Exact Measures of Income in a Hyperbolic Economy
AbstractExact 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.
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, Economics and Environment Network in its series Economics and Environment Network Working Papers with number 0203.
Length: 27 pages
Date of creation: Jan 2002
Date of revision:
Contact details of provider:
Web page: http://een.anu.edu.au/
national income; discounting; hyperbolic; accounting; sustainability;
Other versions of this item:
- D90 - Microeconomics - - Intertemporal Choice - - - General
- O47 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Measurement of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence
- Q01 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - General - - - Sustainable Development
This paper has been announced in the following NEP Reports:
- NEP-ALL-2002-08-19 (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.:
- Weitzman, Martin L, 1997. " Sustainability and Technical Progress," Scandinavian Journal of Economics, Wiley Blackwell, vol. 99(1), pages 1-13, March.
- Martin L. Weitzman, 1998.
Harvard Institute of Economic Research Working Papers
1843, Harvard - Institute of Economic Research.
- Laibson, David I., 1997.
"Golden Eggs and Hyperbolic Discounting,"
4481499, Harvard University Department of Economics.
- 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.
- 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.
- 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.
- 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
- Tjalling C. Koopmans, 1959. "Stationary Ordinal Utility and Impatience," Cowles Foundation Discussion Papers 81, Cowles Foundation for Research in Economics, Yale University.
- Asheim, Geir B, 1997. " Adjusting Green NNP to Measure Sustainability," Scandinavian Journal of Economics, Wiley Blackwell, vol. 99(3), pages 355-70, September.
- 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.
- 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.
- R. M. Solow, 1973. "Intergenerational Equity and Exhaustable Resources," Working papers 103, Massachusetts Institute of Technology (MIT), Department of Economics.
- William D. Nordhaus, 2000. "New Directions in National Economic Accounting," American Economic Review, American Economic Association, vol. 90(2), pages 259-263, May.
- Vincent, Jeffrey R., 2000. "Green accounting: from theory to practice," Environment and Development Economics, Cambridge University Press, vol. 5(01), pages 13-24, February.
- 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.
- Asheim, G.B., 1998.
"Green National Accounting: Why and How?,"
08/1998, Oslo University, Department of Economics.
- 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.
- Christian Groth & Karl-Josef Koch & Thomas M. Steger, 2009.
"When economic growth is less than exponential,"
MAGKS Papers on Economics
200931, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
- Christian Groth & Karl-Josef Koch & Thomas M. Steger, . "When Economic Growth is Less than Exponential," EPRU Working Paper Series 2009-03, Economic Policy Research Unit (EPRU), University of Copenhagen. Department of Economics, revised May 2009.
- Christian Groth & Karl-Josef Koch & Thomas M. Steger, 2009. "When economic growth is less than exponential," Volkswirtschaftliche DiskussionsbeitrÃ¤ge 129-09, Universität Siegen, Fakultät Wirtschaftswissenschaften, Wirtschaftsinformatik und Wirtschaftsrecht.
- Andrei Bazhanov, 2012. "A Closed-Form Solution to Stollery’s Problem with Damage in Utility," Computational Economics, Society for Computational Economics, vol. 39(4), pages 365-386, April.
- Bazhanov, A., 2011.
"The Dependence of the Potential Sustainability of a Resource Economy on the Initial State: a Comparison of Models Using the Example of Russian Oil Extraction,"
Journal of the New Economic Association,
New Economic Association, issue 12, pages 77-100.
- Bazhanov, Andrei, 2011. "The dependence of the potential sustainability of a resource economy on the initial state: a comparison of models using the example of Russian oil extraction," MPRA Paper 35870, University Library of Munich, Germany.
- Geir B. Asheim & Wolfgang Buchholz & John M. Hartwick & Tapan Mitra & Cees A. Withagen, 2005.
"Constant Savings Rates and Quasi-Arithmetic Population Growth under Exhaustible Resource Constraints,"
CESifo Working Paper Series
1573, CESifo Group Munich.
- 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.
- Asheim, Geir B. & Buchholz, Wolfgang & Hartwick, John M. & Mitra, Tapan & Withagen, Cees, 2005. "Constant savings rates and quasi-arithmetic population growth under exhaustible resource constraints," Memorandum 23/2005, Oslo University, Department of Economics.
- Bazhanov, Andrei, 2008. "Sustainable growth in a resource-based economy: the extraction-saving relationship," MPRA Paper 12350, University Library of Munich, Germany.
- Bazhanov, Andrei V., 2010. "Sustainable growth: Compatibility between a plausible growth criterion and the initial state," Resources Policy, Elsevier, vol. 35(2), pages 116-125, June.
- Christian Groth & Karl-Josef Koch & Thomas M. Steger, 2006.
"Rethinking the Concept of Long-Run Economic Growth,"
06-06, University of Copenhagen. Department of Economics.
- Christian Groth & Karl-Josef Koch & Thomas Steger, 2006. "Rethinking the Concept of Long-Run Economic Growth," CESifo Working Paper Series 1701, CESifo Group Munich.
- Bazhanov, Andrei, 2010. "A closed form solution to Stollery's global warming problem with temperature in utility," MPRA Paper 22406, University Library of Munich, Germany.
- John C. V. Pezzey, 2005. "Sustained growth from non-renewable resources: constant absolute genuine savings and constant relative genuine savings compared," Economics and Environment Network Working Papers 0502, Australian National University, Economics and Environment Network.
- Hamilton, Kirk & Ruta, Giovanni & Tajibaeva, Liaila, 2005.
"Capital accumulation and resources depletion - a Hartwick rule counterfactual,"
Policy Research Working Paper Series
3480, The World Bank.
- Kirk Hamilton & Giovanni Ruta & Liaila Tajibaeva, 2006. "Capital Accumulation and Resource Depletion: A Hartwick Rule Counterfactual," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 34(4), pages 517-533, August.
- Bazhanov, Andrei, 2010.
"Constant-utility paths in a resource-based economy,"
27619, University Library of Munich, Germany, revised 20 Dec 2010.
- Bazhanov, Andrei V., 2013. "Constant-utility paths in a resource-based economy," Resource and Energy Economics, Elsevier, vol. 35(3), pages 342-355.
- John C. V. Pezzey, 2002. "A One-sided Sustainability Test With Multiple Consumption Goods," Working Papers in Ecological Economics 0201, Australian National University, Centre for Resource and Environmental Studies, Ecological Economics Program.
- Bazhanov, Andrei, 2011. "Зависимость Долгосрочного Роста Ресурсной Экономики От Начального Состояния: Сравнение Моделей На Примере �," MPRA Paper 35888, University Library of Munich, Germany.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Jack Pezzey).
If references are entirely missing, you can add them using this form.