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Share equilibrium in local public good economies

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  • van den Nouweland, Anne
  • Wooders, Myrna

Abstract

We define a concept of share equilibrium for local public good (or club) economies where individual members of the population may have preferences over the membership of their jurisdiction. A share equilibrium specifies one share index for each individual. These indices determine each individual’s cost shares in any jurisdiction that he might join. We demonstrate that the same axioms as those that characterize the Lindahl equilibrium, as discussed in Lindahl’s 1919 paper, also characterize the share equilibrium. Share equilibrium extends the notions of ratio equilibrium and cost share equilibrium (due to Kaneko, 1977; Mas-Colell and Silvestre, 1989) to economies with a local public good and possibly multiple jurisdictions.

Suggested Citation

  • van den Nouweland, Anne & Wooders, Myrna, 2011. "Share equilibrium in local public good economies," Journal of Mathematical Economics, Elsevier, vol. 47(3), pages 376-381.
    • Handle: RePEc:eee:mateco:v:47:y:2011:i:3:p:376-381
    DOI: 10.1016/j.jmateco.2010.12.008
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    References listed on IDEAS

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    1. Allouch, Nizar & Wooders, Myrna, 2008. "Price taking equilibrium in economies with multiple memberships in clubs and unbounded club sizes," Journal of Economic Theory, Elsevier, vol. 140(1), pages 246-278, May.
    2. Kaneko, Mamoru, 1977. "The Ratio Equilibria and the Core of the Voting Game G(N, W) in a Public Goods Economy," Econometrica, Econometric Society, vol. 45(7), pages 1589-1594, October.
    3. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
    4. Reny, Philip J. & Holtz Wooders, Myrna, 1996. "The Partnered Core of a Game without Side Payments," Journal of Economic Theory, Elsevier, vol. 70(2), pages 298-311, August.
    5. Foley, Duncan K, 1970. "Lindahl's Solution and the Core of an Economy with Public Goods," Econometrica, Econometric Society, vol. 38(1), pages 66-72, January.
    6. van den Nouweland, A. & Peleg, B. & Tijs, S., 1996. "Axiomatic characterizations of the Walras correspondence for generalized economies," Journal of Mathematical Economics, Elsevier, vol. 25(3), pages 355-372.
    7. Amrita Dhillon & Jean-Francois Mertens, 1999. "Relative Utilitarianism," Econometrica, Econometric Society, vol. 67(3), pages 471-498, May.
    8. Mas-Colell, Andreu & Silvestre, Joaquim, 1989. "Cost share equilibria: A Lindahlian approach," Journal of Economic Theory, Elsevier, vol. 47(2), pages 239-256, April.
    9. Anne van den Nouweland & Myrna H. Wooders & S. Tijs, 2002. "Axiomatization of ratio equilibria in public good economies," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 627-636.
    10. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    11. Andreu Mas-Colell, 1980. "Efficiency and Decentralization in the Pure Theory of Public Goods," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 94(4), pages 625-641.
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    1. Anne van den Nouweland & Agnieszka Rusinowska, 2020. "Bargaining foundation for ratio equilibrium in public‐good economies," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 22(2), pages 302-319, April.
    2. van den Nouweland, A. & Wooders, M., 2017. "Existence of share equilibrium in symmetric local public good economies," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 50-60.
    3. A. van den Nouweland, 2019. "Demand for public good as a correspondence of cost shares," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 155-164, May.
    4. Anne Van den nouweland & Myrna Wooders, 2016. "Existence of Share Equilibrium in Symmetric Local Public Good Economies∗," Vanderbilt University Department of Economics Working Papers 16-00008, Vanderbilt University Department of Economics.
    5. Chan, Nathan W. & van den Nouweland, Anne, 2025. "Local public good equilibrium," Games and Economic Behavior, Elsevier, vol. 149(C), pages 32-42.

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