Abstract
The purpose of this chapter is to give an approximation of short-run equilibrium of the N-region core-periphery model in an urban setting. The approximation is sufficiently accurate and expressed explicitly in terms of the distribution of workers that is contained as known function in the model. Making use of this approximation, we can analyze the behavior of each short-run equilibrium.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ago, T., Isono, I., Tabuchi, T.: Locational disadvantage of the hub. Ann. Reg. Sci. 40(4), 819–848 (2006)
Akamatsu, T., Takayama, Y., Ikeda, K.: Spatial discounting, Fourier, and racetrack economy: a recipe for the analysis of spatial agglomeration models. J. Econ. Dyn. Control 36(11), 1729–1759 (2012)
Anastassiou, G.A., Merve, K.: Discrete Approximation Theory, vol. 20. World Scientific (2016)
Bisci, G.M., Repovš, D.: Existence of solutions for p-Laplacian discrete equations. Appl. Math. Comput. 242, 454–461 (2014)
Castro, S.B.S.D., Correia-da-Silva, J., Mossay, P.: The core-periphery model with three regions and more. Pap. Reg. Sci. 91(2), 401–418 (2012)
Conte, R., Musette, M.: Discrete nonlinear equations. In: The Painlevé Handbook, pp. 163–186 (2008)
Fujita, M., Thisse, J.F.: Economics of Agglomeration, Cities, Industrial Location, and Regional Growth. Cambridge University Press, Cambridge (2002)
Fujita, M.: The evolution of spatial economics: from Thönen to the new economic geography. Jpn. Econ. Rev. 61(1), 1–32 (2010)
Fujita, M., Krugman, P., Venables, A.J.: The Spatial Economy. The MIT Press, Cambridge (1999)
Hennig, D., et al.: Spatial properties of integrable and nonintegrable discrete nonlinear Schrödinger equations. Phys. Rev. E 52(1), 255 (1995)
Hritonenko, N., Yatsenko, Y.: Mathematical Modeling in Economics. Ecology and the Environment. Kluwer Academic Publishers, Dordrecht, Boston, London (1999)
Ikeda, K., Akamatsu, T., Kono, T.: Spatial period-doubling agglomeration of a core-periphery model with a system of cities. J. Econ. Dyn. Control 36(5), 754–778 (2012)
Ikeda, K., Murota, K.: Bifurcation Theory for Hexagonal Agglomeration in Economic Geography. Springer, Japan (2014)
Kevrekidis, P.G.: The Discrete Nonlinear Schrödinger Equation: Mathematical Analysis, Numerical Computations and Physical Perspectives, vol. 232. Springer (2009)
Krugman, P.: The official homepage of the Nobel Prize in Economic Sciences. (2008). http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/
Krugman, P.: The Self-Organizing Economy. Blackwell Publishers (1996)
Krugman, P.: Increasing returns and economic geography. J. Polit. Econ. 99(3), 483–499 (1991)
Krugman, P.: Scale economies, product differentiation, and the pattern of trade. Am. Econ. Rev. 70(5), 950–959 (1980)
Mori, T., Nishikimi, K.: Economies of transport density and industrial agglomeration. Reg. Sci. Urban Econ. 32(2), 167–200 (2002)
Mossay, P.: The core-periphery model: a note on the existence and uniqueness of short-run equilibrium. J. Urban Econ. 59(3), 389–393 (2006)
Ottaviano, Gi.I.P., Puga, D.: Agglomeration in the global economy: a survey of the ‘new economic geography’. World Econ. 21(6), 707–731 (1998)
Pavlidis, N.G., Vrahatis, M.N., Mossay, P.: Existence and computation of short-run equilibria in economic geography. Appl. Math. Comput. 184(1), 93–103 (2007)
Tabata, M., Eshima, N., Sakai, Y.: Existence, uniqueness, and computation of short-run and long-run equilibria of the Dixit-Stiglitz-Krugman model in an urban setting. Appl. Math. Comput. Elsevier 234, 339–355 (2014)
Tabata, M., Eshima, N., Kiyonari, Y., Takagi, I.: The existence and uniqueness of short-run equilibrium of the Dixit-Stiglitz-Krugman model in an urban-rural setting. IMA J. Appl. Math. 80(2), 474–493 (2015). Oxford University Press
Tabata, M., Eshima, N.: Existence and uniqueness of solutions to the wage equation of Dixit-Stiglitz-Krugman model with no restriction on transport costs. Discrete Dyn. Nat. Soc. Article ID 9341502 (2017)
Acknowledgements
Minoru Tabata is supported in part by Grant-in-aid for Scientific Research of Japan Grant Number 15K05005. Nobuoki Eshima is supported in part by Grant-in-aid for Scientific Research of Japan Grant Number 26330045. The authors declare that they have no competing interests. Each author equally contributed to this chapter, read and approved the final manuscript. This manuscript has not been published or presented elsewhere in part or in entirety, and is not under consideration by another journal.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Tabata, M., Eshima, N. (2019). Approximation of Short-Run Equilibrium of the N-Region Core-Periphery Model in an Urban Setting. In: Smith, F.T., Dutta, H., Mordeson, J.N. (eds) Mathematics Applied to Engineering, Modelling, and Social Issues. Studies in Systems, Decision and Control, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-030-12232-4_17
Download citation
DOI: https://doi.org/10.1007/978-3-030-12232-4_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-12231-7
Online ISBN: 978-3-030-12232-4
eBook Packages: EngineeringEngineering (R0)