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Harris And Wilson (1978) Model Revisited: The Spatial Period‐Doubling Cascade In An Urban Retail Model

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  • Minoru Osawa
  • Takashi Akamatsu
  • Yuki Takayama

Abstract

Harris and Wilson (1978)'s retail location model is a pioneering work that utilizes the combination of the “fast” and “slow” dynamics to describe the space economy. This paper elucidates the model's previously unknown comparative static (bifurcation) properties in a many‐location setting beyond two. We show that the spatial structure's evolutionary path in line with decreasing transport costs exhibits a remarkable property, namely, a “spatial period‐doubling cascade.” Furthermore, we reveal strong linkages between the model and “new economic geography” models in terms of their model structures and bifurcation properties, offering a new theoretical perspective for understanding agglomeration behaviors in multilocation settings.

Suggested Citation

  • Minoru Osawa & Takashi Akamatsu & Yuki Takayama, 2017. "Harris And Wilson (1978) Model Revisited: The Spatial Period‐Doubling Cascade In An Urban Retail Model," Journal of Regional Science, Wiley Blackwell, vol. 57(3), pages 442-466, June.
    • Handle: RePEc:bla:jregsc:v:57:y:2017:i:3:p:442-466
    DOI: 10.1111/jors.12306
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    Cited by:

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    2. Kogure, Yosuke & Ikeda, Kiyohiro, 2022. "Group-theoretic Study of Economic Agglomerations on a Square Lattice," MPRA Paper 112842, University Library of Munich, Germany.
    3. Slavko, Bohdan & Glavatskiy, Kirill S. & Prokopenko, Mikhail, 2021. "Revealing configurational attractors in the evolution of modern Australian and US cities," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    4. Akamatsu, Takashi & Mori, Tomoya & Osawa, Minoru & Takayama, Yuki, 2017. "Spatial scale of agglomeration and dispersion: Theoretical foundations and empirical implications," MPRA Paper 80689, University Library of Munich, Germany.
    5. Takashi Akamatsu & Tomoya Mori & Yuki Takayama, 2015. "Agglomerations in a multi-region economy: Poly-centric versus mono-centric patterns," KIER Working Papers 929, Kyoto University, Institute of Economic Research.
    6. Xu, Fei & Liu, Qian & Zheng, Xingdong & Cao, Luqi & Yang, Mian, 2022. "Research on the impact of China's high-speed rail opening on enterprise market power: Based on the perspective of market segmentation," Transport Policy, Elsevier, vol. 128(C), pages 121-137.
    7. Emanuele Crosato & Ramil Nigmatullin & Mikhail Prokopenko, 2018. "On critical dynamics and thermodynamic efficiency of urban transformations," Papers 1806.03758, arXiv.org.
    8. Kiyohiro Ikeda & Mikihisa Onda & Yuki Takayama, 2019. "Bifurcation Theory of a Racetrack Economy in a Spatial Economy Model," Networks and Spatial Economics, Springer, vol. 19(1), pages 57-82, March.
    9. Stef Proost & Jacques-François Thisse, 2019. "What Can Be Learned from Spatial Economics?," Journal of Economic Literature, American Economic Association, vol. 57(3), pages 575-643, September.
    10. Aizawa, Hiroki & Kono, Tatsuhito, 2022. "Two-dimensional Geographical Position as a Factor in Determining the Growth and Decline of Retail Agglomeration," MPRA Paper 112274, University Library of Munich, Germany.
    11. Osawa, Minoru & Akamatsu, Takashi, 2019. "Emergence of Urban Landscapes: Equilibrium Selection in a Model of Internal Structure of the Cities," MPRA Paper 92395, University Library of Munich, Germany.
    12. Osawa, Minoru & Akamatsu, Takashi, 2020. "Equilibrium refinement for a model of non-monocentric internal structures of cities: A potential game approach," Journal of Economic Theory, Elsevier, vol. 187(C).
    13. Minoru Osawa & Takashi Akamatsu & Yosuke Kogure, 2020. "Stochastic stability of agglomeration patterns in an urban retail model," Papers 2011.06778, arXiv.org.
    14. Ikeda, Kiyohiro & Onda, Mikihisa & Takayama, Yuki, 2018. "Spatial period doubling, invariant pattern, and break point in economic agglomeration in two dimensions," Journal of Economic Dynamics and Control, Elsevier, vol. 92(C), pages 129-152.

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    More about this item

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • F12 - International Economics - - Trade - - - Models of Trade with Imperfect Competition and Scale Economies; Fragmentation
    • F15 - International Economics - - Trade - - - Economic Integration
    • 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

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