The wealth substitution rate, which describes the substitution relationship between agents’ investment in wealth, is introduced into the collision kernel of the Boltzmann equation to study wealth distribution. Using the continuous trading limit, the Fokker–Planck equation is derived and the steady-state solution is obtained. The results show that the inequality of wealth distribution decreases as the wealth substitution rate increases under certain assumptions. The wealth distribution has a bimodal shape if the wealth substitution rate does not equal one.

中文翻译：

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具有线性碰撞核的财富分配模型研究

将描述代理人对财富投资的替代关系的财富替代率引入玻尔兹曼方程的碰撞核来研究财富分配。使用连续交易限制，推导出 Fokker-Planck 方程并获得稳态解。结果表明，在一定的假设下，财富分配的不平等随着财富替代率的增加而减少。如果财富替代率不等于 1，则财富分布呈双峰形。