IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v54y2014icp22-35.html
   My bibliography  Save this article

Indivisible commodities and an equivalence theorem on the strong core

Author

Listed:
  • Inoue, Tomoki

Abstract

We consider a pure exchange economy with finitely many indivisible commodities that are available only in integer quantities. We prove that in such an economy with a sufficiently large number of agents, but finitely many agents, the strong core coincides with the set of expenditure-minimizing Walrasian allocations. Because of the indivisibility, the preference maximization does not imply the expenditure minimization. An expenditure-minimizing Walrasian equilibrium is a state where, under some price vector, all agents satisfy both the preference maximization and the expenditure minimization.

Suggested Citation

  • Inoue, Tomoki, 2014. "Indivisible commodities and an equivalence theorem on the strong core," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 22-35.
    • Handle: RePEc:eee:mateco:v:54:y:2014:i:c:p:22-35
    DOI: 10.1016/j.jmateco.2014.07.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406814000901
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2014.07.002?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. Schmeidler, David, 1972. "A Remark on the Core of an Atomless Economy," Econometrica, Econometric Society, vol. 40(3), pages 579-580, May.
    2. Kaneko, Mamoru, 1982. "The central assignment game and the assignment markets," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 205-232, September.
    3. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702.
    4. Inoue, Tomoki, 2008. "Indivisible commodities and the nonemptiness of the weak core," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 96-111, January.
    5. Bewley, Truman F, 1973. "Edgeworth's Conjecture," Econometrica, Econometric Society, vol. 41(3), pages 425-454, May.
    6. Inoue, Tomoki, 2011. "Core allocations may not be Walras allocations in any large finite economy with indivisible commodities," Center for Mathematical Economics Working Papers 419, Center for Mathematical Economics, Bielefeld University.
    7. Anderson, Robert M, 1978. "An Elementary Core Equivalence Theorem," Econometrica, Econometric Society, vol. 46(6), pages 1483-1487, November.
    8. Wako, Jun, 1984. "A note on the strong core of a market with indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 13(2), pages 189-194, October.
    9. Inoue, Tomoki, 2011. "Strong core equivalence theorem in an atomless economy with indivisible commodities," Center for Mathematical Economics Working Papers 418, Center for Mathematical Economics, Bielefeld University.
    10. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    11. Gerard Debreu, 1963. "On a Theorem of Scarf," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 177-180.
    12. Anderson, Robert M., 1992. "The core in perfectly competitive economies," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 14, pages 413-457, Elsevier.
    13. Roth, Alvin E. & Postlewaite, Andrew, 1977. "Weak versus strong domination in a market with indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 131-137, August.
    14. Henry, Claude, 1970. "Indivisibilites dans une Economie d'Echanges. (With English summary.)," Econometrica, Econometric Society, vol. 38(3), pages 542-558, May.
    15. Green, Jerry R., 1972. "On the inequitable nature of core allocations," Journal of Economic Theory, Elsevier, vol. 4(2), pages 132-143, April.
    16. Inoue, Tomoki, 2005. "Do pure indivisibilities prevent core equivalence? Core equivalence theorem in an atomless economy with purely indivisible commodities only," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 571-601, August.
    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. Michael Florig & Jorge Rivera, 2015. "Existence of a competitive equilibrium when all goods are indivisible," Working Papers wp403, University of Chile, Department of Economics.
    2. Florig, Michael & Rivera, Jorge, 2017. "Existence of a competitive equilibrium when all goods are indivisible," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 145-153.

    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. Inoue, Tomoki, 2011. "Indivisible commodities and an equivalence theorem on the strong core," Center for Mathematical Economics Working Papers 417, Center for Mathematical Economics, Bielefeld University.
    2. Inoue, Tomoki, 2005. "Do pure indivisibilities prevent core equivalence? Core equivalence theorem in an atomless economy with purely indivisible commodities only," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 571-601, August.
    3. Roberto Serrano & Oscar Volij, 2008. "Mistakes in Cooperation: the Stochastic Stability of Edgeworth's Recontracting," Economic Journal, Royal Economic Society, vol. 118(532), pages 1719-1741, October.
    4. Wooders, Myrna H., 2001. "Some corrections to claims about the literature in Engl and Scotchmer (1996)," Journal of Mathematical Economics, Elsevier, vol. 36(4), pages 295-309, December.
    5. Alejandro Manelli, 1990. "Core Convergence Without Monotone Preferences or Free Disposal," Discussion Papers 891, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Inoue, Tomoki, 2011. "Strong core equivalence theorem in an atomless economy with indivisible commodities," Center for Mathematical Economics Working Papers 418, Center for Mathematical Economics, Bielefeld University.
    7. Federico Echenique & Sumit Goel & SangMok Lee, 2022. "Stable allocations in discrete exchange economies," Papers 2202.04706, arXiv.org, revised Feb 2024.
    8. Greenberg, Joseph & Weber, Shlomo & Yamazaki, Akira, 2007. "On blocking coalitions: Linking Mas-Colell with Grodal-Schmeidler-Vind," Journal of Mathematical Economics, Elsevier, vol. 43(5), pages 615-628, June.
    9. Satoru Fujishige & Zaifu Yang, 2022. "Barter markets, indivisibilities, and Markovian core," Bulletin of Economic Research, Wiley Blackwell, vol. 74(1), pages 39-48, January.
    10. Ivan Balbuzanov & Maciej H. Kotowski, 2019. "Endowments, Exclusion, and Exchange," Econometrica, Econometric Society, vol. 87(5), pages 1663-1692, September.
    11. Charalambos Aliprantis & Kim Border & Owen Burkinshaw, 1996. "Market economies with many commodities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 19(1), pages 113-185, March.
    12. Aslan, Fatma & Lainé, Jean, 2020. "Competitive equilibria in Shapley–Scarf markets with couples," Journal of Mathematical Economics, Elsevier, vol. 89(C), pages 66-78.
    13. Péter Biró & Flip Klijn & Xenia Klimentova & Ana Viana, 2021. "Shapley-Scarf Housing Markets: Respecting Improvement, Integer Programming, and Kidney Exchange," Working Papers 1235, Barcelona School of Economics.
    14. Anderson, Robert M., 2010. "Core allocations and small income transfers," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 373-381, July.
    15. Furth, Dave, 1998. "The core of the inductive limit of a direct system of economies with a communication structure," Journal of Mathematical Economics, Elsevier, vol. 30(4), pages 433-472, November.
    16. Kamijo, Yoshio & Kawasaki, Ryo, 2010. "Dynamics, stability, and foresight in the Shapley-Scarf housing market," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 214-222, March.
    17. Hervés-Beloso, Carlos & Moreno-García, Emma, 2009. "Walrasian analysis via two-player games," Games and Economic Behavior, Elsevier, vol. 65(1), pages 220-233, January.
    18. Michael Florig & Jorge Rivera, 2015. "Existence of a competitive equilibrium when all goods are indivisible," Working Papers wp403, University of Chile, Department of Economics.
    19. Robert M. Anderson, 1994. "Convergence of the Aumann-Davis-Maschler and Geanakoplos Bargaining Sets," Game Theory and Information 9403002, University Library of Munich, Germany.
    20. Committee, Nobel Prize, 2012. "Alvin E. Roth and Lloyd S. Shapley: Stable allocations and the practice of market design," Nobel Prize in Economics documents 2012-1, Nobel Prize Committee.

    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:54:y:2014:i:c:p:22-35. 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.