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Bifurcations in Regional Migration Dynamics

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Author Info
Berliant, Marcus
Kung, Fan-chin

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Abstract

The tomahawk bifurcation is used by Fujita et al. (1999) in a model with two regions to explain the formation of a core-periphery urban pattern from an initial uniform distribution. Baldwin et al. (2003) show that the tomahawk bifurcation disappears when the two regions have an uneven population of immobile agricultural workers. Thus, the appearance of this type of bifurcation is the result of assumed exogenous model symmetry. We provide a general analysis in a regional model of the class of bifurcations that have crossing equilibrium loci, including the tomahawk bifurcation, by examining arbitrary smooth parameter paths in a higher dimensional parameter space. We find that, in a parameter space satisfying a mild rank condition, generically in all parameter paths this class of bifurcations does not appear. In other words, conclusions drawn from the use of this bifurcation to generate a core-periphery pattern are not robust. Generically, this class of bifurcations is a myth, an urban legend.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 13053.

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Date of creation: 28 Jan 2009
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Handle: RePEc:pra:mprapa:13053

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Related research
Keywords: Bifurcation; Genericity Analysis; Migration Dynamics;

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Find related papers by JEL classification:
F12 - International Economics - - Trade - - - Models of Trade with Imperfect Competition and Scale Economies
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
R23 - Urban, Rural, and Regional Economics - - Household Analysis - - - Regional Migration; Regional Labor Markets; Population

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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. Marcus Berliant & Yves Zenou, 2004. "Labor Differentiation and Agglomeration in General Equilibrium," Urban/Regional 0408003, EconWPA. [Downloadable!]
  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. [Downloadable!] (restricted)
  3. Kehoe, Timothy J, 1985. "Multiplicity of Equilibria and Comparative Statics," The Quarterly Journal of Economics, MIT Press, vol. 100(1), pages 119-47, February. [Downloadable!] (restricted)
  4. 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)
  5. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215.
  6. Alex Anas & Richard Arnott & Kenneth A. Small, 1998. "Urban Spatial Structure," Journal of Economic Literature, American Economic Association, vol. 36(3), pages 1426-1464, September. [Downloadable!] (restricted)
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  7. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-92, May. [Downloadable!] (restricted)
  8. Marcus Berliant & Fan- chin Kung, 2004. "The Indeterminacy of Equilibrium City Formation under Monopolistic Competition and Increasing Returns," Urban/Regional 0407011, EconWPA, revised 29 Apr 2005. [Downloadable!]
    Other versions:
  9. 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)
  10. Zeng, Dao-Zhi, 2002. "Equilibrium stability for a migration model," Regional Science and Urban Economics, Elsevier, vol. 32(1), pages 123-138, January. [Downloadable!] (restricted)
  11. 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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  12. 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)
    Other versions:
  13. Masahisa Fujita & Paul Krugman & Anthony J. Venables, 2001. "The Spatial Economy: Cities, Regions, and International Trade," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262561476.
  14. T Tabuchi, 1986. "Existence and stability of city-size distribution in the gravity and logit models," Environment and Planning A, Pion Ltd, London, vol. 18(10), pages 1375-1389, October. [Downloadable!] (restricted)
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