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

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Author Info
Marcus Berliant (Washington University in St. Louis)
Fan- chin Kung (Academia Sinica, City University of Hong Kong)

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Abstract

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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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
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Related research
Keywords: city formation; smooth economies; increasing returns; indeterminacy of city systems;

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Find related papers by JEL classification:
D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
F12 - International Economics - - Trade - - - Models of Trade with Imperfect Competition and Scale Economies
O18 - Economic Development, Technological Change, and Growth - - Economic Development - - - Regional, Urban, and Rural Analyses
R12 - Urban, Rural, and Regional Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)
R14 - Urban, Rural, and Regional Economics - - General Regional Economics - - - Land Use Patterns

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
  2. Marcus Berliant & Yves Zenou, 2004. "Labor Differentiation and Agglomeration in General Equilibrium," Urban/Regional 0408003, EconWPA. [Downloadable!]
  3. 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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
  6. Dierker, Egbert & Dierker, Hildegard, 1972. "The Local Uniqueness of Equilibria," Econometrica, Econometric Society, vol. 40(5), pages 867-81, September. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-92, May. [Downloadable!] (restricted)
  9. Glenn Ellison & Drew Fudenberg, 2003. "Knife-Edge or Plateau: When do Market Models Tip?," Levine's Bibliography 506439000000000098, UCLA Department of Economics. [Downloadable!]
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  10. 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. [Downloadable!] (restricted)
  11. 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. [Downloadable!] (restricted)
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  12. Henderson, J V, 1974. "The Sizes and Types of Cities," American Economic Review, American Economic Association, vol. 64(4), pages 640-56, September. [Downloadable!] (restricted)
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  13. 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. [Downloadable!] (restricted)
  14. Mas-Colell, Andreu, 1974. "Continuous and smooth consumers: Approximation theorems," Journal of Economic Theory, Elsevier, vol. 8(3), pages 305-336, July. [Downloadable!] (restricted)
  15. Fujita, Masahisa & Thisse, Jacques-François, 1996. "Economics of Agglomeration," CEPR Discussion Papers 1344, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  16. 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. [Downloadable!] (restricted)
  17. Krugman, Paul, 1993. "On the number and location of cities," European Economic Review, Elsevier, vol. 37(2-3), pages 293-298, April. [Downloadable!] (restricted)
  18. Debreu, Gerard, 1976. "Regular Differentiable Economies," American Economic Review, American Economic Association, vol. 66(2), pages 280-87, May. [Downloadable!] (restricted)
  19. 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. [Downloadable!] (restricted)
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  20. Kehoe, Timothy J, 1980. "An Index Theorem for General Equilibrium Models with Production," Econometrica, Econometric Society, vol. 48(5), pages 1211-32, July. [Downloadable!] (restricted)
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  21. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-99, June. [Downloadable!] (restricted)
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  22. 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. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Berliant, Marcus, 2006. "Prospects for a unified urban general equilibrium theory," MPRA Paper 379, University Library of Munich, Germany. [Downloadable!]
    Other versions:
  2. Fan-chin Kung, 2004. "Bifurcations in regional migration dynamics," Urban/Regional 0409008, EconWPA, revised 12 Sep 2004. [Downloadable!]
    Other versions:
  3. Marcus Berliant & Ping Wang, 2004. "Dynamic Urban Models: Agglomeration and Growth," Urban/Regional 0404006, EconWPA. [Downloadable!]
    Other versions:
  4. Fan-chin Kung, 2004. "Genericity analysis of split bifurcations," GE, Growth, Math methods 0410008, EconWPA, revised 13 Oct 2004. [Downloadable!]
  5. Marcus Berliant, 2005. "Well Isn't That Spatial?! Handbook of Regional and Urban Economics: A View From Economic Theory," Urban/Regional 0503001, EconWPA, revised 08 Apr 2005. [Downloadable!]
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