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Stability of Spatial Equilibrium

  • Takatoshi Tabuchi

    (Faculty of Economics, University of Tokyo)

  • Dao-Zhi Zeng

    (Faculty of Economics, Kagawa University)

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.

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Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-79.

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Length: 29 pages
Date of creation: Jul 2000
Date of revision:
Handle: RePEc:tky:fseres:2000cf79
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  1. Ed Hopkins, 1995. "Learning, Matching and Aggregation," Game Theory and Information 9512001, EconWPA.
  2. Anderson, James E, 1979. "A Theoretical Foundation for the Gravity Equation," American Economic Review, American Economic Association, vol. 69(1), pages 106-16, March.
  3. 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.
  4. 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 474-81, August.
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  7. T Tabuchi, 1982. "Optimal distribution of city sizes in a region," Environment and Planning A, Pion Ltd, London, vol. 14(1), pages 21-32, January.
  8. Krugman, Paul, 1993. "On the number and location of cities," European Economic Review, Elsevier, vol. 37(2-3), pages 293-298, April.
  9. 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.
  10. 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.
  11. 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.
  12. Kanemoto, Yoshitsugu, 1980. "Theories of urban externalities," MPRA Paper 24614, University Library of Munich, Germany.
  13. 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 143-53, February.
  14. 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.
  15. Zeng, Dao-Zhi, 2002. "Equilibrium stability for a migration model," Regional Science and Urban Economics, Elsevier, vol. 32(1), pages 123-138, January.
  16. 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.
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