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

Author

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  • Marcus Berliant

    (Washington University in St. Louis)

  • Fan- chin Kung

    (Academia Sinica, City University of Hong Kong)

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.

Suggested Citation

  • Marcus Berliant & Fan- chin Kung, 2004. "The Indeterminacy of Equilibrium City Formation under Monopolistic Competition and Increasing Returns," Urban/Regional 0407011, University Library of Munich, Germany, revised 31 Jul 2005.
  • Handle: RePEc:wpa:wuwpur:0407011
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    References listed on IDEAS

    as
    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.
    2. Marcus Berliant & Yves Zenou, 2014. "Labor Differentiation and Agglomeration in General Equilibrium," International Regional Science Review, , vol. 37(1), pages 36-65, January.
    3. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, January.
    4. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
    5. 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.
    6. Henderson, J V, 1974. "The Sizes and Types of Cities," American Economic Review, American Economic Association, vol. 64(4), pages 640-656, September.
    7. 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.
    8. Krugman, Paul, 1980. "Scale Economies, Product Differentiation, and the Pattern of Trade," American Economic Review, American Economic Association, vol. 70(5), pages 950-959, December.
    9. 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.
    10. 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.
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    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. Dierker, Egbert & Dierker, Hildegard, 1972. "The Local Uniqueness of Equilibria," Econometrica, Econometric Society, vol. 40(5), pages 867-881, September.
    21. 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.
    22. Kehoe, Timothy J, 1980. "An Index Theorem for General Equilibrium Models with Production," Econometrica, Econometric Society, vol. 48(5), pages 1211-1232, July.
    23. 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.
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    Cited by:

    1. Marcus Berliant & Yves Zenou, 2014. "Labor Differentiation and Agglomeration in General Equilibrium," International Regional Science Review, , vol. 37(1), pages 36-65, January.
    2. Berliant, Marcus, 2007. "Prospects for a unified urban general equilibrium theory," Regional Science and Urban Economics, Elsevier, vol. 37(4), pages 466-471, July.
    3. Fan-chin Kung, 2004. "Genericity analysis of split bifurcations," GE, Growth, Math methods 0410008, University Library of Munich, Germany, revised 24 Nov 2004.
    4. Berliant, Marcus & Kung, Fan-chin, 2009. "Bifurcations in regional migration dynamics," Regional Science and Urban Economics, Elsevier, vol. 39(6), pages 714-720, November.
    5. Berliant, Marcus & Wang, Ping, 2003. "Dynamic Urban Models: Agglomeration and Growth," Working Papers 1167, California Institute of Technology, Division of the Humanities and Social Sciences.
    6. Ericson Richard E. & Kung Fan-chin, 2015. "Fundamental Non-convexity and Externalities: A Differentiable Approach," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 15(1), pages 1-14, January.
    7. Marcus Berliant, 2005. "Well Isn't That Spatial?! Handbook of Regional and Urban Economics: A View From Economic Theory," Urban/Regional 0503001, University Library of Munich, Germany, revised 08 Apr 2005.
    8. Kung, Fan-chin, 2008. "Voluntary contributions to multiple public goods in a production economy with widespread externalities," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1364-1378, December.

    More about this item

    Keywords

    city formation; smooth economies; increasing returns; indeterminacy of city systems;

    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; Fragmentation
    • O18 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Urban, Rural, Regional, and Transportation Analysis; Housing; Infrastructure
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)
    • R14 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Land Use Patterns

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