一种用于具有税收和再分配的随机乘法财富模型的福克 - 普朗克方法
A Fokker-Planck approach to a stochastic multiplicative wealth model with taxation and redistribution
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中文总结 AI 辅助
研究具有税收和再分配的随机乘法财富模型，采用福克 - 普朗克方法，扩展原始公式涵盖多种再分配协议，推导平稳财富分布表达式，经模拟验证，用基尼指数量化，揭示特定再分配方案可减轻财富差距。
中文摘要 AI 辅助
我们为P.M.C. de Oliveira提出的具有税收和再分配的随机乘法经济增长模型中的财富分配动态发展了一种福克 - 普朗克描述。扩展原始公式，我们的理论框架包括一般再分配协议，涵盖广泛的状态依赖转移机制。作为一个特殊情况，我们研究了一个旨在模拟有条件现金转移计划的两态协议。推导了平稳财富分布的解析表达式，揭示了乘法噪声、税收和再分配之间的相互作用如何塑造不平等的出现。理论结果通过基于代理的模拟得到证实。为了量化和比较不同协议的影响，我们使用基尼指数作为不平等的度量。我们的分析强调了特定的非均匀再分配方案如何能显著减轻财富差距。
英文摘要
We develop a Fokker-Planck description of the dynamics of wealth distribution in a stochastic multiplicative economic growth model with taxation and redistribution, as introduced by P.M.C. de Oliveira. Extending the original formulation, our theoretical framework includes general redistribution protocols, encompassing a broad class of state-dependent transfer mechanisms. As a particular case, we investigate a two-state protocol designed to emulate conditional cash transfer programs. Analytical expressions for the stationary wealth distributions are derived, revealing how the interplay between multiplicative noise, taxation, and redistribution shapes the emergence of inequality. The theoretical results are corroborated by agent-based simulations. To quantify and compare the impact of the different protocols, we employ the Gini index as a measure of inequality. Our analysis highlights how specific nonuniform redistribution schemes can significantly mitigate wealth disparities.
