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Stability of Spatial Equilibrium

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  • Takatoshi Tabuchi

    (Faculty of Economics, University of Tokyo)

  • Dao-Zhi Zeng

    (Faculty of Economics, Kagawa University)

Abstract

This paper focuses on externalities between economic agents. We consider spatial dis- tribution of economic activities in a multiregional dynamical system, where regions may be interpreted as clubs, social subgroups, species, or strategies. Our dynamics includes gravity models and replicator dynamics as special cases. Assuming that other variables, such as prices are solved as a function of the population distribution, we analyze both interior and corner equilibria of spatial distribution in a general class of dynamics, including the replicator dynamics and the gravity model. We derive the exact conditions for stable equilibrium and give some interpretations of the stability conditions. We show that interior equilibria are stable in the presence of strong agglomeration economies, but unstable in the presence of strong congestion diseconomies.

Suggested Citation

  • Takatoshi Tabuchi & Dao-Zhi Zeng, 2000. "Stability of Spatial Equilibrium," CIRJE F-Series CIRJE-F-79, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2000cf79
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    Cited by:

    1. Zeng, Dao-Zhi & Zhao, Laixun, 2010. "Globalization, interregional and international inequalities," Journal of Urban Economics, Elsevier, vol. 67(3), pages 352-361, May.
    2. 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.
    3. 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.
    4. Picard, Pierre M. & Zeng, Dao-Zhi, 2005. "Agricultural sector and industrial agglomeration," Journal of Development Economics, Elsevier, vol. 77(1), pages 75-106, June.
    5. 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.
    6. 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.
    7. 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.
    8. Kristian Behrens & Frédéric Robert-Nicoud, 2008. "Survival of the Fittest in Cities: Agglomeration, Selection and Polarisation," SERC Discussion Papers 0012, Centre for Economic Performance, LSE.
    9. 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.
    10. Berliant, Marcus & Tabuchi, Takatoshi, 2011. "Local Politics and Economic Geography," MPRA Paper 29771, University Library of Munich, Germany.
    11. 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.
    12. 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.
    13. Hideo Konishi, 2004. "Uniqueness of User Equilibrium in Transportation Networks with Heterogeneous Commuters," Transportation Science, INFORMS, vol. 38(3), pages 315-330, August.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.

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