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Bifurcations in regional migration dynamics

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  • Berliant, Marcus
  • Kung, Fan-chin

Abstract

The tomahawk bifurcation is used by Fujita et al. [Fujita, M., Krugman P., Venables A.J., 1999, The Spatial Economy: Cities, Regions, and International Trade, MIT Press: Cambridge, MA.] in a model with two regions to explain the formation of a core-periphery urban pattern from an initial uniform distribution. Baldwin et al. [Baldwin, R., Forslid, R., Martin, P., Ottaviano, G.I.P., Robert-Nicoud, F., 2003, Economic Geography and Public Policy, Princeton University Press: Princeton, NJ.] 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.

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Bibliographic Info

Article provided by Elsevier in its journal Regional Science and Urban Economics.

Volume (Year): 39 (2009)
Issue (Month): 6 (November)
Pages: 714-720

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Handle: RePEc:eee:regeco:v:39:y:2009:i:6:p:714-720

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Keywords: Bifurcation Genericity analysis Migration dynamics;

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References

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  1. 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.
  2. Zeng, Dao-Zhi, 2002. "Equilibrium stability for a migration model," Regional Science and Urban Economics, Elsevier, vol. 32(1), pages 123-138, January.
  3. Diego Puga, 1996. "The rise and fall of regional inequalities," LSE Research Online Documents on Economics 20643, London School of Economics and Political Science, LSE Library.
  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.
  5. 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, December.
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Citations

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Cited by:
  1. Oyama, Daisuke, 2009. "Agglomeration under forward-looking expectations: Potentials and global stability," Regional Science and Urban Economics, Elsevier, vol. 39(6), pages 696-713, November.
  2. Alexander V. Sidorov, 2011. "International Trade and Agglomeration in Asymmetric World: Core-Periphery Approach," DEGIT Conference Papers c016_020, DEGIT, Dynamics, Economic Growth, and International Trade.
  3. Marcus Berliant & Yves Zenou, 2004. "Labor Differentiation and Agglomeration in General Equilibrium," Urban/Regional 0408003, EconWPA.
  4. Christian Ghiglino & Antonella Nocco, 2012. "When Veblen meets Krugman," DEGIT Conference Papers c017_030, DEGIT, Dynamics, Economic Growth, and International Trade.
  5. Sidorov, A., 2013. "Stability of Totally Agglomerated Equilibrium in a Multiregional Core-Periphery Model," Journal of the New Economic Association, New Economic Association, vol. 17(1), pages 44-62.
  6. Ikeda, Kiyohiro & Akamatsu, Takashi & Kono, Tatsuhito, 2012. "Spatial period-doubling agglomeration of a core–periphery model with a system of cities," Journal of Economic Dynamics and Control, Elsevier, vol. 36(5), pages 754-778.
  7. Leung, Charles Ka Yui & Teo, Wing Leong, 2010. "Should the optimal portfolio be region-specific? A multi-region model with monetary policy and asset price co-movements," MPRA Paper 28216, University Library of Munich, Germany.

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