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Clubs and the Market: Large Finite Economies

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  • Bryan Ellickson

    (University of California, Los Angeles)

  • Birgit Grodal

    (Institute of Economics, University of Copenhagen)

  • Suzanne Scotchmer

    (University of California, Berkeley)

  • William R. Zame

    (University of California, Los Angeles)

Abstract

We study large finite club economies in which agents can belong to several clubs, and care about the characteristics of the other club members. Club memberships must be integer consistent in aggregate. We show that states in the approximate core can approximately be decentralized by prices for private goods and for club memberships, that the approximate core is nonempty, and that approximate club equilibria exist. Our arguments use the convexification tools used for private goods economies, but we also develop a new tool to address the consistency requirement on memberships that are special to club economies. This tool allows us to overcome the integer consistency problems that are avoided in our (1999) paper by assuming a continuum of agents.

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Bibliographic Info

Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 99-05.

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Length: 43 pages
Date of creation: Jan 1999
Date of revision:
Publication status: Published in: Journal of Econ Theory 101(1) 2001, 40-77
Handle: RePEc:kud:kuiedp:9905

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Keywords: clubs; e-cores; approximate equilibrium; decentralization;

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References

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  1. Scotchmer, Suzanne, 1996. "Externality Pricing in Club Economics," Department of Economics, Working Paper Series, Department of Economics, Institute for Business and Economic Research, UC Berkeley qt4vs6f9w3, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  2. HILDENBRAND, Werner & SCHMEIDLER, David & ZAMIR, Shmuel, . "Existence of approximate equilibria and cores," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -169, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Greenberg, Joseph & Weber, Shlomo, 1986. "Strong tiebout equilibrium under restricted preferences domain," Journal of Economic Theory, Elsevier, Elsevier, vol. 38(1), pages 101-117, February.
  4. Harold L Cole & Edward C Prescott, 1997. "Valuation equilibrium with Clubs," Levine's Working Paper Archive 912, David K. Levine.
  5. Bryan Ellickson and Birgit Grodal, Suzanne Scotchmer, and William R. Zame., 1997. "Clubs and the Market: Continuum Economies," Economics Working Papers, University of California at Berkeley 97-254, University of California at Berkeley.
  6. Brueckner, J.K., 1990. "Tastes, Skills, And Local Public Goods," Working Papers, John Deutsch Institute for the Study of Economic Policy 8, John Deutsch Institute for the Study of Economic Policy.
  7. Berglas, Eitan, 1976. "Distribution of tastes and skills and the provision of local public goods," Journal of Public Economics, Elsevier, Elsevier, vol. 6(4), pages 409-423, November.
  8. Diamantaras, Dimitrios & Gilles, Robert P, 1996. "The Pure Theory of Public Goods: Efficiency, Dencentralization, and the Core," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(4), pages 851-60, November.
  9. Anderson, Robert M, 1985. "Strong Core Theorems with Nonconvex Preferences," Econometrica, Econometric Society, Econometric Society, vol. 53(6), pages 1283-94, November.
  10. Grodal, Birgit & Trockel, Walter & Weber, Shlomo, 1984. "On approximate cores of non-convex economies," Economics Letters, Elsevier, Elsevier, vol. 15(3-4), pages 197-202.
  11. Ellickson, Bryan & Grodal, Birgit & Scotchmer, Suzanne & Zame, William R., 2001. "Clubs and the Market: Large Finite Economies," Journal of Economic Theory, Elsevier, Elsevier, vol. 101(1), pages 40-77, November.
