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Stability of Spatial Equilibrium

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  • Takatoshi Tabuchi
  • Dao‐Zhi Zeng

Abstract

. Asymptotic stability of equilibrium is often difficult to know when the number of variables exceeds four, since all eigenvalues of the Jacobian matrix are not analytically solvable. However, we obtain stability conditions for a general class of migration dynamics without computing eigenvalues. We show that a spatial equilibrium is stable in the presence of strong congestion diseconomies, but unstable in the presence of strong agglomeration economies. We also show existence of a stable equilibrium in the case of negligible interregional externalities, which is applicable to club goods, local public goods, and new economic geography.

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  • Takatoshi Tabuchi & Dao‐Zhi Zeng, 2004. "Stability of Spatial Equilibrium," Journal of Regional Science, Wiley Blackwell, vol. 44(4), pages 641-660, November.
    • Handle: RePEc:bla:jregsc:v:44:y:2004:i:4:p:641-660
    DOI: 10.1111/j.0022-4146.2004.00352.x
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    Cited by:

    1. Hideo Konishi, 2004. "Uniqueness of User Equilibrium in Transportation Networks with Heterogeneous Commuters," Transportation Science, INFORMS, vol. 38(3), pages 315-330, August.
    2. Takanori Ago & Tadashi Morita & Takatoshi Tabuchi & Kazuhiro Yamamoto, 2018. "Elastic labor supply and agglomeration," Journal of Regional Science, Wiley Blackwell, vol. 58(2), pages 350-362, March.
    3. Hiroshi Aiura & Yasuhiro Sato, 2014. "A model of urban demography," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 47(3), pages 981-1009, August.
    4. Berliant, Marcus & Tabuchi, Takatoshi, 2011. "Local Politics and Economic Geography," MPRA Paper 29771, University Library of Munich, Germany.
    5. Rainald Borck & Takatoshi Tabuchi, 2019. "Pollution and city size: can cities be too small?," Journal of Economic Geography, Oxford University Press, vol. 19(5), pages 995-1020.
    6. Zeng, Dao-Zhi & Zhao, Laixun, 2009. "Pollution havens and industrial agglomeration," Journal of Environmental Economics and Management, Elsevier, vol. 58(2), pages 141-153, September.
    7. Zeng, Dao-Zhi, 2008. "New economic geography with heterogeneous preferences: An explanation of segregation," Journal of Urban Economics, Elsevier, vol. 63(1), pages 306-324, January.
    8. Pflüger, Michael & Tabuchi, Takatoshi, 2010. "The size of regions with land use for production," Regional Science and Urban Economics, Elsevier, vol. 40(6), pages 481-489, November.
    9. Takatoshi Tabuchi & Jacques-Francois Thisse & Dao-Zhi Zeng, 2000. "On the Evolution of a Multi-regional System," CIRJE F-Series CIRJE-F-93, CIRJE, Faculty of Economics, University of Tokyo.
    10. Xinmeng Li & Dao-Zhi Zeng, 2022. "Frictional unemployment, bargaining, and agglomeration," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 68(1), pages 151-179, February.
    11. Zeng, Dao-Zhi & Zhao, Laixun, 2010. "Globalization, interregional and international inequalities," Journal of Urban Economics, Elsevier, vol. 67(3), pages 352-361, May.
    12. Kanemoto, Yoshitsugu, 2013. "Second-best cost–benefit analysis in monopolistic competition models of urban agglomeration," Journal of Urban Economics, Elsevier, vol. 76(C), pages 83-92.
    13. Picard, Pierre M. & Zeng, Dao-Zhi, 2005. "Agricultural sector and industrial agglomeration," Journal of Development Economics, Elsevier, vol. 77(1), pages 75-106, June.
    14. Behrens, Kristian & Robert-Nicoud, Frédéric, 2008. "Survival of the fittest in cities: agglomeration, selection, and polarisation," LSE Research Online Documents on Economics 28506, London School of Economics and Political Science, LSE Library.
    15. Pierre M. Picard & Dao‐Zhi Zeng, 2010. "A Harmonization Of First And Second Natures," Journal of Regional Science, Wiley Blackwell, vol. 50(5), pages 973-994, December.
    16. Marcus Berliant & Takatoshi Tabuchi, 2014. "Local Politics And Economic Geography: Information Aggregation And Polarization," Journal of Regional Science, Wiley Blackwell, vol. 54(5), pages 806-827, November.
    17. Thisse, Jacques-François & Tabuchi, Takatoshi & Zeng, Dao-Zhi, 2002. "On the Number and Size of Cities," CEPR Discussion Papers 3386, C.E.P.R. Discussion Papers.
    18. Dao-Zhi Zeng, 2006. "Redispersion is different from dispersion: spatial economy of multiple industries," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 40(2), pages 229-247, June.
    19. Juan Carlos G. Lopez, 2019. "Cultural workers and the character of cities," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 62(1), pages 211-246, February.

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