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Existence and Stability of City-Size Distribution in the Gravity and Logit Models

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  • T Tabuchi

    (Institute of Socio-Economic Planning, University of Tsukuba, Sakura, Ibaraki 305, Japan)

Abstract

An attempt is made to analyze reasons for and consequences of migration under zero population growth by use of a system of simultaneous differential equations. Intercity migration is assumed to take place based upon differences in utilities, where the utility function is expressed as a function of city size. It is revealed that a deterministic specification of the utility leads to an unstable distribution of city sizes, whereas a stochastic specification does not. Existence and stability of equilibria are examined for two representative stochastic migration models: the origin-constrained gravity model and the logit model. It is then argued that population concentration can be explained by an increase in urbanization economies, and population decentralization can be due to a decrease in intercity transportation and communication costs.

Suggested Citation

  • T Tabuchi, 1986. "Existence and Stability of City-Size Distribution in the Gravity and Logit Models," Environment and Planning A, , vol. 18(10), pages 1375-1389, October.
    • Handle: RePEc:sae:envira:v:18:y:1986:i:10:p:1375-1389
    DOI: 10.1068/a181375
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    References listed on IDEAS

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    1. Segal, David, 1976. "Are There Returns to Scale in City Size?," The Review of Economics and Statistics, MIT Press, vol. 58(3), pages 339-350, August.
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    Cited by:

    1. Ottaviano, Gianmarco & Thisse, Jacques-Francois, 2004. "Agglomeration and economic geography," Handbook of Regional and Urban Economics, in: J. V. Henderson & J. F. Thisse (ed.), Handbook of Regional and Urban Economics, edition 1, volume 4, chapter 58, pages 2563-2608, Elsevier.
    2. Tabuchi, Takatoshi & Thisse, Jacques-Francois, 2002. "Taste heterogeneity, labor mobility and economic geography," Journal of Development Economics, Elsevier, vol. 69(1), pages 155-177, October.
    3. Takatoshi Tabuchi & Jacques-Francois Thisse, 2001. "Labor Mobility and Economic Geography," CIRJE F-Series CIRJE-F-99, CIRJE, Faculty of Economics, University of Tokyo.
    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. Zeng, Dao-Zhi, 2002. "Equilibrium stability for a migration model," Regional Science and Urban Economics, Elsevier, vol. 32(1), pages 123-138, January.
    6. Nakajima, Tetsuya, 1995. "Equilibrium with an underpopulated region and an overpopulated region," Regional Science and Urban Economics, Elsevier, vol. 25(1), pages 109-123, February.
    7. Takatoshi Tabuchi & Dao‐Zhi Zeng, 2004. "Stability of Spatial Equilibrium," Journal of Regional Science, Wiley Blackwell, vol. 44(4), pages 641-660, November.
    8. 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.
    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. Berliant, Marcus & Kung, Fan-chin, 2009. "Bifurcations in regional migration dynamics," Regional Science and Urban Economics, Elsevier, vol. 39(6), pages 714-720, November.
    11. Gabaix, Xavier & Ioannides, Yannis M., 2004. "The evolution of city size distributions," Handbook of Regional and Urban Economics, in: J. V. Henderson & J. F. Thisse (ed.), Handbook of Regional and Urban Economics, edition 1, volume 4, chapter 53, pages 2341-2378, Elsevier.
    12. Lööf, Hans & Nabavi, Pardis, 2013. "Learning and Productivity of Swedish Exporting Firms: The importance of Innovation Efforts and the Geography of Innovation," Working Paper Series in Economics and Institutions of Innovation 296, Royal Institute of Technology, CESIS - Centre of Excellence for Science and Innovation Studies.

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