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The Indeterminacy of Equilibrium City Formation under Monopolistic Competition and Increasing Returns

  • Marcus Berliant

    (Washington University in St. Louis)

  • Fan- chin Kung

    (Academia Sinica, City University of Hong Kong)

We study the indeterminacy of equilibrium in the Fujita-Krugman (1995) model of city formation under monopolistic competition and increasing returns. Both the number and the locations of cities are endogenously determined. Assuming smooth transportation costs, we examine equilibria in city-economies where a finite number of cities form endogenously. For any positive integer K, the set of equilibria with K distinct cities has a smooth manifold of dimension K-1 as its interior for almost all parameter values in a regular parameterization. The disjoint union of these sets over all positive integers K constitutes the entire equilibrium set.

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File URL: http://econwpa.repec.org/eps/urb/papers/0407/0407011.pdf
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Paper provided by EconWPA in its series Urban/Regional with number 0407011.

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Length: 40 pages
Date of creation: 29 Jul 2004
Date of revision: 29 Apr 2005
Handle: RePEc:wpa:wuwpur:0407011
Note: Type of Document - pdf; pages: 40
Contact details of provider: Web page: http://econwpa.repec.org

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  1. Dierker, Egbert & Dierker, Hildegard, 1972. "The Local Uniqueness of Equilibria," Econometrica, Econometric Society, vol. 40(5), pages 867-81, September.
  2. Fudenberg, Drew & Ellison, Glenn, 2003. "Knife-Edge or Plateau: When Do Market Models Tip?," Scholarly Articles 3160493, Harvard University Department of Economics.
  3. Berliant, Marcus & Zenou, Yves, 2012. "Labor Differentiation and Agglomeration in General Equilibrium," CEPR Discussion Papers 8840, C.E.P.R. Discussion Papers.
  4. Fujita, Masahisa & Krugman, Paul, 1995. "When is the economy monocentric?: von Thunen and Chamberlin unified," Regional Science and Urban Economics, Elsevier, vol. 25(4), pages 505-528, August.
  5. Dixit, Avinash K & Stiglitz, Joseph E, 1977. "Monopolistic Competition and Optimum Product Diversity," American Economic Review, American Economic Association, vol. 67(3), pages 297-308, June.
  6. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-92, May.
  7. Krugman, Paul, 1980. "Scale Economies, Product Differentiation, and the Pattern of Trade," American Economic Review, American Economic Association, vol. 70(5), pages 950-59, December.
  8. Berliant, Marcus & Papageorgiou, Yorgos Y. & Wang, Ping, 1990. "On welfare theory and urban economics," Regional Science and Urban Economics, Elsevier, vol. 20(2), pages 245-261, September.
  9. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-99, June.
  10. Fujita, Masahisa & Krugman, Paul & Mori, Tomoya, 1999. "On the evolution of hierarchical urban systems1," European Economic Review, Elsevier, vol. 43(2), pages 209-251, February.
  11. Berliant, Marcus & Raa, Thijs ten, 1988. "A foundation of location theory: Consumer preferences and demand," Journal of Economic Theory, Elsevier, vol. 44(2), pages 336-353, April.
  12. Mas-Colell, Andreu, 1974. "Continuous and smooth consumers: Approximation theorems," Journal of Economic Theory, Elsevier, vol. 8(3), pages 305-336, July.
  13. Fujita, M. & Thisse, J.-F., . "Economics of agglomeration," CORE Discussion Papers RP -1250, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  14. Timothy J. Kehoe, 1979. "An Index Theorem for General Equilibrium Models with Production," Cowles Foundation Discussion Papers 516, Cowles Foundation for Research in Economics, Yale University.
  15. J.V. Henderson, 1972. "The Sizes and Types of Cities," Working Papers 75, Queen's University, Department of Economics.
  16. Berliant, Marcus, 1985. "Equilibrium models with land : A criticism and an alternative," Regional Science and Urban Economics, Elsevier, vol. 15(2), pages 325-340, June.
  17. Starrett, David, 1978. "Market allocations of location choice in a model with free mobility," Journal of Economic Theory, Elsevier, vol. 17(1), pages 21-37, February.
  18. Krugman, Paul, 1993. "On the number and location of cities," European Economic Review, Elsevier, vol. 37(2-3), pages 293-298, April.
  19. Smale, S., 1974. "Global analysis and economics IV : Finiteness and stability of equilibria with general consumption sets and production," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 119-127, August.
  20. Berliant, Marcus & ten Raa, Thijs, 1991. "On the continuum approach of spatial and some local public goods or product differentiation models: Some problems," Journal of Economic Theory, Elsevier, vol. 55(1), pages 95-120, October.
  21. Debreu, Gerard, 1976. "Regular Differentiable Economies," American Economic Review, American Economic Association, vol. 66(2), pages 280-87, May.
  22. Abdel-Rahman, H. M., 1988. "Product differentiation, monopolistic competition and city size," Regional Science and Urban Economics, Elsevier, vol. 18(1), pages 69-86, February.
  23. Marcus Berliant & Shin-Kun Peng & Ping Wang, 2000. "Production Externalities and Urban Configuration," Vanderbilt University Department of Economics Working Papers 0011, Vanderbilt University Department of Economics.
  24. Smale, S., 1974. "Global analysis and economics IIA : Extension of a theorem of Debreu," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 1-14, March.
  25. Fujita, Masahisa & Mori, Tomoya, 1997. "Structural stability and evolution of urban systems," Regional Science and Urban Economics, Elsevier, vol. 27(4-5), pages 399-442, August.
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