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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. Fujita, Masahisa & Thisse, Jacques-François, 1996. "Economics of Agglomeration," CEPR Discussion Papers 1344, C.E.P.R. Discussion Papers.
  2. 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.
  3. Paul Krugman, 1990. "Increasing Returns and Economic Geography," NBER Working Papers 3275, National Bureau of Economic Research, Inc.
  4. Henderson, J V, 1974. "The Sizes and Types of Cities," American Economic Review, American Economic Association, vol. 64(4), pages 640-56, September.
  5. Berliant, Marcus & Zenou, Yves, 2012. "Labor differentiation and agglomeration in general equilibrium," MPRA Paper 36207, University Library of Munich, Germany.
  6. Debreu, Gerard, 1976. "Regular Differentiable Economies," American Economic Review, American Economic Association, vol. 66(2), pages 280-87, May.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. Mas-Colell, Andreu, 1974. "Continuous and smooth consumers: Approximation theorems," Journal of Economic Theory, Elsevier, vol. 8(3), pages 305-336, July.
  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. Krugman, Paul, 1993. "On the number and location of cities," European Economic Review, Elsevier, vol. 37(2-3), pages 293-298, April.
  14. 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.
  15. 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.
  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.
  17. 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.
  18. 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.
  19. 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.
  20. 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).
  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. 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.
  23. Dierker, Egbert & Dierker, Hildegard, 1972. "The Local Uniqueness of Equilibria," Econometrica, Econometric Society, vol. 40(5), pages 867-81, September.
  24. 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.
  25. 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.
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Citations

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Cited by:
  1. Berliant, Marcus & Kung, Fan-chin, 2009. "Bifurcations in regional migration dynamics," Regional Science and Urban Economics, Elsevier, vol. 39(6), pages 714-720, November.
  2. Berliant, Marcus & Zenou, Yves, 2012. "Labor Differentiation and Agglomeration in General Equilibrium," CEPR Discussion Papers 8840, C.E.P.R. Discussion Papers.
  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, 2007. "Prospects for a unified urban general equilibrium theory," Regional Science and Urban Economics, Elsevier, vol. 37(4), pages 466-471, July.
  5. Marcus Berliant & Ping Wang, 2004. "Dynamic Urban Models: Agglomeration and Growth," Urban/Regional 0404006, EconWPA.
  6. Fan-chin Kung, 2004. "Genericity analysis of split bifurcations," GE, Growth, Math methods 0410008, EconWPA, revised 13 Oct 2004.
  7. 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.

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