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Indivisible commodities and an equivalence theorem on the strong core

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  • Inoue, Tomoki

    (Center for Mathematical Economics, Bielefeld University)

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 cost-minimized Walras allocations. Because of the indivisibility, the preference maximization does not imply the cost minimization. A cost-minimized Walras equilibrium is a state where, under some price vector, all agents satisfy both the preference maximization and the cost minimization.

Suggested Citation

  • 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.
    • Handle: RePEc:bie:wpaper:417
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    File URL: https://pub.uni-bielefeld.de/download/2316412/2319862
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    References listed on IDEAS

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    1. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702.
    2. Inoue, Tomoki, 2008. "Indivisible commodities and the nonemptiness of the weak core," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 96-111, January.
    3. Bewley, Truman F, 1973. "Edgeworth's Conjecture," Econometrica, Econometric Society, vol. 41(3), pages 425-454, May.
    4. 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.
    5. Anderson, Robert M, 1978. "An Elementary Core Equivalence Theorem," Econometrica, Econometric Society, vol. 46(6), pages 1483-1487, November.
    6. 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.
    7. 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.
    8. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
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    11. Henry, Claude, 1970. "Indivisibilites dans une Economie d'Echanges. (With English summary.)," Econometrica, Econometric Society, vol. 38(3), pages 542-558, May.
    12. Green, Jerry R., 1972. "On the inequitable nature of core allocations," Journal of Economic Theory, Elsevier, vol. 4(2), pages 132-143, April.
    13. 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.
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    Cited by:

    1. 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.
    2. 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.

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    Keywords

    Cost-minimized Walras equilibrium; Core equivalence; Indivisible commodities; Strong core;
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