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

Author

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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, 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. 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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