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Exact measures of income in a hyperbolic economy

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  • PEZZEY, JOHN C.V.

Abstract

For a closed economy with human-made capital, non-renewable resource depletion and (possibly) exogenous, hyperbolic technical progress as explicit-form inputs to a production function, there is a feasible development path that is ‘as if’ optimal with respect to hyperbolic utility discounting. On this path, typically, welfare-equivalent income > wealth-equivalent income > Sefton-Weale income > net national product, with possibly dramatic differences among these measures; and sustainable income can be greater than, equal to, or less than NNP. For low enough discounting, growing consumption is optimal even when technical progress is zero. A particular discount rate makes all income measures and consumption constant and (except net national product) equal; and zero technical progress then gives the Solow (1974) maximin as a special case. The optimal path is time-consistent because of the way the utility discount rate is chosen to depend on the economy's stocks, and hence on absolute time.

Suggested Citation

  • Pezzey, John C.V., 2004. "Exact measures of income in a hyperbolic economy," Environment and Development Economics, Cambridge University Press, vol. 9(4), pages 473-484, August.
    • Handle: RePEc:cup:endeec:v:9:y:2004:i:04:p:473-484_00
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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 economy on the initial state: a comparison of models usi," MPRA Paper 35888, University Library of Munich, Germany.
    5. 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.
    6. 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.
    7. 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.
    8. 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).
    9. Bazhanov, Andrei, 2008. "Sustainable growth in a resource-based economy: the extraction-saving relationship," MPRA Paper 12350, University Library of Munich, Germany.
    10. Christian Groth & Karl-Josef Koch & Thomas M. Steger, 2006. "Rethinking the Concept of Long-Run Economic Growth," Discussion Papers 06-06, University of Copenhagen. Department of Economics.
    11. 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.
    12. Bazhanov, Andrei V., 2013. "Constant-utility paths in a resource-based economy," Resource and Energy Economics, Elsevier, vol. 35(3), pages 342-355.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.

    More about this item

    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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