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Unique global solution of an integral-differential equation of Footloose Entrepreneur model in new economic geography

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  • Kensuke Ohtake

Abstract

This paper studies the Footloose Entrepreneur model in new economic geography in continuous space. In an appropriate function space, the model is formulated as an initial value problem for an infinite-dimensional ordinary differential equation. A unique global solution is constructed based on the Banach fixed point theorem. The stability of a homogeneous stationary solution is then investigated and numerical simulations of the asymptotic behavior of the solution are performed. Numerical solutions starting near the unstable homogeneous stationary solution converge to spike-shaped stationary solutions, and the number of spikes decreases with decreasing transport costs and strengthening preference for variety.

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  • Kensuke Ohtake, 2025. "Unique global solution of an integral-differential equation of Footloose Entrepreneur model in new economic geography," Papers 2505.11241, arXiv.org.
    • Handle: RePEc:arx:papers:2505.11241
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    References listed on IDEAS

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    7. 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.
    8. Kensuke Ohtake, 2022. "Agglomeration triggered by the number of regions: a NEG model with a quadratic subutility function," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(1), pages 129-145, May.
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