Urban Scale and Inequality: A Mean Field Game Approach to Zipf's Law, Gibrat's Law, and Endogenous City Growth

Heng-Fu Zou ()

No 757, CEMA Working Papers from China Economics and Management Academy, Central University of Finance and Economics

Abstract: This paper develops a dynamic mean field game model to explain the emergence of heavy-tailed city size distributions and persistent urban inequality. Each city optimizes intertemporal consumption and investment in infrastructure to maximize utility from both consumption and population scale. City size follows a stochastic process with investment-driven drift, while productivity evolves as a mean-reverting diffusion. We derive the equilibrium using the Lasry–Lions Master Equation and simulate the resulting stationary distribution. The model generates high Gini coefficients and Pareto-like upper tails, consistent with Zipf’s law and Gibrat’s law. These patterns arise endogenously through capital accumulation, productivity shocks, and scale feedbacks, offering a unified framework to understand urban size inequality.

Keywords: City size distribution; Zipf's law; Gibrat's law; Mean field games; Urban inequality; Capital accumulation (search for similar items in EconPapers)
Pages: 10 pages
Date: 2025-05-15
New Economics Papers: this item is included in nep-gth and nep-upt
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Persistent link: https://EconPapers.repec.org/RePEc:cuf:wpaper:757

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