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Strong core equivalence theorem in an atomless economy with indivisible commodities

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  • Tomoki Inoue

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    (Institute of Mathematical Economics, Bielefeld University)

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    Abstract

    We consider an atomless exchange economy with indivisible commodities. Every commodity can be consumed only in integer amounts. In such an economy, because of the indivisibility, the preference maximization does not imply the cost minimization. We prove that the strong core coincides with the set of cost-minimized Walras allocations which satisfy both the preference maximization and the cost minimization under the same price vector.

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    File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-418.pdf
    File Function: First version, 2009
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    Bibliographic Info

    Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 418.

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    Length: 17 pages
    Date of creation: Mar 2009
    Date of revision:
    Handle: RePEc:bie:wpaper:418

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    Web page: http://www.imw.uni-bielefeld.de/
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    Keywords: indivisible commodities; core equivalence; strong core; cost-minimized Walras equilibrium;

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    References

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    1. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    2. Mas-Colell, Andreu, 1977. "Indivisible commodities and general equilibrium theory," Journal of Economic Theory, Elsevier, vol. 16(2), pages 443-456, December.
    3. Yamazaki, Akira, 1981. "Diversified Consumption Characteristics and Conditionally Dispersed Endowment Distribution: Regularizing Effect and Existence of Equilibria," Econometrica, Econometric Society, vol. 49(3), pages 639-54, May.
    4. Tomoki Inoue, 2009. "Indivisible commodities and an equivalence theorem on the strong core," Working Papers 417, Bielefeld University, Center for Mathematical Economics.
    5. 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.
    6. 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. Tomoki Inoue, 2009. "Indivisible commodities and an equivalence theorem on the strong core," Working Papers 417, Bielefeld University, Center for Mathematical Economics.

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