Zipf's Law: A Microfoundation

47 Pages Posted: 13 Jul 2016 Last revised: 16 May 2017

See all articles by Alexis Akira Toda

Alexis Akira Toda

University of California, San Diego (UCSD) - Department of Economics

Date Written: March 29, 2017


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.

Keywords: Gibrat's law, homogeneous problem, power law

JEL Classification: D30, D52, D58, L11, R12

Suggested Citation

Toda, Alexis Akira, Zipf's Law: A Microfoundation (March 29, 2017). Available at SSRN: or

Alexis Akira Toda (Contact Author)

University of California, San Diego (UCSD) - Department of Economics ( email )

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Mail Code 0508
La Jolla, CA 92093-0508
United States

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