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Exact Measures of Income in a Hyperbolic Economy

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  • John C. V. Pezzey

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

Abstract

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.

Suggested Citation

  • John C. V. Pezzey, 2002. "Exact Measures of Income in a Hyperbolic Economy," Economics and Environment Network Working Papers 0203, Australian National University, Economics and Environment Network.
    • Handle: RePEc:anu:eenwps:0203
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    File URL: http://een.anu.edu.au/download_files/een0203.pdf
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    References listed on IDEAS

    as
    1. 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, Elsevier.
    2. Norman Henderson & Ian Bateman, 1995. "Empirical and public choice evidence for hyperbolic social discount rates and the implications for intergenerational discounting," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 5(4), pages 413-423, June.
    3. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    4. Martin L. Weitzman, 1976. "On the Welfare Significance of National Product in a Dynamic Economy," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(1), pages 156-162.
    5. Martin L. Weitzman, 2001. "Gamma Discounting," American Economic Review, American Economic Association, vol. 91(1), pages 260-271, March.
    6. Vincent, Jeffrey R., 2000. "Green accounting: from theory to practice," Environment and Development Economics, Cambridge University Press, vol. 5(1), pages 13-24, February.
    7. Robert M. Solow, 1974. "The Economics of Resources or the Resources of Economics," Palgrave Macmillan Books, in: Chennat Gopalakrishnan (ed.), Classic Papers in Natural Resource Economics, chapter 12, pages 257-276, Palgrave Macmillan.
    8. repec:bla:revinw:v:40:y:1994:i:2:p:123-41 is not listed on IDEAS
    9. William D. Nordhaus, 2000. "New Directions in National Economic Accounting," American Economic Review, American Economic Association, vol. 90(2), pages 259-263, May.
    10. Asheim, Geir B., 2000. "Green national accounting: why and how?," Environment and Development Economics, Cambridge University Press, vol. 5(1), pages 25-48, February.
    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 972-974, December.
    13. R. M. Solow, 1974. "Intergenerational Equity and Exhaustible Resources," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(5), pages 29-45.
    14. Geir B. Asheim, 1997. "Adjusting Green NNP to Measure Sustainability," Scandinavian Journal of Economics, Wiley Blackwell, vol. 99(3), pages 355-370, September.
    15. Tjalling C. Koopmans, 1959. "Stationary Ordinal Utility and Impatience," Cowles Foundation Discussion Papers 81, Cowles Foundation for Research in Economics, Yale University.
    16. repec:bla:scandj:v:100:y:1998:i:2:p:513-27 is not listed on IDEAS
    17. Joseph Stiglitz, 1974. "Growth with Exhaustible Natural Resources: Efficient and Optimal Growth Paths," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(5), pages 123-137.
    18. Martin L. Weitzman, 1997. "Sustainability and Technical Progress," Scandinavian Journal of Economics, Wiley Blackwell, vol. 99(1), pages 1-13, March.
    19. Partha Dasgupta & Geoffrey Heal, 1974. "The Optimal Depletion of Exhaustible Resources," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(5), pages 3-28.
    20. repec:bla:scandj:v:99:y:1997:i:3:p:355-70 is not listed on IDEAS
    21. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 443-478.
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    Cited by:

    1. Bazhanov, Andrei V., 2013. "Constant-utility paths in a resource-based economy," Resource and Energy Economics, Elsevier, vol. 35(3), pages 342-355.
    2. Christian Groth & Karl-Josef Koch & Thomas Steger, 2006. "Rethinking the Concept of Long-Run Economic Growth," CESifo Working Paper Series 1701, CESifo.
    3. Christian Groth & Karl-Josef Koch & Thomas Steger, 2010. "When economic growth is less than exponential," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(2), pages 213-242, August.
    4. 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.
    5. 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.
    6. Cairns, Robert D. & Martinet, Vincent, 2021. "Growth and long-run sustainability," Environment and Development Economics, Cambridge University Press, vol. 26(4), pages 381-402, August.
    7. 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.
    8. Bazhanov, Andrei, 2011. "Зависимость Долгосрочного Роста Ресурсной Экономики От Начального Состояния: Сравнение Моделей На Примере Российской Нефтедобычи [The dependence of the potential sustainability of a resource econom," MPRA Paper 35888, University Library of Munich, Germany.
    9. Cabo, Francisco & Martín-Herrán, Guiomar & Martínez-García, María Pilar, 2016. "Unbounded growth in the Neoclassical growth model with non-constant discounting," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 93-104.
    10. 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.
    11. 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.
    12. 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.
    13. Asheim, Geir B. & Hartwick, John M. & Mitra, Tapan, 2021. "Investment rules and time invariance under population growth," Journal of Economic Dynamics and Control, Elsevier, vol. 123(C).
    14. Bazhanov, Andrei, 2008. "Sustainable growth in a resource-based economy: the extraction-saving relationship," MPRA Paper 12350, University Library of Munich, Germany.
    15. Kirk Hamilton & Giovanni Ruta & Liaila Tajibaeva, 2006. "Capital Accumulation and Resource Depletion: A Hartwick Rule Counterfactual," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 34(4), pages 517-533, August.
    16. Anna M. Dugan & Timo Trimborn, 2020. "The Optimal Extraction of Non-Renewable Resources under Hyperbolic Discounting," Economics Working Papers 2020-17, Department of Economics and Business Economics, Aarhus University.
    17. Andrei Bazhanov, 2012. "A Closed-Form Solution to Stollery’s Problem with Damage in Utility," Computational Economics, Springer;Society for Computational Economics, vol. 39(4), pages 365-386, April.

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    More about this item

    Keywords

    national income; discounting; hyperbolic; accounting; sustainability;
    All these keywords.

    JEL classification:

    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • O47 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Empirical Studies of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence
    • Q01 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - General - - - Sustainable Development

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