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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. 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.
  2. 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.
  3. Fujita, Masahisa & Thisse, Jacques-François, 1996. "Economics of Agglomeration," CEPR Discussion Papers 1344, C.E.P.R. Discussion Papers.
  4. Kehoe, Timothy J, 1980. "An Index Theorem for General Equilibrium Models with Production," Econometrica, Econometric Society, vol. 48(5), pages 1211-32, July.
  5. DEBREU, Gérard, . "Economies with a finite set of equilibria," CORE Discussion Papers RP 67, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. 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.
  7. Glenn Ellison & Drew Fudenberg, 2003. "Knife-Edge or Plateau: When Do Market Models Tip?," The Quarterly Journal of Economics, Oxford University Press, vol. 118(4), pages 1249-1278.
  8. 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.
  9. Berliant, Marcus & Peng, Shin-Kun & Wang, Ping, 2002. "Production Externalities and Urban Configuration," Journal of Economic Theory, Elsevier, vol. 104(2), pages 275-303, June.
  10. 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.
  11. Berliant, Marcus & Zenou, Yves, 2012. "Labor differentiation and agglomeration in general equilibrium," MPRA Paper 36207, University Library of Munich, Germany.
  12. Dixit, Avinash K & Stiglitz, Joseph E, 1975. "Monopolistic Competition and Optimum Product Diversity," The Warwick Economics Research Paper Series (TWERPS) 64, University of Warwick, Department of Economics.
  13. 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.
  14. Glenn Ellison & Drew Fudenberg, 2003. "Knife Edge of Plateau: When Do Market Models Tip?," NBER Working Papers 9528, National Bureau of Economic Research, Inc.
  15. J.V. Henderson, 1972. "The Sizes and Types of Cities," Working Papers 75, Queen's University, Department of Economics.
  16. Mas-Colell, Andreu, 1974. "Continuous and smooth consumers: Approximation theorems," Journal of Economic Theory, Elsevier, vol. 8(3), pages 305-336, July.
  17. 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.
  18. Krugman, Paul, 1993. "On the number and location of cities," European Economic Review, Elsevier, vol. 37(2-3), pages 293-298, April.
  19. 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.
  20. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, 1.
  21. 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.
  22. Dierker, Egbert & Dierker, Hildegard, 1972. "The Local Uniqueness of Equilibria," Econometrica, Econometric Society, vol. 40(5), pages 867-81, September.
  23. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-99, June.
  24. Debreu, Gerard, 1976. "Regular Differentiable Economies," American Economic Review, American Economic Association, vol. 66(2), pages 280-87, May.
  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.
  26. 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.
  27. 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.
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