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The mutual influence of knowledge and individual wealth growth

  • Regular Article - Statistical and Nonlinear Physics
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Abstract

Employing the kinetic theory, we investigate the mutual role of knowledge accumulation and individual wealth growth. For the accumulation of individual knowledge, we introduce a learning function with the spirit of prospect theory to describe the microscopic variation of agents’ knowledge and develop a kinetic model of knowledge evolution. Considering the wealth depending on knowledge and their mutual dependence, we construct a joint evolutionary model of knowledge and individual wealth. Our numerical experiments demonstrate that if knowledge reduces the risk of individual wealth growth or increases the wealth of low-wealth groups, wealth inequality decreases. In the case that the wealthy have more opportunities to choose good educational environment to learn knowledge, both knowledge and wealth inequality increase. When considering the government or state educational input, the inequality of knowledge and wealth decreases.

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Data availability statement

Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

Notes

  1. The data in Table 1 are from [17], where the second column shows the number of citizens in per type of school degree, and the fourth column shows the (inverse) cumulated number of people for school degrees. The first basic level of school knowledge includes every citizen who holds the middle school degree. The second and third levels include those who get a high school degree and an undergraduate degree, respectively. The fourth level includes Italians with a “short” (less than 1 year of study) post graduate degree. The last two levels are for citizens who hold a “specialization” or PhD degree.

  2. The knowledge interaction rule (2) considers the selection and learning behavior of agents. Based on (2), we introduce the influence of the agent’s psychological factors on knowledge accumulation and obtain the interaction rule (1) by choosing a suitable learning function \(\psi ^{\epsilon }_{\vartheta }(\cdot )\) to model the agent’s selection and learning behaviors as well as psychological factors. Actually, the interaction rule (1) is derived from (2).

  3. The graph of the function \(\sigma (x)\) is analogous to that of \(\delta (x),\) since they have similar expression form.

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Acknowledgements

This research is supported by the National Natural Science Foundation of China (No. 11471263). The authors are very grateful to the reviewers for their helpful and valuable comments, which have led to a meaningful improvement of the paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Yili Normal University, Yining, 835000, China

    Xia Zhou & Shaoyong Lai

  2. School of Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130, China

    Xia Zhou & Shaoyong Lai

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  1. Xia Zhou
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  2. Shaoyong Lai
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Both authors have contributed equally to the model construction and theoretical results in this paper. The numerical analysis is presented by XZ.

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Correspondence to Xia Zhou.

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Zhou, X., Lai, S. The mutual influence of knowledge and individual wealth growth. Eur. Phys. J. B 96, 73 (2023). https://doi.org/10.1140/epjb/s10051-023-00543-w

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