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Anonymous Price Taking Equilibrium in Tiebout Economies with a Continuum of Agents; Existence and Characterization

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Author Info
Nizar Allouch () (Department of Economics, Queen Mary, University of London)
John P. Conley () (Department of Economics, Vanderbilt University)
Myrna Wooders () (Department of Economics, Vanderbilt University)

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Abstract

We introduce a model of a local public goods economy with a continuum of agents and jurisdictions with finite, but unbounded populations, where the set of possible projects for each jurisdiction/club is unrestricted in size. Under boundedness of per capita payoffs, which simply ensures that equal treatment payoffs are bounded above, we apply results of Kaneko and Wooders (1986) to obtain nonemptiness of the core of the economy. We then demonstrate, under the stronger condition of strict small group effectiveness, that the equal treatment core coincides with the set of price-taking equilibrium outcomes with anonymous prices -- that is, prices for public goods depend only on observable characteristics of agents. Existence of equilibrium follows from nonemptiness of the core and equivalence of the core to the set of equilibrium outcomes. Our approach provides a new technique for showing existence of equilibrium in economies with a continuum of agents.

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File URL: http://www.vanderbilt.edu/Econ/wparchive/workpaper/vu08-w11.pdf
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File Function: First version, 2008
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Paper provided by Department of Economics, Vanderbilt University in its series Working Papers with number 0811.

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Date of creation: Jun 2008
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Handle: RePEc:van:wpaper:0811

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Related research
Keywords: Tiebout; jurisdictions; f-core; core-equilibrium equivalence; Edgeworth equivalence; continuum economies; crowding types; core; equal treatment core; large games;

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Find related papers by JEL classification:
C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
D5 - Microeconomics - - General Equilibrium and Disequilibrium
H4 - Public Economics - - Publicly Provided Goods

