Browsing by Author "Ikeda, Kiyohiro"
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- Global bifurcation mechanism and local stability of identical and equidistant regionsPublication . Gaspar, José; Ikeda, Kiyohiro; Onda, MikihasaWe provide an analytical description of possible spatial patterns in economic geography models with three identical and equidistant regions by applying results from General Bifurcation mechanisms. We then use Pflüger’s (2004, Reg Sci Urb Econ) model to show what spatial patterns can be uncovered analytically. As the freeness of trade increases, a uniform distribution undergoes a direct bifurcation that leads to a state with two identical large regions and one small region. Before this bifurcation, the model encounters a minimum point above which a curve of dual equilibria with two small identical regions and one small region emerges. From further bifurcations, the equilibrium with one large region encounters agglomeration in a single region, while the equilibrium with one small region encounters a state with two evenly populated regions and one empty region. A secondary bifurcation then leads to partial agglomeration with one small region and one large region. We show that an asymmetric equilibrium with populated regions cannot be connected with other types of equilibria. Therefore, an initially asymmetric state will remain so and preserve the ordering between region sizes.
- Global bifurcation mechanism and local stability of identical and equidistant regions: application to three regions and morePublication . Gaspar, José M.; Ikeda, Kiyohiro; Onda, MikihasaWe 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.
- How and where satellite cities form around a large city: bifurcation mechanism of a long narrow economyPublication . Ikeda, Kiyohiro; Aizawa, Hiroki; Gaspar, J. M.We investigate economic agglomerations in a long narrow economy, in which discrete locations are evenly spread over a line segment. The bifurcation mechanism of a monocentric city at the center is analyzed analytically to show how and where satellite cities form. This is an important step to elucidate the mechanism of the competition between a large central city and satellite cities, which is taking place worldwide. By the analysis of the Forslid & Ottaviano (J Econ Geo, 2003) model, we show that the larger the agglomeration forces, the farther from the monocentric city satellite cities emerge. As the trade freeness increases from a low value, there occurs a spatial period doubling in which every other city grows. Thereafter a central city with two satellite cities appears, en route to a complete agglomeration to the central city.
- 線分都市経済における単一中心型集積の分岐解析Publication . Aizawa, Hiroki; Ikeda, Kiyohiro; Kogure, Yosuke; Osawa, Minoru; Gaspar, José MariaIn new economic geography, economic agglomeration is known to be governed by bifurcation. However, the majority of theoretical researches focuses on two-place economy and racetrack economy and abstract from geographical advantage which are pervasive in the real world. In this paper, we focus on a long narrow economy, in which discrete locations are equally spread over a line segment. By group-theoretic bifurcation theory, we elucidate the bifurcation mechanism of monocentric city on this economy analytically. Emergence of satellite cities around a primary city is shown to be exist. By numerical analysis of Forslid & Ottaviano model with replicator dynamics, we show that the higher the expenditure share of manufactured goods is or the lower the elasticity of substitution is, the farther from the monocentric city satellite cities emerge.