Abstract
A simple and effective lattice–gas–automaton (LGA) economic model is proposed for the income distribution. It consists of four stages: random propagation, economic transaction, income tax, and charity. Two types of discrete models are introduced: two-dimensional four-neighbor model (D2N4) and D2N8. For the former, an agent either remains motionless or travels to one of its four neighboring empty sites randomly. For the latter, the agent may travel to one of its nearest four sites or the four diagonal sites. Afterwards, an economic transaction takes place randomly when two agents are located in the nearest (plus the diagonal) neighboring sites for the D2N4 (D2N8). During the exchange, the Matthew effect could be taken into account in the way that the rich own a higher probability of earning money than the poor. Moreover, two kinds of income tax models are incorporated. One is the detailed taxable income brackets and rates, and the other is a simplified tax model based on a fitting power function. Meanwhile, charity is considered with the assumption that a richer agent donates a part of his income to charity with a certain probability. Finally, the LGA economic model is validated by using two kinds of benchmarks. One is the income distributions of individual agents and two-earner families in a free market. The other is the shares of total income in the USA and UK, respectively. Besides, impacts of the Matthew effect, income tax and charity upon the redistribution of income are investigated. It is confirmed that the model has the potential to offer valuable references for formulating financial laws and regulations.
Highlights
Econophysics is a heterodox interdiscipline where economics and finance problems are solved with statistical physics methods, usually including uncertainty or stochastic processes and nonlinear dynamics [1,2,3,4]
The income distribution of agents in a closed system could be expressed by an exponential Boltzmann–Gibbs function, which is in analogy with the energy distribution in statistical physics [3,13,14]
We present an LGA economic model for the income distribution in an ideal free market or a realistic social market
Summary
Econophysics is a heterodox interdiscipline where economics and finance problems are solved with statistical physics methods, usually including uncertainty or stochastic processes and nonlinear dynamics [1,2,3,4]. In 2013, Cerdá et al proposed an econophysics model based on a lattice–gas–automaton (LGA) for income distribution under charity strategies (i.e., a richer agent voluntarily gives money to the one without money) [21]. The basic idea of LGA is that different microscopic behaviors can lead to similar macroscopic performance and artificial particles move on lattices with interactions which conserve physical quantities such as mass and momentum [31]. The microdynamics of such an artificial world should be as simple as possible for the sake of high computational efficiency [31,36].
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