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

Akamatsu, Takashi and Takayama, Yuki and Ikeda, Kiyohiro (2009): Spatial Discounting, Fourier, and Racetrack Economy: A Recipe for the Analysis of Spatial Agglomeration Models.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: economic geography; agglomeration; stability; bifurcation; gravity laws
• Subjects: F - International Economics > F1 - Trade > F15 - Economic Integration; F - International Economics > F2 - International Factor Movements and International Business > F22 - International Migration; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics > R13 - General Equilibrium and Welfare Economic Analysis of Regional Economies; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C65 - Miscellaneous Mathematical Tools; F - International Economics > F1 - Trade > F12 - Models of Trade with Imperfect Competition and Scale Economies ; Fragmentation; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics > R12 - Size and Spatial Distributions of Regional Economic Activity; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium

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