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Global bifurcation mechanism and local stability of identical and equidistant regions

Author

Listed:
  • José Gaspar

    (Universidade Católica Portuguesa, Católica Porto Business School and CEGE)

  • Kiyohiro Ikeda

    (Department of Civil and Environmental Engineering, Tohoku University)

  • Mikihasa Onda

    (Department of Civil and Environmental Engineering, Tohoku University)

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 UrbEcon) 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 h 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

  • José Gaspar & Kiyohiro Ikeda & Mikihasa Onda, 2019. "Global bifurcation mechanism and local stability of identical and equidistant regions," Working Papers de Economia (Economics Working Papers) 04, Católica Porto Business School, Universidade Católica Portuguesa.
    • Handle: RePEc:cap:wpaper:042019
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. José Gaspar & Kiyohiro Ikeda & Mikihasa Onda, 2019. "Global bifurcation mechanism and local stability of identical and equidistant regions," Working Papers de Economia (Economics Working Papers) 04, Católica Porto Business School, Universidade Católica Portuguesa.

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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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