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

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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.

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File URL: http://128.118.178.162/eps/urb/papers/0407/0407011.pdf
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Bibliographic Info

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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Web page: http://128.118.178.162

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

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References

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  1. 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.
  2. 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.
  3. Marcus Berliant & Yves Zenou, 2014. "Labor Differentiation and Agglomeration in General Equilibrium," International Regional Science Review, , vol. 37(1), pages 36-65, January.
  4. Debreu, Gerard, 1976. "Regular Differentiable Economies," American Economic Review, American Economic Association, vol. 66(2), pages 280-87, May.
  5. 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.
  6. Mas-Colell, Andreu, 1974. "Continuous and smooth consumers: Approximation theorems," Journal of Economic Theory, Elsevier, vol. 8(3), pages 305-336, July.
  7. 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.
  8. 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.
  9. Fujita,Masahisa & Thisse,Jacques-François, 2013. "Economics of Agglomeration," Cambridge Books, Cambridge University Press, number 9780521171960, October.
  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. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-99, June.
  12. 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.
  13. Glenn Ellison & Drew Fudenberg, 2003. "Knife-Edge Or Plateau: When Do Market Models Tip?," The Quarterly Journal of Economics, MIT Press, vol. 118(4), pages 1249-1278, November.
  14. J.V. Henderson, 1972. "The Sizes and Types of Cities," Working Papers 75, Queen's University, Department of Economics.
  15. 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.
  16. 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.
  17. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-92, May.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. Dierker, Egbert & Dierker, Hildegard, 1972. "The Local Uniqueness of Equilibria," Econometrica, Econometric Society, vol. 40(5), pages 867-81, September.
  23. 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.
  24. Krugman, Paul, 1993. "On the number and location of cities," European Economic Review, Elsevier, vol. 37(2-3), pages 293-298, April.
  25. 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.
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Citations

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Cited by:
  1. Berliant, Marcus, 2006. "Prospects for a unified urban general equilibrium theory," MPRA Paper 379, University Library of Munich, Germany.
  2. Marcus Berliant & Yves Zenou, 2004. "Labor Differentiation and Agglomeration in General Equilibrium," Urban/Regional 0408003, EconWPA.
  3. Marcus Berliant & Ping Wang, 2004. "Dynamic Urban Models: Agglomeration and Growth," Urban/Regional 0404006, EconWPA.
  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. Fan-chin Kung, 2004. "Genericity analysis of split bifurcations," GE, Growth, Math methods 0410008, EconWPA, revised 13 Oct 2004.
  6. 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.
  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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