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A formula for the elasticity of substitution of a large class of smooth utility functions

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  • Ludovic A. Julien

    (EconomiX - EconomiX - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique)

Abstract

We derive a general formula for the elasticity of substitution of a large class of smooth utility functions. This formula depends critically on two terms: the marginal rate of substitution and the elasticity of marginal utility, which may be interpreted according to the context either as the coefficient of relative risk aversion or as the intertemporal elasticity of substitution. This formula works for homothetic and non-homothetic utility functions. Besides, it holds for two important class utility functions often used in both empirical and theoretical works: the quasi-linear utility and the Stone-Geary utility functions.
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Suggested Citation

  • Ludovic A. Julien, 2023. "A formula for the elasticity of substitution of a large class of smooth utility functions," Post-Print halshs-05019863, HAL.
    • Handle: RePEc:hal:journl:halshs-05019863
    DOI: 10.1016/j.econlet.2023.111196
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-05019863v1
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    References listed on IDEAS

    as
    1. An, Zidong & Zhang, Feinan & Li, Haibo, 2022. "Elasticity of substitution between public and private capital: Evidence from manufacturing firms in Europe," Economics Letters, Elsevier, vol. 219(C).
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    3. Okubo, Masakatsu, 2008. "Intertemporal substitution and nonhomothetic preferences," Economics Letters, Elsevier, vol. 98(1), pages 41-47, January.
    4. Quaas, Martin F. & Baumgärtner, Stefan & Drupp, Moritz A. & Meya, Jasper N., 2020. "Intertemporal utility with heterogeneous goods and constant elasticity of substitution," Economics Letters, Elsevier, vol. 191(C).
    5. Deaton, Angus, 1992. "Understanding Consumption," OUP Catalogue, Oxford University Press, number 9780198288244.
    6. Masao Ogaki & Carmen M. Reinhart, 1998. "Measuring Intertemporal Substitution: The Role of Durable Goods," Journal of Political Economy, University of Chicago Press, vol. 106(5), pages 1078-1098, October.
    7. 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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