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Harris and Wilson (1978) Model Revisited: The Spatial Period-doubling Cascade in an Urban Retail Model

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  • Akamatsu, Takashi
  • Osawa, Minoru
  • Takayama, Yuki

Abstract

Harris and Wilson (1978)’s retail location model is one of the pioneering works in regional sciences on the combination of the “fast” and “slow” dynamic describing spatial pattern formation processes in the economic landscape, which is a current well-established modeling technique. Although proposed some time ago, the comparative static (bifurcation) properties of the model have not yet been sufficiently explored. We employ a simple analytical approach developed by Akamatsu et al. (2012) to reveal previously unknown bifurcation properties of the model in a space with a large number of locations. It is analytically shown that the evolutionary path of spatial structure exhibits a remarkable property, namely “spatial period- doubling cascade,” which we cannot observe in the popular two-location setup. We also discuss strong linkages between the model and the models of “new economic geography” regarding the modeling strategies and their bifurcation properties.

Suggested Citation

  • Akamatsu, Takashi & Osawa, Minoru & Takayama, Yuki, 2015. "Harris and Wilson (1978) Model Revisited: The Spatial Period-doubling Cascade in an Urban Retail Model," MPRA Paper 67974, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:67974
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    1. Weidlich, Wolfgang & Munz, Martin, 1990. "Settlement Formation: Part 1: A Dynamic Theory," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 24(2), pages 83-106.
    2. Alex Anas & Richard Arnott & Kenneth A. Small, 1998. "Urban Spatial Structure," Journal of Economic Literature, American Economic Association, vol. 36(3), pages 1426-1464, September.
    3. Rikard Forslid & Gianmarco I.P. Ottaviano, 2003. "An analytically solvable core-periphery model," Journal of Economic Geography, Oxford University Press, vol. 3(3), pages 229-240, July.
    4. Masahisa Fujita & Paul Krugman & Anthony J. Venables, 2001. "The Spatial Economy: Cities, Regions, and International Trade," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262561476, December.
    5. Papageorgiou, Yorgo Y & Smith, Terrence R, 1983. "Agglomeration as Local Instability of Spatially Uniform Steady-States," Econometrica, Econometric Society, vol. 51(4), pages 1109-1119, July.
    6. Fujita,Masahisa, 1991. "Urban Economic Theory," Cambridge Books, Cambridge University Press, number 9780521396455.
    7. Treb Allen & Costas Arkolakis, 2014. "Trade and the Topography of the Spatial Economy," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(3), pages 1085-1140.
    8. Stephen J. Redding & Daniel M. Sturm, 2008. "The Costs of Remoteness: Evidence from German Division and Reunification," American Economic Review, American Economic Association, vol. 98(5), pages 1766-1797, December.
    9. Ikeda, Kiyohiro & Murota, Kazuo & Akamatsu, Takashi & Kono, Tatsuhito & Takayama, Yuki, 2014. "Self-organization of hexagonal agglomeration patterns in new economic geography models," Journal of Economic Behavior & Organization, Elsevier, vol. 99(C), pages 32-52.
    10. Tabuchi, Takatoshi & Thisse, Jacques-François, 2011. "A new economic geography model of central places," Journal of Urban Economics, Elsevier, vol. 69(2), pages 240-252, March.
    11. Pines,David & Sadka,Efraim & Zilcha,Itzhak (ed.), 1998. "Topics in Public Economics," Cambridge Books, Cambridge University Press, number 9780521561365.
    12. Paul Krugman, 2011. "The New Economic Geography, Now Middle-aged," Regional Studies, Taylor & Francis Journals, vol. 45(1), pages 1-7.
    13. 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.
    14. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-499, June.
    15. Akamatsu, Takashi & Takayama, Yuki & Ikeda, Kiyohiro, 2012. "Spatial discounting, Fourier, and racetrack economy: A recipe for the analysis of spatial agglomeration models," Journal of Economic Dynamics and Control, Elsevier, vol. 36(11), pages 1729-1759.
    16. A G Wilson & M J Oulton, 1983. "The Corner-Shop to Supermarket Transition in Retailing: The Beginnings of Empirical Evidence," Environment and Planning A, , vol. 15(2), pages 265-274, February.
