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Wealth Concentration and Pareto Tails in Stochastic Mean Field Economies

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  • Heng-fu Zou

Abstract

This paper develops a continuous-time mean field game model of capital accumulation with heterogeneous agents facing idiosyncratic stochastic productivity. Agents optimize infinite-horizon consumption under linear production and quadratic utility. The model yields a coupled Hamilton-Jacobi-Bellman and Fokker-Planck system, whose stationary solution ex hibits a Pareto-tailed wealth distribution. We derive the Pareto exponent analytically and show it depends on productivity and volatility. Numerical simulations confirm that realistic parameter values generate Gini coeffcients exceeding 0.7, consistent with empirical inequality. We evaluate the effectiveness of wealth taxation, consumption subsidies, and productivity equalization, finding these policies have limited long-run impact. Inequal ity emerges as a structural property of decentralized optimization under uncertainty, offering a micro-founded explanation for persistent wealth Concentration in capitalist economies.

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  • Heng-fu Zou, 2025. "Wealth Concentration and Pareto Tails in Stochastic Mean Field Economies," CEMA Working Papers 758, China Economics and Management Academy, Central University of Finance and Economics.
    • Handle: RePEc:cuf:wpaper:758
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