TY - JOUR
T1 - Global bifurcation mechanism and local stability of identical and equidistant regions
T2 - application to three regions and more
AU - Gaspar, José M.
AU - Ikeda, Kiyohiro
AU - Onda, Mikihasa
N1 - Funding Information:
We thank Minoru Osawa, two anonymous referees, and the Editor Kristian Behrens for useful comments and suggestions. Financial support from Fundação para a Ciência e Tecnologia (through projects UIDB/04105/2020, UIDB/00731/2020, PTDC/EGE-ECO/30080/2017 and CEECIND/02741/2017) and from the Grant-in-Aid for JSPS 18K04380/18K18874/19K15108 are greatly appreciated.
Funding Information:
We thank Minoru Osawa, two anonymous referees, and the Editor Kristian Behrens for useful comments and suggestions. Financial support from Fundação para a Ciência e Tecnologia (through projects UIDB/04105/2020 , UIDB/00731/2020 , PTDC/EGE-ECO/30080/2017 and CEECIND/02741/2017 ) and from the Grant-in-Aid for JSPS 18K04380/18K18874/19K15108 are greatly appreciated.
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2021/1
Y1 - 2021/1
N2 - 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.
AB - 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.
KW - Bifurcation
KW - Economic geography
KW - Footloose entrepreneur
KW - Multi-regional economy
UR - http://www.scopus.com/inward/record.url?scp=85096956332&partnerID=8YFLogxK
U2 - 10.1016/j.regsciurbeco.2020.103597
DO - 10.1016/j.regsciurbeco.2020.103597
M3 - Article
AN - SCOPUS:85096956332
SN - 0166-0462
VL - 86
JO - Regional Science and Urban Economics
JF - Regional Science and Urban Economics
M1 - 103597
ER -