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Spatial Discounting, Fourier, and Racetrack Economy: A Recipe for the Analysis of Spatial Agglomeration Models

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  • Akamatsu, Takashi
  • Takayama, Yuki
  • Ikeda, Kiyohiro

Abstract

We provide an analytical approach that facilitates understanding the bifurcation mechanism of a wide class of economic models involving spatial agglomeration of economic activities. The proposed method overcomes the limitations of the Turing (1952) approach that has been used to analyze the emergence of agglomeration in the multi-regional core-periphery (CP) model of Krugman (1993, 1996). In other words, the proposed method allows us to examine whether agglomeration of mobile factors emerges from a uniform distribution and to analytically trace the evolution of spatial agglomeration patterns (i.e., bifurcations from various polycentric patterns as well as a uniform pattern) that these models exhibit when the values of some structural parameters change steadily. Applying the proposed method to the multi-regional CP model, we uncover a number of previously unknown properties of the CP model, and notably, the occurrence of “spatial period doubling bifurcation” in the CP model is proved.

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  • Akamatsu, Takashi & Takayama, Yuki & Ikeda, Kiyohiro, 2009. "Spatial Discounting, Fourier, and Racetrack Economy: A Recipe for the Analysis of Spatial Agglomeration Models," MPRA Paper 21738, University Library of Munich, Germany, revised 25 Dec 2009.
    • Handle: RePEc:pra:mprapa:21738
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    More about this item

    Keywords

    economic geography; agglomeration; stability; bifurcation; gravity laws;
    All these keywords.

    JEL classification:

    • F15 - International Economics - - Trade - - - Economic Integration
    • F22 - International Economics - - International Factor Movements and International Business - - - International Migration
    • R13 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - General Equilibrium and Welfare Economic Analysis of Regional Economies
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • F12 - International Economics - - Trade - - - Models of Trade with Imperfect Competition and Scale Economies; Fragmentation
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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