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

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  • 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)

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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Bibliographic Info

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

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Web page: http://www.vanderbilt.edu/econ/wparchive/index.html

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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  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. 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).
  7. Bryan Ellickson & Birgit Grodal & Suzanne Scotchmer & William R. Zame, 1999. "Clubs and the Market," Econometrica, Econometric Society, vol. 67(5), pages 1185-1218, September.
  8. 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.
  9. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
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  12. Bryan Ellickson & Birgit Grodal & Suzanne Scotchmer & William R. Zame, 1999. "Clubs and the Market: Large Finite Economies," Discussion Papers 99-05, University of Copenhagen. Department of Economics.
  13. 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.
  14. 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.
  15. Martin Shubik & Myrna Holtz Wooders, 1982. "Near-Markets and Market Games," Cowles Foundation Discussion Papers 657, Cowles Foundation for Research in Economics, Yale University.
  16. Harold L. Cole & Edward C. Prescott, 1996. "Valuation equilibria with clubs," Staff Report 174, Federal Reserve Bank of Minneapolis.
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  20. 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.
  21. 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.
  22. 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.
  23. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, vol. 62(5), pages 1141-60, September.
  24. 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.
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  29. McGuire, Martin, 1974. "Group Segregation and Optimal Jurisdictions," Journal of Political Economy, University of Chicago Press, vol. 82(1), pages 112-32, Jan.-Feb..
  30. 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.
  31. 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.
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  33. 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.
  34. 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.
  35. 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.
  36. 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.
  37. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, vol. 64, pages 416.
  38. 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.
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  40. 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.
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Citations

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Cited by:
  1. Konishi, Hideo, 2013. "Entrepreneurial land developers: Joint production, local externalities, and mixed housing developments," Journal of Urban Economics, Elsevier, vol. 75(C), pages 68-79.
  2. Jaime Luque, 2014. "Wages, local amenities and the rise of the multi-skilled city," The Annals of Regional Science, Springer, vol. 52(2), pages 457-467, March.
  3. Wooders, Myrna, 2008. "Market games and clubs," MPRA Paper 33968, University Library of Munich, Germany, revised Dec 2010.
  4. Luque, Jaime, 2013. "Heterogeneous Tiebout communities with private production and anonymous crowding," Regional Science and Urban Economics, Elsevier, vol. 43(1), pages 117-123.
  5. Hans Gersbach & Hans Haller & Hideo Konishi, 2013. "Household Formation and Markets," CESifo Working Paper Series 4414, CESifo Group Munich.

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