    17. Kiyohiro Ikeda & Kazuo Murota & Yuki Takayama, 2017. "Stable Economic Agglomeration Patterns In Two Dimensions: Beyond The Scope Of Central Place Theory," Journal of Regional Science, Wiley Blackwell, vol. 57(1), pages 132-172, January.
    18. M Clarke, 1981. "A Note on the Stability of Equilibrium Solutions of Production-Constrained Spatial-Interaction Models," Environment and Planning A, , vol. 13(5), pages 601-604, May.
    19. Duranton, Gilles & Puga, Diego, 2004. "Micro-foundations of urban agglomeration economies," Handbook of Regional and Urban Economics, in: J. V. Henderson & J. F. Thisse (ed.), Handbook of Regional and Urban Economics, edition 1, volume 4, chapter 48, pages 2063-2117, Elsevier.
    20. 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.
    21. Alan Wilson & Joel Dearden, 2011. "Phase transitions and path dependence in urban evolution," Journal of Geographical Systems, Springer, vol. 13(1), pages 1-16, March.
    22. David L. Huff, 1963. "A Probabilistic Analysis of Shopping Center Trade Areas," Land Economics, University of Wisconsin Press, vol. 39(1), pages 81-90.
    23. Alan Wilson, 2010. "The general urban model: Retrospect and prospect," Papers in Regional Science, Wiley Blackwell, vol. 89(1), pages 27-42, March.
    24. Gianmarco I P Ottaviano & Jacques-François Thisse, 2005. "New Economic Geography: What about the N?," Environment and Planning A, , vol. 37(10), pages 1707-1725, October.
    25. Behrens, Kristian & Thisse, Jacques-Francois, 2007. "Regional economics: A new economic geography perspective," Regional Science and Urban Economics, Elsevier, vol. 37(4), pages 457-465, July.
    26. Rijk, F. J. A. & Vorst, A. C. F., 1983. "Equilibrium points in an urban retail model and their connection with dynamical systems," Regional Science and Urban Economics, Elsevier, vol. 13(3), pages 383-399, August.
    27. B Harris & A G Wilson, 1978. "Equilibrium Values and Dynamics of Attractiveness Terms in Production-Constrained Spatial-Interaction Models," Environment and Planning A, , vol. 10(4), pages 371-388, April.
    28. Munz, M & Weidlich, W, 1990. "Settlement Formation: Part II: Numerical Simulation," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 24(3), pages 177-196.
    29. Pfluger, Michael, 2004. "A simple, analytically solvable, Chamberlinian agglomeration model," Regional Science and Urban Economics, Elsevier, vol. 34(5), pages 565-573, September.
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    Cited by:

    1. 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.
    2. Xu, Fei & Li, Qiangyi & Yang, Mian, 2022. "The impacts of high-speed rail on the transformation of resource-based cities in China: A market segmentation perspective," Resources Policy, Elsevier, vol. 78(C).
    3. 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.
    4. 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.
    5. Emanuele Crosato & Ramil Nigmatullin & Mikhail Prokopenko, 2018. "On critical dynamics and thermodynamic efficiency of urban transformations," Papers 1806.03758, arXiv.org.
    6. 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.
    7. Minoru Osawa & Takashi Akamatsu & Yosuke Kogure, 2020. "Stochastic stability of agglomeration patterns in an urban retail model," Papers 2011.06778, arXiv.org.
    8. Kogure, Yosuke & Ikeda, Kiyohiro, 2022. "Group-theoretic Study of Economic Agglomerations on a Square Lattice," MPRA Paper 112842, University Library of Munich, Germany.
    9. 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).
    10. 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.
    11. 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.
    12. 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).
    13. 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.
    14. 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.

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    More about this item

    Keywords

    agglomeration; multiple agglomerations; stability; bifurcation; new economic geography model;
    All these keywords.

    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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