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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

    (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
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    References listed on IDEAS

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    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

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