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Tiebout--Weibull equilibrium: Reconciliation of Gibrat's and Zipf's laws for cities population

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  • Kazmierczak, Anna
  • Shapoval, Alexander
  • Weber, Shlomo

Abstract

While the existing literature on city formation recognizes two empirical regularities: Zipf's law, which describes the rank distribution of cities, and Gibrat's law, which describes their growth in proportion to their actual size, the aim of this paper is to identify a mechanism which places these two very different laws into a single, unified framework. We consider a Tiebout model of jurisdiction formation and introduce a new equilibrium notion that divides the population into a large core, immune against group deviations, and a tiny fringe. We then endow our model with the Weibull probability density of individuals' locations and show that our equilibrium city distribution approximates Zipf's and Gibrat's laws. Moreover, our theoretical results are consistent with the U.S. Census data.

Suggested Citation

  • Kazmierczak, Anna & Shapoval, Alexander & Weber, Shlomo, 2024. "Tiebout--Weibull equilibrium: Reconciliation of Gibrat's and Zipf's laws for cities population," CEPR Discussion Papers 19038, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:19038
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    More about this item

    Keywords

    Zipf's law; Gibrat's law;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D30 - Microeconomics - - Distribution - - - General
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

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