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Strong core equivalence theorem in an atomless economy with indivisible commodities

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  • Inoue, Tomoki

    (Center for Mathematical Economics, Bielefeld University)

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.

Suggested Citation

  • 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.
    • Handle: RePEc:bie:wpaper:418
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    File URL: https://pub.uni-bielefeld.de/download/2316262/2319859
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    References listed on IDEAS

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    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. Yamazaki, Akira, 1981. "Diversified Consumption Characteristics and Conditionally Dispersed Endowment Distribution: Regularizing Effect and Existence of Equilibria," Econometrica, Econometric Society, vol. 49(3), pages 639-654, May.
    3. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    4. Mas-Colell, Andreu, 1977. "Indivisible commodities and general equilibrium theory," Journal of Economic Theory, Elsevier, vol. 16(2), pages 443-456, December.
    5. Gerard Debreu, 1963. "On a Theorem of Scarf," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 177-180.
    6. 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.
    7. 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, 2014. "Indivisible commodities and an equivalence theorem on the strong core," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 22-35.
    2. 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.

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    Keywords

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