Econophysics: Analytical Modelling of Wealth Distribution in a Closed Economy

Econophysics applies statistical physics to formulate mathematical models for complex economic systems, offering insights into wealth distribution dynamics. This study presents an analytical model describing wealth distribution in a closed economy by applying a binomial distribution framework that incorporates saving propensity and group stratification. The model demonstrates that as saving propensity increases, wealth distribution gradually shifts from a Boltzmann-Gibbs form to an asymmetric Gaussian-like form, indicating a reduction in the number of agents with near-zero wealth. Additionally, the Lorenz curve and Gini coefficient are derived to quantify income inequality, highlighting the influence of parameters such as saving propensity, group structure, and success probability on economic disparity. The analytical results align closely with those obtained through simulation approaches, confirming the robustness of the model. This approach elucidates how macroeconomic patterns and inequality measures emerge from micro-level transactional interactions within closed systems. The model provides a quantitative framework for understanding the underlying dynamics of wealth accumulation and distribution, offering potential applications in evaluating economic policies aimed at reducing inequality and promoting equitable wealth distribution in society.