Zipf’s Law: A Microfoundation

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 appear and disappear at a small constant rate (e.g., rare disasters), and at least one production factor in the economy 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.