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Breaking and sustaining bifurcations in SN-Invariant equidistant economy

Publication . Aizawa, H.; Ikeda, K.; Osawa, M.; Gaspar, J. M.

This paper elucidates the bifurcation mechanism of an equidistant economy in spatial economics. To this end, we derive the rules of secondary and further bifurcations as a major theoretical contribution of this paper. Then we combine them with pre-existing results of direct bifurcation of the symmetric group SN [Elmhirst, 2004]. Particular attention is devoted to the existence of invariant solutions which retain their spatial distributions when the value of the bifurcation parameter changes. Invariant patterns of an equidistant economy under the replicator dynamics are obtained. The mechanism of bifurcations from these patterns is elucidated. The stability of bifurcating branches is analyzed to demonstrate that most of them are unstable immediately after bifurcation. Numerical analysis of spatial economic models confirms that almost all bifurcating branches are unstable. Direct bifurcating curves connect the curves of invariant solutions, thereby creating a mesh-like network, which appears as threads of warp and weft. The theoretical bifurcation mechanism and numerical examples of networks advanced herein might be of great assistance in the study of spatial economics.

2020Journal article

Open access

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

Publication . Gaspar, José M.; Ikeda, Kiyohiro; Onda, Mikihasa

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.

2020Journal article

Restricted access

Paul Krugman: contributions to Geography and Trade

Publication . Gaspar, José M.

This work consists of a survey of the academic work of Paul Robin Krugman. It seeks to shed light on his main contributions to economic theory, mainly those for which he was awarded the Nobel Prize in Economics in 2008. His legacy in academia can be assessed through the recognition of his work on the identification of international trade patterns and the explanation on why spatial imbalances in the distribution of economic activities arise in an increasingly globalized economy. Through these contributions to trade theory and economic geography, Krugman is often credited as being one of the pioneering researchers in the New Trade Theory and the founding father (together with Masahisa Fujita) of the New Economic Geography.

2020Journal article

Restricted access