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Approximation of Short-Run Equilibrium of the N-Region Core-Periphery Model in an Urban Setting

  • Minoru TabataEmail author
  • Nobuoki Eshima
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 200)

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.

Keywords

Discrete nonlinear equation Krugman model Spatial economics 

Mathematical Subject Classification

39B72 91B72 

Notes

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.

References

  1. 1.
    Ago, T., Isono, I., Tabuchi, T.: Locational disadvantage of the hub. Ann. Reg. Sci. 40(4), 819–848 (2006)CrossRefGoogle Scholar
  2. 2.
    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)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Anastassiou, G.A., Merve, K.: Discrete Approximation Theory, vol. 20. World Scientific (2016)Google Scholar
  4. 4.
    Bisci, G.M., Repovš, D.: Existence of solutions for p-Laplacian discrete equations. Appl. Math. Comput. 242, 454–461 (2014)MathSciNetzbMATHGoogle Scholar
  5. 5.
    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)Google Scholar
  6. 6.
    Conte, R., Musette, M.: Discrete nonlinear equations. In: The Painlevé Handbook, pp. 163–186 (2008)Google Scholar
  7. 7.
    Fujita, M., Thisse, J.F.: Economics of Agglomeration, Cities, Industrial Location, and Regional Growth. Cambridge University Press, Cambridge (2002)CrossRefGoogle Scholar
  8. 8.
    Fujita, M.: The evolution of spatial economics: from Thönen to the new economic geography. Jpn. Econ. Rev. 61(1), 1–32 (2010)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Fujita, M., Krugman, P., Venables, A.J.: The Spatial Economy. The MIT Press, Cambridge (1999)CrossRefGoogle Scholar
  10. 10.
    Hennig, D., et al.: Spatial properties of integrable and nonintegrable discrete nonlinear Schrödinger equations. Phys. Rev. E 52(1), 255 (1995)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Hritonenko, N., Yatsenko, Y.: Mathematical Modeling in Economics. Ecology and the Environment. Kluwer Academic Publishers, Dordrecht, Boston, London (1999)zbMATHGoogle Scholar
  12. 12.
    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)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Ikeda, K., Murota, K.: Bifurcation Theory for Hexagonal Agglomeration in Economic Geography. Springer, Japan (2014)CrossRefGoogle Scholar
  14. 14.
    Kevrekidis, P.G.: The Discrete Nonlinear Schrödinger Equation: Mathematical Analysis, Numerical Computations and Physical Perspectives, vol. 232. Springer (2009)Google Scholar
  15. 15.
    Krugman, P.: The official homepage of the Nobel Prize in Economic Sciences. (2008). http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/
  16. 16.
    Krugman, P.: The Self-Organizing Economy. Blackwell Publishers (1996)Google Scholar
  17. 17.
    Krugman, P.: Increasing returns and economic geography. J. Polit. Econ. 99(3), 483–499 (1991)CrossRefGoogle Scholar
  18. 18.
    Krugman, P.: Scale economies, product differentiation, and the pattern of trade. Am. Econ. Rev. 70(5), 950–959 (1980)Google Scholar
  19. 19.
    Mori, T., Nishikimi, K.: Economies of transport density and industrial agglomeration. Reg. Sci. Urban Econ. 32(2), 167–200 (2002)CrossRefGoogle Scholar
  20. 20.
    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)CrossRefGoogle Scholar
  21. 21.
    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)Google Scholar
  22. 22.
    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)MathSciNetzbMATHGoogle Scholar
  23. 23.
    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)MathSciNetCrossRefGoogle Scholar
  24. 24.
    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 PressGoogle Scholar
  25. 25.
    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)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesOsaka Prefecture UniversityOsakaJapan
  2. 2.Center for Educational Outreach and Admissions, Kyoto UniversityKyotoJapan

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