中国物理B ›› 2024, Vol. 33 ›› Issue (7): 70501-070501.doi: 10.1088/1674-1056/ad3dc6

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A wealth distribution model with a non-Maxwellian collision kernel

Jun Meng(孟俊)1, Xia Zhou(周霞)2,†, and Shaoyong Lai(赖绍永)3   

  1. 1 College of Mathematics and Statistics, Kashi University, Kashi 844006, China;
    2 College of Mathematics and Physics, Mianyang Teacher's College, Mianyang 621000, China;
    3 School of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China
  • 收稿日期:2023-11-21 修回日期:2024-03-19 接受日期:2024-04-12 出版日期:2024-06-18 发布日期:2024-06-28
  • 通讯作者: Xia Zhou E-mail:xiazhou2017@163.com
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 11471263), the Natural Science Foundation of Xinjiang Uygur Autonomous Region, China (Grant No. 2021D01B09), the Initial Research Foundation of Kashi University (Grant No. 022024076), and “Mathematics and Finance Research Centre Funding Project”, Dazhou Social Science Federation (Grant No. SCMF202305).

A wealth distribution model with a non-Maxwellian collision kernel

Jun Meng(孟俊)1, Xia Zhou(周霞)2,†, and Shaoyong Lai(赖绍永)3   

  1. 1 College of Mathematics and Statistics, Kashi University, Kashi 844006, China;
    2 College of Mathematics and Physics, Mianyang Teacher's College, Mianyang 621000, China;
    3 School of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China
  • Received:2023-11-21 Revised:2024-03-19 Accepted:2024-04-12 Online:2024-06-18 Published:2024-06-28
  • Contact: Xia Zhou E-mail:xiazhou2017@163.com
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 11471263), the Natural Science Foundation of Xinjiang Uygur Autonomous Region, China (Grant No. 2021D01B09), the Initial Research Foundation of Kashi University (Grant No. 022024076), and “Mathematics and Finance Research Centre Funding Project”, Dazhou Social Science Federation (Grant No. SCMF202305).

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摘要： A non-Maxwellian collision kernel is employed to study the evolution of wealth distribution in a multi-agent society. The collision kernel divides agents into two different groups under certain conditions. Applying the kinetic theory of rarefied gases, we construct a two-group kinetic model for the evolution of wealth distribution. Under the continuous trading limit, the Fokker-Planck equation is derived and its steady-state solution is obtained. For the non-Maxwellian collision kernel, we find a suitable redistribution operator to match the taxation. Our results illustrate that taxation and redistribution have the property to change the Pareto index.

关键词: kinetic theory, non-Maxwellian collision kernel, wealth distribution, Pareto index

Abstract: A non-Maxwellian collision kernel is employed to study the evolution of wealth distribution in a multi-agent society. The collision kernel divides agents into two different groups under certain conditions. Applying the kinetic theory of rarefied gases, we construct a two-group kinetic model for the evolution of wealth distribution. Under the continuous trading limit, the Fokker-Planck equation is derived and its steady-state solution is obtained. For the non-Maxwellian collision kernel, we find a suitable redistribution operator to match the taxation. Our results illustrate that taxation and redistribution have the property to change the Pareto index.

Key words: kinetic theory, non-Maxwellian collision kernel, wealth distribution, Pareto index

中图分类号:  (Kinetic theory)

  • 05.20.Dd
89.65.Gh (Economics; econophysics, financial markets, business and management) 47.45.Ab (Kinetic theory of gases) 05.10.Gg (Stochastic analysis methods)