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Intertemporal Utility with Heterogeneous Goods and Constant Elasticity of Substitution

Author

Listed:
  • Martin F. Quaas
  • Stefan Baumgärtner
  • Moritz A. Drupp
  • Jasper N. Meya

Abstract

We characterize intertemporal utility functions over heterogeneous goods that feature (i) a constant elasticity of substitution between goods at each point in time and (ii) a constant intertemporal elasticity of substitution for at least one of the goods. We find that a standard (stationary) intertemporal utility function is consistent with these two properties if and only if it either is of the intertemporal constant elasticity of substitution (ICES) form, that is, if all elasticities of substitution are identical, or if the instantaneous utility function is Cobb-Douglas. We also characterize the families of standard intertemporal utility functions that feature either (i) or (ii), but not the respective other property. The ICES utility function offers a simple and consistent solution for applications that use constant good-specific intertemporal substitutability. This is, for example, relevant for dual discounting of market and non-market goods.

Suggested Citation

  • Martin F. Quaas & Stefan Baumgärtner & Moritz A. Drupp & Jasper N. Meya, 2019. "Intertemporal Utility with Heterogeneous Goods and Constant Elasticity of Substitution," CESifo Working Paper Series 7999, CESifo.
    • Handle: RePEc:ces:ceswps:_7999
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    References listed on IDEAS

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    1. Emmerling, Johannes & Groom, Ben & Wettingfeld, Tanja, 2017. "Discounting and the representative median agent," Economics Letters, Elsevier, vol. 161(C), pages 78-81.
    2. Ben Groom & Cameron Hepburn, 2017. "Reflections—Looking Back at Social Discounting Policy: The Influence of Papers, Presentations, Political Preconditions, and Personalities," Review of Environmental Economics and Policy, Association of Environmental and Resource Economists, vol. 11(2), pages 336-356.
    3. Thomas Sterner & U. Martin Persson, 2008. "An Even Sterner Review: Introducing Relative Prices into the Discounting Debate," Review of Environmental Economics and Policy, Association of Environmental and Resource Economists, vol. 2(1), pages 61-76, Winter.
    4. Gollier, Christian, 2010. "Expected net present value, expected net future value, and the Ramsey rule," Journal of Environmental Economics and Management, Elsevier, vol. 59(2), pages 142-148, March.
    5. J. R. Hicks, 1963. "The Theory of Wages," Palgrave Macmillan Books, Palgrave Macmillan, number 978-1-349-00189-7, October.
    6. Gollier, Christian, 2010. "Ecological discounting," Journal of Economic Theory, Elsevier, vol. 145(2), pages 812-829, March.
    7. Roger Guesnerie, 2004. "Calcul économique et développement durable," Revue économique, Presses de Sciences-Po, vol. 55(3), pages 363-382.
    8. Traeger, Christian P., 2011. "Sustainability, limited substitutability, and non-constant social discount rates," Journal of Environmental Economics and Management, Elsevier, vol. 62(2), pages 215-228, September.
    9. Moritz A. Drupp & Martin C. Hänsel, 2021. "Relative Prices and Climate Policy: How the Scarcity of Nonmarket Goods Drives Policy Evaluation," American Economic Journal: Economic Policy, American Economic Association, vol. 13(1), pages 168-201, February.
    10. Dixit, Avinash K & Stiglitz, Joseph E, 1977. "Monopolistic Competition and Optimum Product Diversity," American Economic Review, American Economic Association, vol. 67(3), pages 297-308, June.
    11. Blackorby, Charles & Russell, R Robert, 1989. "Will the Real Elasticity of Substitution Please Stand Up? (A Comparison of the Allen/Uzawa and Morishima Elasticities)," American Economic Review, American Economic Association, vol. 79(4), pages 882-888, September.
    12. Daniel McFadden, 1963. "Constant Elasticity of Substitution Production Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(2), pages 73-83.
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    Cited by:

    1. Jie Xu & Ming Gao & Yina Zhang, 2021. "The variations in individual consumption change and the substitution effect under the shock of COVID‐19: Evidence from payment system data in China," Growth and Change, Wiley Blackwell, vol. 52(2), pages 990-1010, June.
    2. Julien, Ludovic A., 2023. "A formula for the elasticity of substitution of a large class of smooth utility functions," Economics Letters, Elsevier, vol. 229(C).
    3. Coralie KERSULEC & Luc DOYEN, 2022. "From fork to fish: The role of consumer preferences on the sustainability of fisheries," Bordeaux Economics Working Papers 2022-10, Bordeaux School of Economics (BSE).
    4. Lingmei Han & Jianqiang You & Jiening Meng, 2023. "Environmental Value Assessment of Plastic Pollution Control: A Study Based on Evidence from a Survey in China," Sustainability, MDPI, vol. 15(13), pages 1-16, June.
    5. Venmans, Frank & Groom, Ben, 2021. "Social discounting, inequality aversion, and the environment," Journal of Environmental Economics and Management, Elsevier, vol. 109(C).
    6. Yacouba Kassouri, 2024. "The Rise of Transnational Financial Crimes and Tropical Deforestation," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 87(10), pages 2795-2831, October.
    7. Jasper N. Meya & Stefan Baumgärtner & Moritz A. Drupp & Martin F. Quaas, 2020. "Inequality and the Value of Public Natural Capital," CESifo Working Paper Series 8752, CESifo.

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    More about this item

    Keywords

    substitutability; CES; CIES; intertemporal utility; non-market goods;
    All these keywords.

    JEL classification:

    • D15 - Microeconomics - - Household Behavior - - - Intertemporal Household Choice; Life Cycle Models and Saving
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • Q51 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Valuation of Environmental Effects

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