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  1. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, vol. 64, pages 416. [Downloadable!] (restricted)
  2. Epple, Dennis & Filimon, Radu & Romer, Thomas, 1984. "Equilibrium among local jurisdictions: toward an integrated treatment of voting and residential choice," Journal of Public Economics, Elsevier, vol. 24(3), pages 281-308, August. [Downloadable!] (restricted)
  3. Kaneko, Mamoru & Wooders, Myrna Holtz, 1986. "The core of a game with a continuum of players and finite coalitions: The model and some results," Mathematical Social Sciences, Elsevier, vol. 12(2), pages 105-137, October. [Downloadable!] (restricted)
  4. Epple, Dennis & Filimon, Radu & Romer, Thomas, 1993. "Existence of voting and housing equilibrium in a system of communities with property taxes," Regional Science and Urban Economics, Elsevier, vol. 23(5), pages 585-610, November. [Downloadable!] (restricted)
  5. Berglas, Eitan & Pines, David, 1981. "Clubs, local public goods and transportation models : A synthesis," Journal of Public Economics, Elsevier, vol. 15(2), pages 141-162, April. [Downloadable!] (restricted)
  6. Thomas. J. Nechyba, 1997. "Existence of equilibrium and stratification in local and hierarchical Tiebout economies with property taxes and voting," Economic Theory, Springer, vol. 10(2), pages 277-304. [Downloadable!] (restricted)
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  7. Nizar Allouch & Myrna Wooders, 2004. "Price Taking Equilibrium in Club Economies with Multiple Memberships and Unbounded Club Sizes," Working Papers 513, Queen Mary, University of London, Department of Economics. [Downloadable!]
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  8. Guesnerie, Roger & Oddou, Claude, 1981. "Second best taxation as a game," Journal of Economic Theory, Elsevier, vol. 25(1), pages 67-91, August. [Downloadable!] (restricted)
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  9. Bryan Ellickson & Birgit Grodal & Suzanne Scotchmer & William R. Zame, 1999. "Clubs and the Market," Econometrica, Econometric Society, vol. 67(5), pages 1185-1218, September.
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  10. Alexander Kovalenkov & Myrna H. Wooders, 1998. "Approximate cores of games and economies with clubs," Working Papers mwooders-00-01, University of Toronto, Department of Economics. [Downloadable!]
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  11. Demange, Gabrielle, 1994. "Intermediate preferences and stable coalition structures," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 45-58, January. [Downloadable!] (restricted)
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  12. Kaneko, Mamoru & Wooders, Myrna Holtz, 1996. "The Nonemptiness of the f-Core of a Game without Side Payments," International Journal of Game Theory, Springer, vol. 25(2), pages 245-58.
  13. Bewley, Truman F, 1981. "A Critique of Tiebout's Theory of Local Public Expenditures," Econometrica, Econometric Society, vol. 49(3), pages 713-40, May. [Downloadable!] (restricted)
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  15. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1998. "Equilibrium in a Finite Local Public Goods Economy," Journal of Economic Theory, Elsevier, vol. 79(2), pages 224-244, April. [Downloadable!] (restricted)
  16. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, vol. 62(5), pages 1141-60, September. [Downloadable!] (restricted)
  17. Konishi, Hideo, 1996. "Voting with Ballots and Feet: Existence of Equilibrium in a Local Public Good Economy," Journal of Economic Theory, Elsevier, vol. 68(2), pages 480-509, February. [Downloadable!] (restricted)
  18. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July. [Downloadable!] (restricted)
  19. Myrna Holtz Wooders, 1996. "Equivalence of Lindahl equilibrium with participation prices and the core (*)," Economic Theory, Springer, vol. 9(1), pages 115-127.
  20. Conley, John P. & Wooders, Myrna H., 1997. "Equivalence of the Core and Competitive Equilibrium in a Tiebout Economy with Crowding Types," Journal of Urban Economics, Elsevier, vol. 41(3), pages 421-440, May. [Downloadable!] (restricted)
  21. Wooders, Myrna, 1980. "The Tiebout Hypothesis: Near Optimality in Local Public Good Economies," Econometrica, Econometric Society, vol. 48(6), pages 1467-85, September. [Downloadable!] (restricted)
  22. Ellickson, Bryan, 1979. "Competitive equilibrium with local public goods," Journal of Economic Theory, Elsevier, vol. 21(1), pages 46-61, August. [Downloadable!] (restricted)
  23. Greenberg, Joseph & Weber, Shlomo, 1986. "Strong tiebout equilibrium under restricted preferences domain," Journal of Economic Theory, Elsevier, vol. 38(1), pages 101-117, February. [Downloadable!] (restricted)
  24. Novshek, William & Sonnenschein, Hugo, 1980. "Small efficient scale as a foundation for Walrasian equilibrium," Journal of Economic Theory, Elsevier, vol. 22(2), pages 243-255, April. [Downloadable!] (restricted)
  25. Gravel, Nicolas & Thoron, Sylvie, 2007. "Does endogenous formation of jurisdictions lead to wealth-stratification?," Journal of Economic Theory, Elsevier, vol. 132(1), pages 569-583, January. [Downloadable!] (restricted)
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  26. Wooders, Myrna Holtz, 1989. "A Tiebout theorem," Mathematical Social Sciences, Elsevier, vol. 18(1), pages 33-55, August. [Downloadable!] (restricted)
  27. Kaneko, Mamoru & Wooders, Myrna Holtz, 1989. "The core of a continuum economy with widespread externalities and finite coalitions: From finite to continuum economies," Journal of Economic Theory, Elsevier, vol. 49(1), pages 135-168, October. [Downloadable!] (restricted)
  28. Harold L. Cole & Edward C. Prescott, 1996. "Valuation equilibria with clubs," Staff Report 174, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  29. Vohra, Rajiv, 1984. "Local public goods and average cost pricing," Journal of Mathematical Economics, Elsevier, vol. 13(1), pages 51-67, April. [Downloadable!] (restricted)
  30. 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. [Downloadable!] (restricted)
  31. Wooders, Myrna, 1978. "Equilibria, the core, and jurisdiction structures in economies with a local public good," Journal of Economic Theory, Elsevier, vol. 18(2), pages 328-348, August. [Downloadable!] (restricted)
  32. Mas-Colell, Andreu, 1980. "Efficiency and Decentralization in the Pure Theory of Public Goods," The Quarterly Journal of Economics, MIT Press, vol. 94(4), pages 625-41, June. [Downloadable!] (restricted)
  33. Greenberg, Joseph & Shitovitz, Benyamin, 1988. "Consistent voting rules for competitive local public goods economies," Journal of Economic Theory, Elsevier, vol. 46(2), pages 223-236, December. [Downloadable!] (restricted)
  34. McGuire, Martin, 1974. "Group Segregation and Optimal Jurisdictions," Journal of Political Economy, University of Chicago Press, vol. 82(1), pages 112-32, Jan.-Feb.. [Downloadable!] (restricted)
  35. Hammond, Peter J. & Kaneko, Mamoru & Wooders, Myrna Holtz, 1989. "Continuum economies with finite coalitions: Core, equilibria, and widespread externalities," Journal of Economic Theory, Elsevier, vol. 49(1), pages 113-134, October. [Downloadable!] (restricted)
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