date of revision:
Handle: RePEc:anu:eenwps:0203
Contact details of provider: Web page: http://een.anu.edu.au/

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  1. Weitzman, Martin L, 1976. "On the Welfare Significance of National Product in a Dynamic Economy," The Quarterly Journal of Economics, MIT Press, vol. 90(1), pages 156-62, February.
  2. Asheim, Geir B, 1997. " Adjusting Green NNP to Measure Sustainability," Scandinavian Journal of Economics, Wiley Blackwell, vol. 99(3), pages 355-70, September.
  3. Heal, G., 1990. "The Optimal Use Of Exhaustible Resources," Papers fb-_90-10, Columbia - Graduate School of Business.
  4. Weitzman, Martin L, 1997. " Sustainability and Technical Progress," Scandinavian Journal of Economics, Wiley Blackwell, vol. 99(1), pages 1-13, March.
  5. Vincent, Jeffrey R., 2000. "Green accounting: from theory to practice," Environment and Development Economics, Cambridge University Press, vol. 5(01), pages 13-24, February.
  6. Tjalling C. Koopmans, 1959. "Stationary Ordinal Utility and Impatience," Cowles Foundation Discussion Papers 81, Cowles Foundation for Research in Economics, Yale University.
  7. Asheim, G.B., 1998. "Green National Accounting: Why and How?," Memorandum 08/1998, Oslo University, Department of Economics.
  8. Laibson, David I., 1997. "Golden Eggs and Hyperbolic Discounting," Scholarly Articles 4481499, Harvard University Department of Economics.
  9. 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.
  10. 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.
  11. R. M. Solow, 1973. "Intergenerational Equity and Exhaustable Resources," Working papers 103, Massachusetts Institute of Technology (MIT), Department of Economics.
  12. Martin L. Weitzman, 2001. "Gamma Discounting," American Economic Review, American Economic Association, vol. 91(1), pages 260-271, March.
  13. William D. Nordhaus, 2000. "New Directions in National Economic Accounting," American Economic Review, American Economic Association, vol. 90(2), pages 259-263, May.
  14. 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.
  15. 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.
  16. 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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