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The indeterminacy of equilibrium city formation under monopolistic competition and increasing returns

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  • Berliant, Marcus
  • Kung, Fan-chin

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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 131 (2006)
Issue (Month): 1 (November)
Pages: 101-133

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Handle: RePEc:eee:jetheo:v:131:y:2006:i:1:p:101-133

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Web page: http://www.elsevier.com/locate/inca/622869

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  1. Debreu, Gerard, 1976. "Regular Differentiable Economies," American Economic Review, American Economic Association, vol. 66(2), pages 280-87, May.
  2. 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.
  3. 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.
  4. Fujita, M. & Thisse, J.-F., . "Economics of agglomeration," CORE Discussion Papers RP -1250, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-92, May.
  6. 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.
  7. Dierker, Egbert & Dierker, Hildegard, 1972. "The Local Uniqueness of Equilibria," Econometrica, Econometric Society, vol. 40(5), pages 867-81, September.
  8. Berliant, Marcus & Zenou, Yves, 2012. "Labor Differentiation and Agglomeration in General Equilibrium," CEPR Discussion Papers 8840, C.E.P.R. Discussion Papers.
  9. 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.
  10. J.V. Henderson, 1972. "The Sizes and Types of Cities," Working Papers 75, Queen's University, Department of Economics.
  11. 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.
  12. Glenn Ellison & Drew Fudenberg, 2003. "Knife Edge of Plateau: When Do Market Models Tip?," NBER Working Papers 9528, National Bureau of Economic Research, Inc.
  13. 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.
  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. 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.
  16. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-99, June.
  17. Raa, M.H. ten & Berliant, M., 1988. "A foundation of location theory: Consumer preferences and demand," Open Access publications from Tilburg University urn:nbn:nl:ui:12-381957, Tilburg University.
  18. 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.
  19. Mas-Colell, Andreu, 1974. "Continuous and smooth consumers: Approximation theorems," Journal of Economic Theory, Elsevier, vol. 8(3), pages 305-336, July.
  20. 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.
  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. 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. 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.
  24. Krugman, Paul, 1993. "On the number and location of cities," European Economic Review, Elsevier, vol. 37(2-3), pages 293-298, April.
  25. 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.
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Citations

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Cited by:
  1. Berliant, Marcus, 2007. "Prospects for a unified urban general equilibrium theory," Regional Science and Urban Economics, Elsevier, vol. 37(4), pages 466-471, July.
  2. 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.
  3. 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.
  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. 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.
  6. Marcus Berliant & Yves Zenou, 2004. "Labor Differentiation and Agglomeration in General Equilibrium," Urban/Regional 0408003, EconWPA.
  7. Fan-chin Kung, 2004. "Genericity analysis of split bifurcations," GE, Growth, Math methods 0410008, EconWPA, revised 13 Oct 2004.

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