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Zipf's Law: A Microfoundation

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  • Toda, Alexis Akira

Abstract

Existing explanations of Zipf's law (Pareto exponent approximately equal to 1) in size distributions require strong assumptions on growth rates or the minimum size. I show that Zipf's law naturally arises in general equilibrium when individual units solve a homogeneous problem (e.g., homothetic preferences, constant-returns-to-scale technology), the units enter/exit the economy at a small constant rate, and at least one production factor is in limited supply. My model explains why Zipf's law is empirically observed in the size distributions of cities and firms, which consist of people, but not in other quantities such as wealth, income, or consumption, which all have Pareto exponents well above 1.

Suggested Citation

  • Toda, Alexis Akira, 2016. "Zipf's Law: A Microfoundation," MPRA Paper 78985, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:78985
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    File URL: https://mpra.ub.uni-muenchen.de/78985/1/MPRA_paper_78985.pdf
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    References listed on IDEAS

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    JEL classification:

    • D30 - Microeconomics - - Distribution - - - General
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • D58 - Microeconomics - - General Equilibrium and Disequilibrium - - - Computable and Other Applied General Equilibrium Models
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • 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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