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Anonymous price taking equilibrium in Tiebout economies with a continuum of agents: Existence and characterization

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  • Allouch, Nizar
  • Conley, John P.
  • Wooders, Myrna

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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  • Allouch, Nizar & Conley, John P. & Wooders, Myrna, 2009. "Anonymous price taking equilibrium in Tiebout economies with a continuum of agents: Existence and characterization," Journal of Mathematical Economics, Elsevier, vol. 45(9-10), pages 492-510, September.
  • Handle: RePEc:eee:mateco:v:45:y:2009:i:9-10:p:492-510
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    1. Guesnerie, Roger & Oddou, Claude, 1981. "Second best taxation as a game," Journal of Economic Theory, Elsevier, vol. 25(1), pages 67-91, August.
    2. McGuire, Martin, 1974. "Group Segregation and Optimal Jurisdictions," Journal of Political Economy, University of Chicago Press, vol. 82(1), pages 112-132, Jan.-Feb..
    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.
    4. 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.
    5. Bewley, Truman F, 1981. "A Critique of Tiebout's Theory of Local Public Expenditures," Econometrica, Econometric Society, vol. 49(3), pages 713-740, May.
    6. 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.
    7. 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.
    8. Vohra, Rajiv, 1984. "Local public goods and average cost pricing," Journal of Mathematical Economics, Elsevier, vol. 13(1), pages 51-67, April.
    9. 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.
    10. Bryan Ellickson & Birgit Grodal & Suzanne Scotchmer & William R. Zame, 1999. "Clubs and the Market," Econometrica, Econometric Society, vol. 67(5), pages 1185-1218, September.
    11. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, vol. 64(5), pages 416-416.
    12. Thomas. J. Nechyba, 1997. "Existence of equilibrium and stratification in local and hierarchical Tiebout economies with property taxes and voting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 277-304.
    13. 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.
    14. Vohra, Rajiv, 1987. "Local public goods as indivisible commodities," Regional Science and Urban Economics, Elsevier, vol. 17(2), pages 191-208.
    15. Wooders, Myrna Holtz, 1994. "Equivalence of Games and Markets," Econometrica, Econometric Society, vol. 62(5), pages 1141-1160, September.
    16. Cole, Harold L. & Prescott, Edward C., 1997. "Valuation Equilibrium with Clubs," Journal of Economic Theory, Elsevier, vol. 74(1), pages 19-39, May.
    17. 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.
    18. Demange, Gabrielle, 1994. "Intermediate preferences and stable coalition structures," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 45-58, January.
    19. 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.
    20. Bruce W. Hamilton, 1975. "Zoning and Property Taxation in a System of Local Governments," Urban Studies, Urban Studies Journal Limited, vol. 12(2), pages 205-211, June.
    21. 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.
    22. 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.
    23. 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.
    24. Konishi, Hideo, 2008. "Tiebout's tale in spatial economies: Entrepreneurship, self-selection, and efficiency," Regional Science and Urban Economics, Elsevier, vol. 38(5), pages 461-477, September.
    25. 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.
    26. 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.
    27. Ellickson, Bryan, 1979. "Competitive equilibrium with local public goods," Journal of Economic Theory, Elsevier, vol. 21(1), pages 46-61, August.
    28. Gerard Debreu, 1963. "On a Theorem of Scarf," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 177-180.
    29. 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.
    30. Mark Pauly, 1970. "Cores and clubs," Public Choice, Springer, vol. 9(1), pages 53-65, September.
    31. Wooders, Myrna, 1980. "The Tiebout Hypothesis: Near Optimality in Local Public Good Economies," Econometrica, Econometric Society, vol. 48(6), pages 1467-1485, September.
    32. 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.
    33. Martin Shubik & Myrna Holtz Wooders, 1982. "Near-Markets and Market Games," Cowles Foundation Discussion Papers 657, Cowles Foundation for Research in Economics, Yale University.
    34. 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.
    35. 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.
    36. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
    37. Kaneko, Mamoru & Wooders, Myrna Holtz, 1996. "The Nonemptiness of the f-Core of a Game without Side Payments," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(2), pages 245-258.
    38. Wooders, Myrna Holtz, 1989. "A Tiebout theorem," Mathematical Social Sciences, Elsevier, vol. 18(1), pages 33-55, August.
    39. 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.
    40. 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.
    41. 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.
    42. 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.
    43. 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).
    44. Greenberg, Joseph & Weber, Shlomo, 1986. "Strong tiebout equilibrium under restricted preferences domain," Journal of Economic Theory, Elsevier, vol. 38(1), pages 101-117, February.
    45. 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.
    46. 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.
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    Cited by:

    1. Philippe Jehiel & Laurent Lamy, 2018. "A Mechanism Design Approach to the Tiebout Hypothesis," Journal of Political Economy, University of Chicago Press, vol. 126(2), pages 735-760.
    2. Nizar Allouch, 2010. "A Core‐Equilibrium Convergence in a Public Goods Economy," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 12(4), pages 857-870, August.
    3. Jaime Luque, 2014. "Wages, local amenities and the rise of the multi-skilled city," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 52(2), pages 457-467, March.
    4. 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.
    5. Hideo Konishi, 2010. "Efficient Mixed Clubs: Nonlinear‐Pricing Equilibria With Entrepreneurial Managers," The Japanese Economic Review, Japanese Economic Association, vol. 61(1), pages 35-63, March.
    6. Hans Gersbach & Hans Haller & Hideo Konishi, 2015. "Household formation and markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(3), pages 461-507, August.
    7. Wooders, Myrna, 2008. "Market games and clubs," MPRA Paper 33968, University Library of Munich, Germany, revised Dec 2010.
    8. Luque, Jaime, 2013. "Heterogeneous Tiebout communities with private production and anonymous crowding," Regional Science and Urban Economics, Elsevier, vol. 43(1), pages 117-123.

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    More about this item

    Keywords

    Tiebout Jurisdictions f-core Core-equilibrium equivalence Edgeworth equivalence Continuum economies Crowding types Core Equal treatment core Large games;

    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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