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Global bifurcation mechanism and local stability of identical and equidistant regions: Application to three regions and more

José Gaspar (), Kiyohiro Ikeda and Mikihasa Onda

Regional Science and Urban Economics, 2021, vol. 86, issue C

Abstract: We provide an analytical description of possible spatial patterns in economic geography models with three identical and equidistant regions by adapting results from General Bifurcation mechanism. We then use Pflüger's (2004, Reg Sci Urb Econ) model to show analytically how such spatial patterns can be uncovered. As the freeness of trade increases, a uniform distribution undergoes a direct bifurcation that leads to either (1) a state with two identical small regions and one large region or (2) a state with two identical large regions and one small region. The former state leads to the agglomeration in a single region. The latter leads to a state with two evenly populated regions and one region with no industry, which further undergoes a secondary bifurcation, en route to a partial agglomeration with one small region and one large region. The stability of these states is investigated. We show that an asymmetric equilibrium such that all regions have different positive industry sizes cannot be connected with other types of equilibria. Therefore, an initially asymmetric state will remain so and preserve the ordering between region sizes. For the n-region model, we show that an equilibrium with more than three groups of identical regions cannot be reached from an interior state, thus precluding any completely asymmetric state with industry in all regions. We also provide insights on other economic geography models with three regions.

Keywords: Bifurcation; Economic geography; Multi-regional economy; Footloose entrepreneur (search for similar items in EconPapers)
JEL-codes: R10 R12 R23 (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:regeco:v:86:y:2021:i:c:s0166046220302829

DOI: 10.1016/j.regsciurbeco.2020.103597

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