社会保障制度对财富分配的影响以及在避免贫富差距进一步加大的作用

伴随着经济的增长，贪富差距逐渐加大和财富朝少数人集中是当今社会中出现的一个现象。在本文中，我们基于财富分布是随机性的这个一般性假设，探讨了在经济增长过程中财富分布的最可几状态。通过对财富在随机状态下的分布函数的建立，证明了如果只考虑人均收入时，财富会以负指数函数的方式作为财富分布的最可几态。并且，随着人均财富的增加，贪富差距不仅不能减小，反而还有扩大的趋势，财富会朝着少数人更集中。如果不仅考虑人均收入（算术平均），还同时考虑几何平均的话。随着经济增长的同时，由于几何平均是不能容许零或负的财富值存在，这正是社会保障系统所起到一个作用。在这种情况下，财富的分布会呈Gamma分布。在Gamma分布中，财富将集中在大多数人中，财富多或财富少的人数在社会总人数中所占的密度较小。

Impact of Social Security on the Distribution of Wealth

It is a common phenomenon that gap between the rich and the poor is getting wider and the rich accumulate wealth at increasing rate in an economy. Based on the general assumption that wealth is randomly distributed, this study establishes a distribution function and proves that wealth will take the distribution of exponential function as its most probable state if income per capita is taken into account only. With the increase of wealth per capita, the gap between the rich and the poor will not shrink, but is getting wider instead. As a result, wealth will be centralized by a few people. Distribution of wealth will be a Gamma distribution if both income per capita (arithmetic average) and geometric average are taken into account since zero or negative wealth is not permitted by geometric average (which is the role of social security). In this case wealth will be concentrated by majority of people.