IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v90y2020icp57-64.html
   My bibliography  Save this article

Equilibria in a large production economy with an infinite dimensional commodity space and price dependent preferences

Author

Listed:
  • Jang, Hyo Seok
  • Lee, Sangjik

Abstract

We prove the existence of a competitive equilibrium in a production economy with infinitely many commodities and a measure space of agents whose preferences are price dependent. We employ a saturated measure space for the set of agents and apply recent results for an infinite dimensional separable Banach space such as Lyapunov’s convexity theorem and an exact Fatou’s lemma to obtain the result.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:mateco:v:90:y:2020:i:c:p:57-64
    DOI: 10.1016/j.jmateco.2020.05.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406820300616
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2020.05.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jiuqiang Liu, 2017. "Existence of competitive equilibrium in coalition production economies with a continuum of agents," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 941-955, November.
    2. Schmeidler, David, 1969. "Competitive Equilibria in Markets with a Continuum of Traders and Incomplete Preferences," Econometrica, Econometric Society, vol. 37(4), pages 578-585, October.
    3. Hildenbrand, Werner, 1970. "Existence of Equilibria for Economies with Production and a Measure Space of Consumers," Econometrica, Econometric Society, vol. 38(5), pages 608-623, September.
    4. Yves Balasko, 2003. "Temporary financial equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(1), pages 1-18, January.
    5. 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.
    6. Shafer, Wayne J, 1974. "The Nontransitive Consumer," Econometrica, Econometric Society, vol. 42(5), pages 913-919, September.
    7. Balasko, Yves, 2003. "Economies with price-dependent preferences," Journal of Economic Theory, Elsevier, vol. 109(2), pages 333-359, April.
    8. Michael Greinecker & Konrad Podczeck, 2013. "Liapounoff’s vector measure theorem in Banach spaces and applications to general equilibrium theory," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 157-173, November.
    9. Konard Podczeck, 1997. "Markets with infinitely many commodities and a continuum of agents with non-convex preferences (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(3), pages 385-426.
    10. Podczeck, Konrad, 2008. "On the convexity and compactness of the integral of a Banach space valued correspondence," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 836-852, July.
    11. Toussaint, Sabine, 1984. "On the existence of equilibria in economies with infinitely many commodities and without ordered preferences," Journal of Economic Theory, Elsevier, vol. 33(1), pages 98-115, June.
    12. GREENBERG, Joseph & SHITOVITZ, Benyamin & WIECZOREK, Andrzej, 1979. "Existence of equilibria in atomless production economies with price dependent preferences," LIDAM Reprints CORE 361, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. 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.
    14. HILDENBRAND, Werner, 1970. "Existence of equilibria for economies with production and a measure space of consumers," LIDAM Reprints CORE 79, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    15. Noguchi, Mitsunori, 1997. "Economies with a continuum of consumers, a continuum of suppliers and an infinite dimensional commodity space," Journal of Mathematical Economics, Elsevier, vol. 27(1), pages 1-21, February.
    16. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, March.
    17. Greenberg, Joseph & Shitovitz, Benyamin & Wieczorek, Andrzej, 1979. "Existence of equilibria in atomless production economies with price dependent preferences," Journal of Mathematical Economics, Elsevier, vol. 6(1), pages 31-41, March.
    18. Sun, Yeneng & Yannelis, Nicholas C., 2008. "Saturation and the integration of Banach valued correspondences," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 861-865, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. He, Wei & Sun, Yeneng, 2022. "Conditional expectation of Banach valued correspondences and economic applications," Journal of Mathematical Economics, Elsevier, vol. 101(C).
    2. Yang, Zhe & Song, Qingping, 2022. "A weak α-core existence theorem of generalized games with infinitely many players and pseudo-utilities," Mathematical Social Sciences, Elsevier, vol. 116(C), pages 40-46.
    3. 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.
    4. 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.
    5. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. Motoki Otsuka, 2024. "The existence of Walrasian equilibrium: infinitely many commodities, measure space of agents, and discontinuous preferences," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(2), pages 119-140, December.
    5. Bernard Cornet & V. Filipe Martins-Da-Rocha, 2021. "Fatou's Lemma for Unbounded Gelfand Integrable Mappings," Post-Print hal-03506933, HAL.
    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.
    7. Bernard Cornet & Mihaela Topuzu, 2005. "Existence of equilibria for economies with externalities and a measure space of consumers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 397-421, August.
    8. 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.
    9. Jiuqiang Liu & Huihui Zhang, 2016. "Coincidence of the Mas-Colell bargaining set and the set of competitive equilibria in a continuum coalition production economy," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1095-1109, November.
    10. M. Ali Khan & Nobusumi Sagara, 2021. "Fuzzy Core Equivalence in Large Economies: A Role for the Infinite-Dimensional Lyapunov Theorem," Papers 2112.15539, arXiv.org.
    11. M. Ali Khan & Metin Uyanik, 2021. "The Yannelis–Prabhakar theorem on upper semi-continuous selections in paracompact spaces: extensions and applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 799-840, April.
    12. Filipe Martins-da-Rocha, V. & Topuzu, Mihaela, 2008. "Cournot-Nash equilibria in continuum games with non-ordered preferences," Journal of Economic Theory, Elsevier, vol. 140(1), pages 314-327, May.
    13. Jiuqiang Liu, 2017. "Existence of competitive equilibrium in coalition production economies with a continuum of agents," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 941-955, November.
    14. Jiuqiang Liu, 2022. "Equivalence of Competitive Equilibria, Fuzzy Cores, and Fuzzy Bargaining Sets in Finite Production Economies," Mathematics, MDPI, vol. 10(18), pages 1-16, September.
    15. Noguchi, Mitsunori, 2005. "Interdependent preferences with a continuum of agents," Journal of Mathematical Economics, Elsevier, vol. 41(6), pages 665-686, September.
    16. Yang, Zhe & Song, Qingping, 2022. "A weak α-core existence theorem of generalized games with infinitely many players and pseudo-utilities," Mathematical Social Sciences, Elsevier, vol. 116(C), pages 40-46.
    17. Robert M. Anderson & Haosui Duanmu & M. Ali Khan & Metin Uyanik, 2022. "Walrasian equilibrium theory with and without free-disposal: theorems and counterexamples in an infinite-agent context," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 387-412, April.
    18. Gerasímou, Georgios, 2010. "Consumer theory with bounded rational preferences," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 708-714, September.
    19. Noguchi, Mitsunori, 1997. "Economies with a continuum of agents with the commodity-price pairing (l[infin], l1)," Journal of Mathematical Economics, Elsevier, vol. 28(3), pages 265-287, October.
    20. Yamazaki, Akira & 山崎, 昭, 2001. "On a Problem of Proving the Existence of an Equilibrium in a Large Economy without Free Disposal: A problem of a purely finitely additive measure arising from the Fatou's lemma in several dimensions," Discussion Papers 2000-10, Graduate School of Economics, Hitotsubashi University.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:90:y:2020:i:c:p:57-64. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.