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Global bifurcation mechanism and local stability of identical and equidistant regions

Author

Listed:
  • Gaspar, José M.
  • Ikeda, Kiyohiro
  • Onda, Mikihisa
Abstract
We provide an analytical description of possible spatial patterns in economic geography models with three identical and equidistant regions by applying results from General Bifurcation mechanisms. We then use Pflüger's (2004, Reg Sci Urb Econ) model to show what spatial patterns can be uncovered analytically. As the freeness of trade increases, a uniform distribution undergoes a direct bifurcation that leads to a state with two identical large regions and one small region. Before this bifurcation, the model encounters a minimum point above which a curve of dual equilibria with two small identical regions and one small region emerges. From further bifurcations, the equilibrium with one large region encounters agglomeration in a single region, while the equilibrium with one small region encounters a state with two evenly populated regions and one empty region. A secondary bifurcation then leads to partial agglomeration with one small region and one large region. We show that an asymmetric equilibrium with populated regions cannot be connected with other types of equilibria. Therefore, an initially asymmetric state will remain so and preserve the ordering between region sizes.

Suggested Citation

  • Gaspar, José M. & Ikeda, Kiyohiro & Onda, Mikihisa, 2019. "Global bifurcation mechanism and local stability of identical and equidistant regions," MPRA Paper 95013, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:95013
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    References listed on IDEAS

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    1. Gaspar, José M. & Ikeda, Kiyohiro & Onda, Mikihisa, 2019. "Global bifurcation mechanism and local stability of identical and equidistant regions," MPRA Paper 95013, University Library of Munich, Germany.
    2. Aizawa, Hiroki & Ikeda, Kiyohiro & Osawa, Minoru & José M, Gasper, 2019. "Break and sustain bifurcations of S_N-invariant equidistant economy," MPRA Paper 97654, University Library of Munich, Germany.

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    More about this item

    Keywords

    bifurcation; economic geography; multi-regional economy; footloose entrepreneur;
    All these keywords.

    JEL classification:

    • R10 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - General
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)
    • R23 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Household Analysis - - - Regional Migration; Regional Labor Markets; Population

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