论文标题
税收动态对随机重置下线性增长过程的影响:一种可能的经济模型
Effect of tax dynamics on linearly growing processes under stochastic resetting: a possible economic model
论文作者
论文摘要
我们研究了$ n $代理的系统,其财富在随机重置和通过类似税收的动态进行互动的效果下进行线性增长 - 所有代理人都捐赠了部分财富,这反过来又是同样重新分配的。这模仿了人们的社会经济情景,人们拥有固定收入,遭受个人经济挫折并向国家缴税的情况。该系统始终达到固定状态,在没有税收动态的情况下,该状态显示出微不足道的指数财富分布。税收动态的引入导致固定财富分布中的几个有趣的特征。特别是,我们在分析上发现,同质系统(所有代理人都是一样)的税收增加导致从一个社会过渡,在这个社会中,代理人最有可能贫穷到富代理人更普遍的社会。我们还研究了不均匀的系统,其中从分布中选择了代理的增长率,并且税收与个人增长率成正比。我们发现一种最佳税收,它产生了完整的经济平等(平均财富与个人增长率无关),在此之后存在反向差异,在这种情况下,低增长率较低的代理人更有可能富裕。我们考虑在现实世界中观察到的三个收入分配,并表明它们具有相同的定性特征。我们的分析结果在$ n \至\ infty $限制中,并得到数值模拟的支持。
We study a system of $N$ agents, whose wealth grows linearly, under the effect of stochastic resetting and interacting via a tax-like dynamics -- all agents donate a part of their wealth, which is, in turn, redistributed equally among all others. This mimics a socio-economic scenario where people have fixed incomes, suffer individual economic setbacks, and pay taxes to the state. The system always reaches a stationary state, which shows a trivial exponential wealth distribution in the absence of tax dynamics. The introduction of the tax dynamics leads to several interesting features in the stationary wealth distribution. In particular, we analytically find that an increase in taxation for a homogeneous system (where all agents are alike) results in a transition from a society where agents are most likely poor to another where rich agents are more common. We also study inhomogeneous systems, where the growth rates of the agents are chosen from a distribution, and the taxation is proportional to the individual growth rates. We find an optimal taxation, which produces a complete economic equality (average wealth is independent of the individual growth rates), beyond which there is a reverse disparity, where agents with low growth rates are more likely to be rich. We consider three income distributions observed in the real world and show that they exhibit the same qualitative features. Our analytical results are in the $N\to\infty$ limit and backed by numerical simulations.