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

  • 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)

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.accessecon.com/pubs/VUECON/vu08-w11.pdf
File Function: First version, 2008
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Paper provided by Vanderbilt University Department of Economics in its series Vanderbilt University Department of Economics Working Papers with number 0811.

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Date of creation: Jun 2008
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Handle: RePEc:van:wpaper:0811
Contact details of provider: Web page: http://www.vanderbilt.edu/econ/wparchive/index.html

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  1. 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.
  2. Nizar Allouch & Myrna Wooders, 2004. "Price taking equilibrium in club economies with multiple memberships and unbounded club sizes," Cahiers de la Maison des Sciences Economiques b04109, Université Panthéon-Sorbonne (Paris 1).
  3. 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.
  4. Guesnerie, Roger & Oddou, Claude, 1981. "Second best taxation as a game," Journal of Economic Theory, Elsevier, vol. 25(1), pages 67-91, August.
  5. Nicolas Gravel & Sylvie Thoron, 2003. "Does endogenous formation of jurisdictions lead to wealth stratification?," IDEP Working Papers 0306, Institut d'economie publique (IDEP), Marseille, France.
  6. Harold L. Cole & Edward C. Prescott, 1996. "Valuation equilibria with clubs," Staff Report 174, Federal Reserve Bank of Minneapolis.
  7. 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.
  8. Conley, John P. & Wooders, Myrna, 1996. "Taste-homogeneity of optimal jurisdictions in a Tiebout economy with crowding types and endogenous educational investment choices," Ricerche Economiche, Elsevier, vol. 50(4), pages 367-387, December.
  9. Ellickson, Bryan, 1979. "Competitive equilibrium with local public goods," Journal of Economic Theory, Elsevier, vol. 21(1), pages 46-61, August.
  10. 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.
  11. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
  12. 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.
  13. 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.
  14. Vohra, Rajiv, 1984. "Local public goods and average cost pricing," Journal of Mathematical Economics, Elsevier, vol. 13(1), pages 51-67, April.
  15. Ellickson, Bryan & Grodal, Birgit & Scotchmer, Suzanne & Zame, William R., 2001. "Clubs and the Market: Large Finite Economies," Journal of Economic Theory, Elsevier, vol. 101(1), pages 40-77, November.
  16. Thomas J. Nechyba, 1996. "Existence of Equilibrium and Stratification in Local and Hierarchical Tiebout Economies with Property Taxes and Voting," NBER Technical Working Papers 0190, National Bureau of Economic Research, Inc.
  17. 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.
  18. Westhoff, Frank, 1977. "Existence of equilibria in economies with a local public good," Journal of Economic Theory, Elsevier, vol. 14(1), pages 84-112, February.
  19. Dunz, Karl, 1989. "Some comments on majority rule equilibria in local public good economies," Journal of Economic Theory, Elsevier, vol. 47(1), pages 228-234, February.
  20. D. K. Foley, 1967. "Lindahl's Solution and the Core of an Economy with Public Goods," Working papers 3, Massachusetts Institute of Technology (MIT), Department of Economics.
  21. McGuire, Martin, 1974. "Group Segregation and Optimal Jurisdictions," Journal of Political Economy, University of Chicago Press, vol. 82(1), pages 112-32, Jan.-Feb..
  22. 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.
  23. Martin Shubik & Myrna Holtz Wooders, 1982. "Near-Markets and Market Games," Cowles Foundation Discussion Papers 657, Cowles Foundation for Research in Economics, Yale University.
  24. 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.
  25. Kovalenkov, Alexander & Wooders, Myrna, 2003. "Approximate cores of games and economies with clubs," Journal of Economic Theory, Elsevier, vol. 110(1), pages 87-120, May.
  26. Wooders, Myrna, 1980. "The Tiebout Hypothesis: Near Optimality in Local Public Good Economies," Econometrica, Econometric Society, vol. 48(6), pages 1467-85, September.
  27. Bryan Ellickson & Birgit Grodal & Suzanne Scotchmer & William R Zame, 2003. "Clubs and the Market," Levine's Working Paper Archive 618897000000000754, David K. Levine.
    • Bryan Ellickson & Birgit Grodal & Suzanne Scotchmer & William R. Zame, 1999. "Clubs and the Market," Econometrica, Econometric Society, vol. 67(5), pages 1185-1218, September.
  28. 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.
  29. Conley, John P. & Wooders, Myrna H., 2001. "Tiebout Economies with Differential Genetic Types and Endogenously Chosen Crowding Characteristics," Journal of Economic Theory, Elsevier, vol. 98(2), pages 261-294, June.
  30. 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.
  31. Vohra, Rajiv, 1987. "Local public goods as indivisible commodities," Regional Science and Urban Economics, Elsevier, vol. 17(2), pages 191-208.
  32. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, vol. 64, pages 416.
  33. 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.
  34. Demange, Gabrielle, 1994. "Intermediate preferences and stable coalition structures," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 45-58, January.
  35. Greenberg, Joseph & Weber, Shlomo, 1986. "Strong tiebout equilibrium under restricted preferences domain," Journal of Economic Theory, Elsevier, vol. 38(1), pages 101-117, February.
  36. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, vol. 62(5), pages 1141-60, September.
  37. 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.
  38. Rose-Ackerman, Susan, 1979. "Market models of local government: Exit, voting, and the land market," Journal of Urban Economics, Elsevier, vol. 6(3), pages 319-337, July.
  39. 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.
  40. Wooders, Myrna Holtz, 1988. "Stability of jurisdiction structures in economies with local public goods," Mathematical Social Sciences, Elsevier, vol. 15(1), pages 29-49, February.
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