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Competitive Equilibrium With An Atomless Measure Space Of Agents And Infinite Dimensional Commodity Spaces Without Convex And Complete Preferences

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  • LEE, SANGJIK

Abstract

We prove the existence of a competitive equilibrium for an economy with an atomless measure space of agents and an infinite dimensional commodity space. The commodity space is a separable Banach space with a non-empty interior in its positive cone. We dispense with convexity and completeness assumptions on preferences. We employ a saturated probability space for the space of agents which enables us to utilize the convexifying effect on aggregation. By applying the Gale-Nikaido-Debreulemma, we provide a direct proof of the existence of a competitive equilibrium.

Suggested Citation

  • Lee, Sangjik, 2013. "Competitive Equilibrium With An Atomless Measure Space Of Agents And Infinite Dimensional Commodity Spaces Without Convex And Complete Preferences," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 54(2), pages 221-230, December.
    • Handle: RePEc:hit:hitjec:v:54:y:2013:i:2:p:221-230
    DOI: 10.15057/26020
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    Citations

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    Cited by:

    1. Niccolò Urbinati, 2020. "Walrasian objection mechanism and Mas Colell's bargaining set in economies with many commodities," Working Papers 07, Venice School of Management - Department of Management, Università Ca' Foscari Venezia.
    2. Niccolò Urbinati, 2023. "The Walrasian objection mechanism and Mas-Colell’s bargaining set in economies with many commodities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(1), pages 45-68, July.
    3. Jang, Hyo Seok & Lee, Sangjik, 2020. "Equilibria in a large production economy with an infinite dimensional commodity space and price dependent preferences," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 57-64.
    4. Bernard Cornet & V. Filipe Martins-Da-Rocha, 2021. "Fatou's Lemma for Unbounded Gelfand Integrable Mappings," Post-Print hal-03506933, HAL.
    5. Hyo Seok Jang & Sangjik Lee, 2019. "Equilibria in a large production economy with an infinite dimensional commodity space and price dependent preferences," Papers 1904.07444, arXiv.org, revised Feb 2020.
    6. Cea-Echenique, Sebastián & Fuentes, Matías, 2024. "On the continuity of the Walras correspondence in distributional economies with an infinite-dimensional commodity space," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 61-69.
    7. Khan, M. Ali & Sagara, Nobusumi, 2016. "Relaxed large economies with infinite-dimensional commodity spaces: The existence of Walrasian equilibria," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 95-107.

    More about this item

    Keywords

    convexifying effect; saturated probability space; the Gale-Nikaido-Debreu lemma;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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