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On the Frequency of Interior Cournot-Nash Equilibria in a Public Good Economy

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Author Info

  • Wolfgang Buchholz
  • Richard Cornes
  • Wolfgang Peters

Abstract

In a public good economy the distribution of initial income is an important determinant of how many individuals contribute to the public good. For the case when all individuals have identical preferences in this paper a simple formula is derived that describes the proportion of all income distributions for which an interior Cournot-Nash equilibrium will result in which every agent makes a strictly positive contribution to the public good. This formula is then applied to a standard Cobb-Douglas utility function showing that the likelihood of interior Cournot-Nash equilibria falls dramatically when the number of individuals is increased. The implications this result might have for the significance of Shibata-Warr neutrality are finally discussed.

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Bibliographic Info

Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 982.

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Date of creation: 2003
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Handle: RePEc:ces:ceswps:_982

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Keywords: private provision of public goods; Cournot-Nash equilibria; Shibata-Warr neutrality;

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References

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  1. Cornes,Richard & Sandler,Todd, 1996. "The Theory of Externalities, Public Goods, and Club Goods," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521477185.
  2. Bergstrom, Theodore & Blume, Lawrence & Varian, Hal, 1986. "On the private provision of public goods," Journal of Public Economics, Elsevier, Elsevier, vol. 29(1), pages 25-49, February.
  3. Shibata, Hirofumi, 1971. "A Bargaining Model of the Pure Theory of Public Expenditure," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 79(1), pages 1-29, Jan.-Feb..
  4. Richard Cornes & Roger Hartley, 2003. "Aggregative Public Goods Games," NajEcon Working Paper Reviews 666156000000000063, www.najecon.org.
  5. Warr, Peter G., 1983. "The private provision of a public good is independent of the distribution of income," Economics Letters, Elsevier, Elsevier, vol. 13(2-3), pages 207-211.
  6. Andreoni, James, 1988. "Privately provided public goods in a large economy: The limits of altruism," Journal of Public Economics, Elsevier, Elsevier, vol. 35(1), pages 57-73, February.
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Cited by:
  1. Joaquim Silvestre, 2012. "All but one free ride when wealth effects are small," SERIEs, Spanish Economic Association, vol. 3(1), pages 201-207, March.
  2. Wolfgang Buchholz & Richard Cornes & Dirk T. G. R├╝bbelke, 2009. "Existence and Warr Neutrality for Matching Equilibria in a Public Good Economy: An Aggregative Game Approach," CESifo Working Paper Series 2884, CESifo Group Munich.

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