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

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  • Julien, Ludovic A.

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.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:ecolet:v:229:y:2023:i:c:s0165176523002215
    DOI: 10.1016/j.econlet.2023.111196
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    References listed on IDEAS

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    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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