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Replica core limit theorem for economies with satiation

Author

Listed:
  • Hiromi Murakami

    (Faculty of Commerce, Doshisha University)

  • Ken Urai

    (Osaka University)

Abstract

Dividend equilibrium, defined by Aumann and Drèze (1986), is one of the most general competitive equilibrium concepts for markets that include satiated consumers. Konovalov (2005) shows a core equivalence theorem to the dividend equilibrium using the concept of rejective core. Konovalov’s argument, however, is based on the setting of a continuum atomless economy with a finite number of types, and the core limit problem for dividend equilibrium remains unsolved. In a previous paper, Urai and Murakami (2016), we provided a generalization of the Debreu–Scarf (1963) core limit theorem for monetary overlapping generations economies under an extended concept of replica core allocation. In this paper, we show that the concept and method also provide rejective core limit and equivalence theorems for economies with satiation.

Suggested Citation

  • Hiromi Murakami & Ken Urai, 2017. "Replica core limit theorem for economies with satiation," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 259-270, October.
  • Handle: RePEc:spr:etbull:v:5:y:2017:i:2:d:10.1007_s40505-017-0119-2
    DOI: 10.1007/s40505-017-0119-2
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    References listed on IDEAS

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    1. Allouch, Nizar & Florenzano, Monique, 2013. "Edgeworth rejective core and dividends equilibria of satiated exchange economies," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 1-6.
    2. Andreu Mas-Colell, 1992. "Equilibrium Theory with Possibly Satiated Preferences," Palgrave Macmillan Books, in: Mukul Majumdar (ed.), Equilibrium and Dynamics, chapter 9, pages 201-213, Palgrave Macmillan.
    3. Gerard Debreu, 1963. "On a Theorem of Scarf," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 177-180.
    4. Aumann, Robert J & Dreze, Jacques H, 1986. "Values of Markets with Satiation or Fixed Prices," Econometrica, Econometric Society, vol. 54(6), pages 1271-1318, November.
    5. Urai, Ken & Murakami, Hiromi, 2016. "Replica core equivalence theorem: An extension of the Debreu–Scarf limit theorem to double infinity monetary economies," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 83-88.
    6. Alexander Konovalov, 2005. "The core of an economy with satiation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(3), pages 711-719, April.
    7. Grandmont, Jean-Michel, 1993. "Temporary general equilibrium theory," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 19, pages 879-922, Elsevier.
    8. Sonnenschein, Hugo, 1974. "An Axiomatic Characterization of the Price Mechanism," Econometrica, Econometric Society, vol. 42(3), pages 425-433, May.
    9. Thomson, William, 1988. "A study of choice correspondences in economies with a variable number of agents," Journal of Economic Theory, Elsevier, vol. 46(2), pages 237-254, December.
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    Cited by:

    1. Kohzo Shiraishi & Ken Urai & Hiromi Murakami, 2018. "Stability and Universal Implementability of the Price Mechanism," Discussion Papers in Economics and Business 18-16, Osaka University, Graduate School of Economics.
    2. Ken Urai & Hiromi Murakami & Daisuke Kobayashi, 2023. "The State Finance and Public Goods from The General Equilibrium Viewpoint: Fundamental Welfare Theorems for Lindahlian General Equilibrium with Money," Discussion Papers in Economics and Business 23-08, Osaka University, Graduate School of Economics.
    3. Bhowmik, Anuj & Dharanan, GVA, 2021. "Core equivalence in presence of satiation and indivisibilities," MPRA Paper 105790, University Library of Munich, Germany.
    4. Ken Urai & Hiromi Murakami & Takahiro Moriya, 2022. "Existence of Monetary Equilibrium for Overlapping Generations Economies with Satiated Agents," Discussion Papers in Economics and Business 22-03, Osaka University, Graduate School of Economics.

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    More about this item

    Keywords

    Dividend equilibrium; Core equivalence; Replica economy; Satiation; Rejective core;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General

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