  12. Scotchmer, Suzanne & Wooders, Myrna Holtz, 1987. "Competitive equilibrium and the core in club economies with anonymous crowding," Journal of Public Economics, Elsevier, Elsevier, vol. 34(2), pages 159-173, November.
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  14. Scotchmer, Suzanne, 1985. "Profit-maximizing clubs," Journal of Public Economics, Elsevier, Elsevier, vol. 27(1), pages 25-45, June.
  15. Berglas, Eitan & Pines, David, 1980. "Clubs as a case of competitive industry with goods of variable quality," Economics Letters, Elsevier, Elsevier, vol. 5(4), pages 363-366.
  16. Pines, David, 1991. "Tiebout without politics," Regional Science and Urban Economics, Elsevier, Elsevier, vol. 21(3), pages 469-489, November.
  17. Bryan Ellickson & Birgit Grodal & Suzanne Scotchmer & William R Zame, 2003. "Clubs and the Market," Levine's Working Paper Archive 618897000000000754, David K. Levine.
  18. Wooders, Myrna Holtz, 1989. "A Tiebout theorem," Mathematical Social Sciences, Elsevier, Elsevier, vol. 18(1), pages 33-55, August.
  19. Greg Engl & Suzanne Scotchmer, 1997. "The law of supply in games, markets and matching models (*)," Economic Theory, Springer, Springer, vol. 9(3), pages 539-550.
  20. Gilles, Robert P. & Scotchmer, Suzanne, 1997. "Decentralization in Replicated Club Economies with Multiple Private Goods," Journal of Economic Theory, Elsevier, Elsevier, vol. 72(2), pages 363-387, February.
  21. Engl, Greg & Scotchmer, Suzanne, 1996. "The core and the hedonic core: Equivalence and comparative statics," Journal of Mathematical Economics, Elsevier, vol. 26(2), pages 209-248.
  22. Greenberg, Joseph & Shitovitz, Benyamin, 1988. "Consistent voting rules for competitive local public goods economies," Journal of Economic Theory, Elsevier, Elsevier, vol. 46(2), pages 223-236, December.
  23. Grodal, Birgit, 1976. "Existence of Approximate Cores with Incomplete Preferences," Econometrica, Econometric Society, Econometric Society, vol. 44(4), pages 829-30, July.
  24. Bewley, Truman F, 1981. "A Critique of Tiebout's Theory of Local Public Expenditures," Econometrica, Econometric Society, Econometric Society, vol. 49(3), pages 713-40, May.
  25. Ellickson, Bryan, 1973. "A Generalization of the Pure Theory of Public Goods," American Economic Review, American Economic Association, American Economic Association, vol. 63(3), pages 417-32, June.
  26. Kannai, Yakar, 1970. "Continuity Properties of the Core of a Market," Econometrica, Econometric Society, Econometric Society, vol. 38(6), pages 791-815, November.
  27. 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.
  28. Ellickson, Bryan, 1979. "Competitive equilibrium with local public goods," Journal of Economic Theory, Elsevier, Elsevier, vol. 21(1), pages 46-61, August.
  29. Boadway, Robin, 1982. "On the Method of Taxation and the Provision of Local Public Goods: Comment," American Economic Review, American Economic Association, American Economic Association, vol. 72(4), pages 846-51, September.
  30. Mas-Colell, Andreu, 1980. "Efficiency and Decentralization in the Pure Theory of Public Goods," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 94(4), pages 625-41, June.
  31. Suzanne Scotchmer, 1985. "Two-Tier Pricing of Shared Facilities in a Free-Entry Equilibrium," RAND Journal of Economics, The RAND Corporation, vol. 16(4), pages 456-472, Winter.
  32. Berglas, Eitan & Pines, David, 1981. "Clubs, local public goods and transportation models : A synthesis," Journal of Public Economics, Elsevier, Elsevier, vol. 15(2), pages 141-162, April.
  33. Diamantaras, Dimitrios & Gilles, Robert P & Scotchmer, Suzanne, 1996. "Decentralization of Pareto Optima in Economies with Public Projects, Nonessential Private Goods and Convex Costs," Economic Theory, Springer, Springer, vol. 8(3), pages 555-64, October.
  34. Charles M. Tiebout, 1956. "A Pure Theory of Local Expenditures," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 64, pages 416.
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