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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. Copyright Blackwell Publishing, Inc. 2004

Suggested Citation

  • Takatoshi Tabuchi & Dao-Zhi Zeng, 2004. "Stability of Spatial Equilibrium," Journal of Regional Science, Wiley Blackwell, vol. 44(4), pages 641-660.
  • Handle: RePEc:bla:jregsc:v:44:y:2004:i:4:p:641-660
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    References listed on IDEAS

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    1. T Tabuchi, 1982. "Optimal Distribution of City Sizes in a Region," Environment and Planning A, , vol. 14(1), pages 21-32, January.
    2. Henderson, J V, 1974. "The Sizes and Types of Cities," American Economic Review, American Economic Association, vol. 64(4), pages 640-656, September.
    3. Bergstrand, Jeffrey H, 1985. "The Gravity Equation in International Trade: Some Microeconomic Foundations and Empirical Evidence," The Review of Economics and Statistics, MIT Press, vol. 67(3), pages 474-481, August.
    4. Hopkins, Ed, 1999. "Learning, Matching, and Aggregation," Games and Economic Behavior, Elsevier, vol. 26(1), pages 79-110, January.
    5. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-666, May.
    6. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1997. "Pure Strategy Nash Equilibrium in a Group Formation Game with Positive Externalities," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 161-182, October.
    7. T Tabuchi, 1986. "Existence and stability of city-size distribution in the gravity and logit models," Environment and Planning A, Pion Ltd, London, vol. 18(10), pages 1375-1389, October.
    8. Zeng, Dao-Zhi, 2002. "Equilibrium stability for a migration model," Regional Science and Urban Economics, Elsevier, vol. 32(1), pages 123-138, January.
    9. Ginsburgh, Victor & Papageorgiou, Yorgo & Thisse, Jacques-Francois, 1985. "On existence and stability of spatial equilibria and steady-states," Regional Science and Urban Economics, Elsevier, vol. 15(2), pages 149-158, June.
    10. Greenwood, Michael J, 1975. "Research on Internal Migration in the United States: A Survey," Journal of Economic Literature, American Economic Association, vol. 13(2), pages 397-433, June.
    11. Bergstrand, Jeffrey H, 1989. "The Generalized Gravity Equation, Monopolistic Competition, and the Factor-Proportions Theory in International Trade," The Review of Economics and Statistics, MIT Press, vol. 71(1), pages 143-153, February.
    12. Krugman, Paul, 1993. "On the number and location of cities," European Economic Review, Elsevier, vol. 37(2-3), pages 293-298, April.
    13. Fujita, Masahisa & Krugman, Paul & Mori, Tomoya, 1999. "On the evolution of hierarchical urban systems1," European Economic Review, Elsevier, vol. 43(2), pages 209-251, February.
    14. Kanemoto, Yoshitsugu, 1980. "Theories of urban externalities," MPRA Paper 24614, University Library of Munich, Germany.
    15. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1997. "Equilibria in a Model with Partial Rivalry," Journal of Economic Theory, Elsevier, vol. 72(1), pages 225-237, January.
    16. Anderson, James E, 1979. "A Theoretical Foundation for the Gravity Equation," American Economic Review, American Economic Association, vol. 69(1), pages 106-116, March.
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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. Hiroshi Aiura & Yasuhiro Sato, 2014. "A model of urban demography," Canadian Journal of Economics, Canadian Economics Association, vol. 47(3), pages 981-1009, August.
    3. Berliant, Marcus & Tabuchi, Takatoshi, 2011. "Local Politics and Economic Geography," MPRA Paper 29771, University Library of Munich, Germany.
    4. 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.
    5. Zeng, Dao-Zhi & Zhao, Laixun, 2010. "Globalization, interregional and international inequalities," Journal of Urban Economics, Elsevier, vol. 67(3), pages 352-361, May.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Borck, Rainald & Tabuchi, Takatoshi, 2015. "Pollution and city size: can cities be too small?," Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113124, Verein für Socialpolitik / German Economic Association.
    11. 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.
    12. repec:bla:jregsc:v:58:y:2018:i:2:p:350-362 is not listed on IDEAS
    13. 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.
    14. 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.
    15. 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.
    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. Picard, Pierre M. & Zeng, Dao-Zhi, 2005. "Agricultural sector and industrial agglomeration," Journal of Development Economics, Elsevier, vol. 77(1), pages 75-106, June.
    18. Tabuchi, Takatoshi & Thisse, Jacques-François & 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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