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Stability of Spatial Equilibrium

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Author Info
Takatoshi Tabuchi (Faculty of Economics, University of Tokyo)
Dao-Zhi Zeng (Faculty of Economics, Kagawa University)

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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.

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Publisher Info
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
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Handle: RePEc:tky:fseres:2000cf79

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This paper has been announced in the following NEP Reports: References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
  2. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. Ed Hopkins & Robert M. Seymour, 2002. "The Stability of Price Dispersion under Seller and Consumer Learning," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(4), pages 1157-1190, November. [Downloadable!] (restricted)
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  5. 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. [Downloadable!] (restricted)
  6. 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. [Downloadable!]
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  7. Gianmarco Ottaviano & Takatoshi Tabuchi & Jacques-FranÁois Thisse, 2002. "Agglomeration and Trade Revisited," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(2), pages 409-436, May. [Downloadable!] (restricted)
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  8. Henderson, J V, 1974. "The Sizes and Types of Cities," American Economic Review, American Economic Association, vol. 64(4), pages 640-56, September. [Downloadable!] (restricted)
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  9. Fujita, Masahisa & Thisse, Jacques-François, 1996. "Economics of Agglomeration," CEPR Discussion Papers 1344, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  10. 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. [Downloadable!] (restricted)
  11. 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. [Downloadable!] (restricted)
  12. Krugman, Paul, 1993. "On the number and location of cities," European Economic Review, Elsevier, vol. 37(2-3), pages 293-298, April. [Downloadable!] (restricted)
  13. Takahiro Miyao, 1978. "A Probabilistic Model of Location Choice with Neighborhood Effects," Working Papers 303, Queen's University, Department of Economics.
  14. Ed Hopkins, . "Learning, Matching and Aggregation," ELSE working papers 033, ESRC Centre on Economics Learning and Social Evolution. [Downloadable!]
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  15. 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. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  17. 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. [Downloadable!] (restricted)
  18. Masahisa Fujita & Paul Krugman & Anthony J. Venables, 2001. "The Spatial Economy: Cities, Regions, and International Trade," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262561476.
  19. Miyao, Takahiro, 1978. "A probabilistic model of location choice with neighborhood effects," Journal of Economic Theory, Elsevier, vol. 19(2), pages 347-358, December. [Downloadable!] (restricted)
  20. 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. [Downloadable!] (restricted)
  21. Anderson, James E, 1979. "A Theoretical Foundation for the Gravity Equation," American Economic Review, American Economic Association, vol. 69(1), pages 106-16, March. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Hideo Konishi, 2001. "Uniqueness of User Equilibrium in Transportation Networks with Heterogeneous Commuters," Boston College Working Papers in Economics 494, Boston College Department of Economics, revised 14 Nov 2002. [Downloadable!]
  2. Dao-Zhi Zeng & Laixun Zhao, 2007. "Globalization, Interregional and International Inequalities," Discussion Paper Series 209, Research Institute for Economics & Business Administration, Kobe University. [Downloadable!]
  3. Hiroshi Aiura & Yasuhiro Sato, 2009. "A model of urban demography," Discussion Papers in Economics and Business 09-18, Osaka University, Graduate School of Economics and Osaka School of International Public Policy (OSIPP).
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  4. Kristian Behrens & Frédéric Robert-Nicoud, 2008. "Survival of the Fittest in Cities: Agglomeration, Selection and Polarisation," SERC Discussion Papers 0012, Spatial Economics Research Centre, LSE. [Downloadable!]
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  5. 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. [Downloadable!] (restricted)
  6. Dao-Zhi Zeng, 2006. "Redispersion is different from dispersion: spatial economy of multiple industries," The Annals of Regional Science, Springer, vol. 40(2), pages 229-247, June. [Downloadable!] (restricted)
  7. TABUCHI, Takatoshi & THISSE, Jacques-Franois & ZENG, Dao-Zhi, 2001. "On the evolution of a multi-regional system," CORE Discussion Papers 2001003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
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