A New Model for the Income Distribution
Abstract
In this study, we propose a kinetic trap--diffusion model to describe the emergence of Pareto distributions in money-exchange systems. Using kinetic Monte Carlo simulations, we show that the Pareto exponent depends explicitly on temperature and takes values in the range 0.5 ≤ ν(T) ≤ 1.5. In the present framework, the temperature T acts as a control parameter that regulates the exchange dynamics through thermally activated diffusion. Unlike conventional kinetic exchange models, where the Pareto exponent is fixed by microscopic rules, the proposed model generates a range of Pareto exponents as a function of T. The temperature-dependent Pareto exponent constitutes the central novelty of the proposed kinetic trap--diffusion framework. This feature provides a natural explanation for the empirically observed variations in Pareto exponents across different countries and economic conditions. In addition, the fraction of zero-wealth agents and the Gini index exhibit a non-monotonic dependence on temperature, revealing distinct dynamical regimes arising from the competition between trapping and money mobility. The persistence of the Pareto-like stationary distribution under strongly nonuniform initial conditions further supports the robustness of the proposed mechanism. These results show that different Pareto-tail and inequality regimes can emerge from the same trap--diffusion dynamics through changes in a single control parameter
Versions
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BibTeX
@misc{aydiner2026model,
title = {{A New Model for the Income Distribution}},
author = {Ekrem Aydiner},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08143},
eprint = {2610.08143},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08143},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A New Model for the Income Distribution
AU - Ekrem Aydiner
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08143
UR - https://arxiv.org/abs/2610.08143
AB - In this study, we propose a kinetic trap--diffusion model to describe the emergence of Pareto distributions in money-exchange systems. Using kinetic Monte Carlo simulations, we show that the Pareto exponent depends explicitly on temperature and takes values in the range 0.5 ≤ ν(T) ≤ 1.5. In the present framework, the temperature T acts as a control parameter that regulates the exchange dynamics through thermally activated diffusion. Unlike conventional kinetic exchange models, where the Pareto exponent is fixed by microscopic rules, the proposed model generates a range of Pareto exponents as a function of T. The temperature-dependent Pareto exponent constitutes the central novelty of the proposed kinetic trap--diffusion framework. This feature provides a natural explanation for the empirically observed variations in Pareto exponents across different countries and economic conditions. In addition, the fraction of zero-wealth agents and the Gini index exhibit a non-monotonic dependence on temperature, revealing distinct dynamical regimes arising from the competition between trapping and money mobility. The persistence of the Pareto-like stationary distribution under strongly nonuniform initial conditions further supports the robustness of the proposed mechanism. These results show that different Pareto-tail and inequality regimes can emerge from the same trap--diffusion dynamics through changes in a single control parameter
ER -