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Indivisible commodities and an equivalence theorem on the strong core

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Author Info
Tomoki Inoue () (Institute of 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.

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File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-417.pdf
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File Function: First version, 2009
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Publisher Info
Paper provided by Bielefeld University, Institute of Mathematical Economics in its series Working Papers with number 417.

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Length: 43 pages
Date of creation: Mar 2009
Date of revision:
Handle: RePEc:bie:wpaper:417

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Related research
Keywords: Indivisible commodities; strong core; cost-minimized Walras equilibrium; core equivalence;

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Find related papers by JEL classification:
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Anderson, Robert M, 1978. "An Elementary Core Equivalence Theorem," Econometrica, Econometric Society, vol. 46(6), pages 1483-87, November. [Downloadable!] (restricted)
  2. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
  6. Bewley, Truman F, 1973. "Edgeworth's Conjecture," Econometrica, Econometric Society, vol. 41(3), pages 425-54, May. [Downloadable!] (restricted)
  7. Tomoki Inoue, 2009. "Strong core equivalence theorem in an atomless economy with indivisible commodities," Working Papers 418, Bielefeld University, Institute of Mathematical Economics. [Downloadable!]
  8. Green, Jerry R., 1972. "On the inequitable nature of core allocations," Journal of Economic Theory, Elsevier, vol. 4(2), pages 132-143, April. [Downloadable!] (restricted)
  9. Tomoki Inoue, 2009. "Core allocations may not be Walras allocations in any large finite economy with indivisible commodities," Working Papers 419, Bielefeld University, Institute of Mathematical Economics. [Downloadable!]
  10. 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. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Tomoki Inoue, 2009. "Strong core equivalence theorem in an atomless economy with indivisible commodities," Working Papers 418, Bielefeld University, Institute of Mathematical Economics. [Downloadable!]
  2. Tomoki Inoue, 2009. "Core allocations may not be Walras allocations in any large finite economy with indivisible commodities," Working Papers 419, Bielefeld University, Institute of Mathematical Economics. [Downloadable!]
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This page was last updated on 2009-12-3.

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