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Bifurcations in Regional Migration Dynamics

  • Berliant, Marcus
  • Kung, Fan-chin

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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  1. Fujita, Masahisa & Thisse, Jacques-François, 1996. "Economics of Agglomeration," CEPR Discussion Papers 1344, C.E.P.R. Discussion Papers.
  2. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
  3. 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.
  4. Diego Puga, 1996. "The Rise and Fall of Regional Inequalities," CEP Discussion Papers dp0314, Centre for Economic Performance, LSE.
  5. 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.
  6. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, June.
  7. Richard Arnott & Alex Anas & Kenneth Small, 1997. "Urban Spatial Structure," Boston College Working Papers in Economics 388., Boston College Department of Economics.
  8. 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, June.
  9. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-99, June.
  10. Oyama, Daisuke, 2009. "History versus expectations in economic geography reconsidered," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 394-408, February.
  11. 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).
  12. 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.
  13. Rikard Forslid & Gianmarco I.P. Ottaviano, 2003. "An analytically solvable core-periphery model," Journal of Economic Geography, Oxford University Press, vol. 3(3), pages 229-240, July.
  14. 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.
  15. Kehoe, Timothy J, 1985. "Multiplicity of Equilibria and Comparative Statics," The Quarterly Journal of Economics, MIT Press, vol. 100(1), pages 119-47, February.
  16. Berliant, Marcus & Zenou, Yves, 2012. "Labor differentiation and agglomeration in general equilibrium," MPRA Paper 36207, University Library of Munich, Germany.
  17. Zeng, Dao-Zhi, 2002. "Equilibrium stability for a migration model," Regional Science and Urban Economics, Elsevier, vol. 32(1), pages 123-138, January.
  18. 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.
  19. 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.
  20. 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.
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