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Spatial period-doubling agglomeration of a core–periphery model with a system of cities

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  • Ikeda, Kiyohiro
  • Akamatsu, Takashi
  • Kono, Tatsuhito

Abstract

The progress of spatial agglomeration of Krugman's core–periphery model is investigated by comparative static analysis of stable equilibria with respect to transport costs. We set forth theoretically possible agglomeration (bifurcation) patterns for a system of cities spread uniformly on a circle. A possible and most likely course predicted is a gradual and successive one, which is called spatial period doubling. For example, eight cities concentrate into four cities and then into two cities en route to the formation of a single city. The existence of this course is ensured by numerical simulation for the model. Such a gradual and successive agglomeration presents a sharp contrast to the agglomeration of two cities, for which spontaneous concentration to a single city is observed in core–periphery models of various kinds. Other bifurcations that do not take place in two cities, such as period tripling, are also observed. The need for study of a system of cities has thus been demonstrated.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:dyncon:v:36:y:2012:i:5:p:754-778
    DOI: 10.1016/j.jedc.2011.08.014
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    More about this item

    Keywords

    Agglomeration of population; Bifurcation; Core–periphery model; Group theory; Spatial period doubling;

    JEL classification:

    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)
    • R13 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - General Equilibrium and Welfare Economic Analysis of Regional Economies
    • F12 - International Economics - - Trade - - - Models of Trade with Imperfect Competition and Scale Economies; Fragmentation
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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