IDEAS home Printed from https://ideas.repec.org/a/kap/netspa/v23y2023i4d10.1007_s11067-023-09604-0.html
   My bibliography  Save this article

A Continuous Space Model of New Economic Geography with a Quasi-Linear Log Utility Function

Author

Listed:
  • Kensuke Ohtake

    (Shinshu University)

Abstract

We consider the extension of a tractable NEG model with a quasi-linear log utility function to continuous space, and investigate the behavior of its solution mathematically. The model is a system of nonlinear integral and differential equations describing the market equilibrium and the time evolution of the spatial distribution of population density. A unique global solution is constructed, and a homogeneous stationary solution with an evenly distributed population is shown to be unstable. Furthermore, it is shown numerically that the destabilized homogeneous stationary solution eventually forms spiky spatial distributions. The number of the spikes decreases as the preference for variety increases or the transport cost decreases.

Suggested Citation

  • Kensuke Ohtake, 2023. "A Continuous Space Model of New Economic Geography with a Quasi-Linear Log Utility Function," Networks and Spatial Economics, Springer, vol. 23(4), pages 905-930, December.
    • Handle: RePEc:kap:netspa:v:23:y:2023:i:4:d:10.1007_s11067-023-09604-0
    DOI: 10.1007/s11067-023-09604-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11067-023-09604-0
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11067-023-09604-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Minoru Tabata & Nobuoki Eshima, 2023. "Approximation of a Continuous Core-periphery Model by Core-periphery Models with a Large Number of Small Regions," Networks and Spatial Economics, Springer, vol. 23(1), pages 223-283, March.
    2. José M. Gaspar & Sofia B. S. D. Castro & João Correia-da-Silva, 2018. "Agglomeration patterns in a multi-regional economy without income effects," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(4), pages 863-899, December.
    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. 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.
    5. Gianmarco Ottaviano & Takatoshi Tabuchi & Jacques-François Thisse, 2021. "Agglomeration And Trade Revisited," World Scientific Book Chapters, in: Firms and Workers in a Globalized World Larger Markets, Tougher Competition, chapter 3, pages 59-85, World Scientific Publishing Co. Pte. Ltd..
    6. Dixit, Avinash K & Stiglitz, Joseph E, 1977. "Monopolistic Competition and Optimum Product Diversity," American Economic Review, American Economic Association, vol. 67(3), pages 297-308, June.
    7. Matsuyama, Kiminori, 1996. "Why Are There Rich and Poor Countries? Symmetry-Breaking in the World Economy," Journal of the Japanese and International Economies, Elsevier, vol. 10(4), pages 419-439, December.
    8. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-499, June.
    9. 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.
    10. Chincarini, Ludwig & Asherie, Neer, 2008. "An analytical model for the formation of economic clusters," Regional Science and Urban Economics, Elsevier, vol. 38(3), pages 252-270, May.
    11. Yannis M. Ioannides, 2012. "From Neighborhoods to Nations: The Economics of Social Interactions," Economics Books, Princeton University Press, edition 1, volume 1, number 9892.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. José M. Gaspar, 2018. "A prospective review on New Economic Geography," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 61(2), pages 237-272, September.
    2. 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.
    3. MORI Tomoya, 2018. "Spatial Pattern and City Size Distribution," Discussion papers 18053, Research Institute of Economy, Trade and Industry (RIETI).
    4. 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.
    5. Akamatsu, Takashi & Takayama, Yuki, 2009. "A Simplified Approach to Analyzing Multi-regional Core-Periphery Models," MPRA Paper 21739, University Library of Munich, Germany, revised 29 Oct 2009.
    6. An-Ming Wang, 2016. "Agglomeration and simplified housing boom," Urban Studies, Urban Studies Journal Limited, vol. 53(5), pages 936-956, April.
    7. Pierre Philippe Combes & Gilles Duranton & Henry G. Overman, 2005. "Agglomeration and the adjustment of the spatial economy§," Papers in Regional Science, Wiley Blackwell, vol. 84(3), pages 311-349, August.
    8. Minoru Tabata & Nobuoki Eshima, 2023. "Approximation of a Continuous Core-periphery Model by Core-periphery Models with a Large Number of Small Regions," Networks and Spatial Economics, Springer, vol. 23(1), pages 223-283, March.
    9. Ottaviano, Gianmarco & Thisse, Jacques-Francois, 2004. "Agglomeration and economic geography," 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 58, pages 2563-2608, Elsevier.
    10. Steven C Bond-Smith & Philip McCann, 2020. "A multi-sector model of relatedness, growth and industry clustering [Distance to frontier, selection, and economic growth]," Journal of Economic Geography, Oxford University Press, vol. 20(5), pages 1145-1163.
    11. Hiroki Aizawa & Kiyohiro Ikeda & Yosuke Kogure, 2023. "Satellite City Formation for a Spatial Economic Model," Networks and Spatial Economics, Springer, vol. 23(3), pages 529-558, September.
    12. Jyh-Fa Tsai, 2019. "Tax competition with spillover public goods in a median location model," Asia-Pacific Journal of Regional Science, Springer, vol. 3(3), pages 831-862, October.
    13. José M. Gaspar & Sofia B. S. D. Castro & João Correia-da-Silva, 2018. "Agglomeration patterns in a multi-regional economy without income effects," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(4), pages 863-899, December.
    14. José Gaspar & Kiyohiro Ikeda & Mikihasa Onda, 2019. "Global bifurcation mechanism and local stability of identical and equidistant regions," Working Papers de Economia (Economics Working Papers) 04, Católica Porto Business School, Universidade Católica Portuguesa.
    15. Fabien Candau, 2008. "Entrepreneurs' Location Choice And Public Policies: A Survey Of The New Economic Geography," Journal of Economic Surveys, Wiley Blackwell, vol. 22(5), pages 909-952, December.
    16. Kensuke Ohtake, 2021. "A continuous space model of new economic geography with a quasi-linear log utility function," Papers 2108.12217, arXiv.org, revised Aug 2023.
    17. 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.
    18. Fabien Candau, 2008. "Urban costs, Trade costs and Tax Competition," Revue d'économie politique, Dalloz, vol. 118(5), pages 625-661.
    19. Takashi Akamatsu & Tomoya Mori & Minoru Osawa & Yuki Takayama, 2019. "Spatial scale of agglomeration and dispersion: Number, spacing, and the spatial extent of cities," Papers 1912.05113, arXiv.org, revised Aug 2024.
    20. Olga Alonso‐Villar, 2008. "A model of economic geography with demand‐pull and congestion costs," Papers in Regional Science, Wiley Blackwell, vol. 87(2), pages 261-276, June.

    More about this item

    Keywords

    New economic geography; Continuous racetrack economy; Self-organization; Spatial patterns; Number of cities;
    All these keywords.

    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)
    • R40 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics - - - General
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:netspa:v:23:y:2023:i:4:d:10.1007_s11067-023-09604-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.