Spatial Period-Doubling Agglomeration of a Core-Periphery Model with a System of Cities

Ikeda, Kiyohiro and Akamatsu, Takashi and Kono, Tatsuhito (2009): Spatial Period-Doubling Agglomeration of a Core-Periphery Model with a System of Cities.

Abstract

The orientation and progress of spatial agglomeration for Krugman's core--periphery model are investigated in this paper. Possible agglomeration patterns for a system of cities spread uniformly on a circle are set forth theoretically. For example, a possible and most likely course predicted for eight cities is a gradual and successive one---concentration into four cities and then into two cities en route to a single city. The existence of this course is ensured by numerical simulation for the model. Such gradual and successive agglomeration, which is called spatial-period doubling, presents a sharp contrast with the agglomeration of two cities, for which spontaneous concentration to a single city is observed in models of various kinds. It exercises caution about the adequacy of the two cities as a platform of the spatial agglomerations and demonstrates the need of the study on a system of cities.

• Item Type: MPRA Paper
• Language: English
• Keywords: Agglomeration of population; Bifurcation; Core-periphery model; Group theory; Spatial period doubling
• Subjects: O - Economic Development, Innovation, Technological Change, and Growth > O1 - Economic Development > O18 - Urban, Rural, Regional, and Transportation Analysis ; Housing ; Infrastructure; F - International Economics > F1 - Trade > F12 - Models of Trade with Imperfect Competition and Scale Economies ; Fragmentation; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics > R12 - Size and Spatial Distributions of Regional Economic Activity

References

[1] Baldwin, R., Forslid, R, Martin, P., Ottaviano G., Robert-Nicoud,F., 2003. Economic Geography and Public Policy. Princeton University Press.

[2] Behrens, K., Thisse, J.-F., 2007. Regional economics: A new economic geography perspective. Regional Science and Urban Economics 37(4) 457–465.

[3] Brakman, S., Garretsen, H., van Marrewijk, C., 2001. The New Introduction to Geographical Economics. Cambridge University Press.

[4] Combes, P. P., Mayer, T., Thisse, J. F., 2008. Economic Geography: The Integration of Regions and Nations. Princeton University Press.

[5] Crisfield, M. A., 1977. Non-linear Finite Element Analysis of Solids and Structures. Wiley.

[6] Dixit, A., Stiglitz, J., 1977. Monopolistic competition and optimum product diversity, American Economic Review 67, 297-308.

[7] Facchinei, F., Pang, J.-S., 2003. Finite-Dimensional Variational Inequalities and Complementarity Problems, Vol.I & II. Springer-Verlag.

[8] Feigenbaum, M. J., 1978. Qualitative universality for a class of nonlinear transformations. Journal of Statistical Physics 19 25–52.

[9] Forslid, R., Ottaviano, G. I. P., 2003. An analytically solvable core–periphery model, Journal of Economic Geography 3 229–240.

[10] Fujita, M., Krugman, P., Venables, A. J., 1999. The Spatial Economy. MIT Press.

[11] Fujita, M., Thisse, J. F., 2002. Economics of Agglomeration. Cambridge University Press.

[12] Fujita, M., Thisse, J. F., 2009. New economic geography: an appraisal on the occasion of Paul Krugman’s 2008 nobel prize in economic sciences. Regional Science and Urban Economics 39(2), 109-250.

[13] Glaeser, E. L., 2008. Cities, Agglomeration and Spatial Equilibrium. Oxford University Press.

[14] Golubitsky, M., Stewart, I., Schaeffer, D. G., 1988. Singularities and Groups in Bifurcation Theory, Vol.II. Springer-Verlag.

[15] Henderson, J. V. Thisse, J. F. eds., 2004. Handbook of Regional and Urban Economics 4, Cities and Geography. Elsevier.

[16] Ikeda, K., Murota, K., 2002. Imperfect Bifurcation in Structures and Materials. Springer-Verlag.

[17] Ikeda, K., Murota, K., Fujii, H., 1991. Bifurcation hierarchy of symmetric structures. International Journal of Solids and Structures 27(12) 1551–1573.

[18] Krugman, P., 1991. Increasing returns and economic geography. Journal of Political Economy 99 483–499.

[19] Krugman, P., 1993. On the number and location of cities. European Economic Review 37 293–298.

[20] Krugman, P., 1996. The Self-Organizing Economy. Blackwell.

[21] Lorenz, H. W., 1997. Nonlinear Dynamical Economics and Chaotic Motion. Springer-Verlag.

[22] Murota, K., Ikeda, K., 1991. Computational use of group theory in bifurcation analysis of symmetric structures. SIAM Journal of Scientific and Statistical Computing 12(2) 273–297.

[23] Nagurney, A., 1993. Network Economics. Kluwer.

[24] Ottaviano, G. I. P., Puga, D., 1998. Agglomeration in the Global Economy: A Survey of the ‘New Economic Geography.’ The World Economy 21(6) 707–731.

[25] Pfl¨uger, M., 2004. A simple, analytically solvable, Chamberlinian agglomeration model. Regional Science and Urban Economics 34(5) 565–573.

[26] Picard, P. M. Tabuchi, T., 2009. Self-organized agglomerations and transport costs. Economic Theory DOI 10.1007/s00199-008-0410-4.

[27] Tabuchi, T., Thisse, J. F., 2009. Self-organizing urban hierarchy. Preprint.