Exact measures of income in two capital-resource-time economies
AbstractExact 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper 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.
Date of creation: Apr 2001
Date of revision:
Contact details of provider:
Web page: http://incres.anu.edu.au/EEP/wp.html
This paper has been announced in the following NEP Reports:
- NEP-ALL-2001-04-21 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- R. M. Solow, 1973. "Intergenerational Equity and Exhaustable Resources," Working papers 103, Massachusetts Institute of Technology (MIT), Department of Economics.
- 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
- Weitzman, Martin L, 1997. " Sustainability and Technical Progress," Scandinavian Journal of Economics, Wiley Blackwell, vol. 99(1), pages 1-13, March.
- 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.
- 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.
- Laibson, David, 1997.
"Golden Eggs and Hyperbolic Discounting,"
The Quarterly Journal of Economics,
MIT Press, vol. 112(2), pages 443-77, May.
- Asheim, Geir B, 1997. " Adjusting Green NNP to Measure Sustainability," Scandinavian Journal of Economics, Wiley Blackwell, vol. 99(3), pages 355-70, September.
- William D. Nordhaus, 2000. "New Directions in National Economic Accounting," American Economic Review, American Economic Association, vol. 90(2), pages 259-263, May.
- 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.
- 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.
- John Hartwick, 1976. "Intergenerational Equity and the Investing of Rents from Exhaustible Resources," Working Papers 220, Queen's University, Department of Economics.
- M. L. Weitzman, 1974.
"On the Welfare Significance of National Product in Dynamic Economy,"
125, Massachusetts Institute of Technology (MIT), Department of Economics.
- 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.
- Asheim, Geir B., 2000.
"Green national accounting: why and how?,"
Environment and Development Economics,
Cambridge University Press, vol. 5(01), pages 25-48, February.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Jack Pezzey) The email address of this maintainer does not seem to be valid anymore. Please ask Jack Pezzey to update the entry or send us the correct address.
If references are entirely missing, you can add them using this form.