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Logarithmically homogeneous preferences

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  • Miyake, Mitsunobu

Abstract

An extended-real-valued function on R+n is called logarithmically homogeneous if it is given by the logarithmic transformation of a homogeneous function on R+n. Specifying a consumer’s preference on the consumption set by a difference comparison relation, this paper provides some axioms on the relation under which the full class of utility functions representing the relation are logarithmically homogeneous. It is also shown that all the utility functions are strongly concave and all the indirect utility functions are logarithmically homogeneous. Moreover, the additively separable logarithmic utility functions are derived by strengthening one of the axioms.

Suggested Citation

  • Miyake, Mitsunobu, 2016. "Logarithmically homogeneous preferences," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 1-9.
    • Handle: RePEc:eee:mateco:v:67:y:2016:i:c:p:1-9
    DOI: 10.1016/j.jmateco.2016.08.005
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    References listed on IDEAS

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    Cited by:

    1. Hosoya, Yuhki, 2022. "An axiom for concavifiable preferences in view of Alt’s theory," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    2. Chen, Yi-Hsuan & Vinogradov, Dmitri V., 2021. "Coins with benefits: On existence, pricing kernel and risk premium of cryptocurrencies," IRTG 1792 Discussion Papers 2021-006, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    3. Yuhki Hosoya, 2021. "An Axiom for Concavifiable Preferences in View of Alt's Theory," Papers 2102.07237, arXiv.org, revised Nov 2021.

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