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Consumer Optimization and a First-Order PDE with a Non-Smooth System

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  • Yuhki Hosoya

    (Chuo University)

Abstract

We study a first-order nonlinear partial differential equation and present a necessary and sufficient condition for the global existence of its solution in a non-smooth environment. Using this result, we prove a local existence theorem for a solution to this differential equation. Moreover, we present two applications of this result. The first concerns an inverse problem called the integrability problem in microeconomic theory and the second concerns an extension of Frobenius’ theorem.

Suggested Citation

  • Yuhki Hosoya, 2021. "Consumer Optimization and a First-Order PDE with a Non-Smooth System," SN Operations Research Forum, Springer, vol. 2(4), pages 1-36, December.
    • Handle: RePEc:spr:snopef:v:2:y:2021:i:4:d:10.1007_s43069-021-00104-w
    DOI: 10.1007/s43069-021-00104-w
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    References listed on IDEAS

    as
    1. Debreu, Gerard, 1976. "Smooth Preferences: A Corrigendum," Econometrica, Econometric Society, vol. 44(4), pages 831-832, July.
    2. Mas-Colell, Andreu, 1977. "The Recoverability of Consumers' Preferences from Market Demand Behavior," Econometrica, Econometric Society, vol. 45(6), pages 1409-1430, September.
    3. Hosoya, Yuhki, 2013. "Measuring utility from demand," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 82-96.
    4. Hosoya, Yuhki, 2020. "Recoverability revisited," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 31-41.
    5. Hosoya, Yuhki, 2017. "The relationship between revealed preference and the Slutsky matrix," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 127-146.
    6. Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-615, July.
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    Citations

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    Cited by:

    1. Yuhki Hosoya, 2022. "Non-Smooth Integrability Theory," Papers 2203.04770, arXiv.org, revised Mar 2024.
    2. Yuhki Hosoya, 2024. "Non-smooth integrability theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(2), pages 475-520, September.
    3. Yuhki Hosoya, 2024. "The Relationship between Consumer Theories with and without Utility Maximization," Papers 2404.10931, arXiv.org.

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