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A continuous space model of new economic geography with a quasi-linear log utility function

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  • Kensuke Ohtake

Abstract

We consider the extension of a tractable NEG model with a quasi-linear log utility 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 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, 2021. "A continuous space model of new economic geography with a quasi-linear log utility function," Papers 2108.12217, arXiv.org, revised Aug 2023.
    • Handle: RePEc:arx:papers:2108.12217
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    References listed on IDEAS

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    1. 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..
    2. 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.
    3. 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.
    4. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-499, June.
    5. Fujita,Masahisa & Thisse,Jacques-François, 2013. "Economics of Agglomeration," Cambridge Books, Cambridge University Press, number 9780521171960, January.
    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.
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    Cited by:

    1. Kensuke Ohtake, 2025. "Continuous space core-periphery model with transport costs in differentiated agriculture," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 24(3), pages 469-502, September.
    2. Kensuke Ohtake, 2025. "Unique global solution of an integral-differential equation of Footloose Entrepreneur model in new economic geography," Papers 2505.11241, arXiv.org.

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