本文在基于财富分布是随机性的一般性假设条件下，主要处理了三个问题：一、在理论上说明为什么人均财富增加没有 导致Gini系数的减少，推导出指数分布理论上的Gini系数相对于人均财富是保持不变的；二、探讨在社会保障固定的条件下， Gini系数是否随着人均财富的增加而减少？三、探讨社会保障随人均财富增加而调整时，Gini系数的变化趋势。 我们得到：如果社会保障不随人均财富的变化而变化，当人均财富增加时， 该分布的Gini系数变大，而且超过了相对合理水平的Gini系数值。然而如果 社会保障随人均财富的变化而调整，当人均财富增加时， Gini系数却 增加的很缓慢，保证了当人均财富值达到比较高的水平时，Gini系数仍处于相对合理水平。 这就说明在社会保障随人均财富变化而变化的制度下，贫富差距会得到有效的解决。

Based on the general assumption that wealth is randomly distributed ,three problems are solved as follows: first, we show the reason why Gini-coefficient does not decrease with income per capital in theory , and educe that the Gini-coefficient of the Exponential distribution function is unchanged when income per capital increases . Second ,since zero or negative wealth is not permitted by geometric mean which is the role of social security ,we take both income per capital (arithmetic average )and geometric mean into account .In this case we discuss whether the Gini-coefficient of wealth distribution decreases when income per capital increases. third ,we consider the case that the social security capital is changed when income per capital increases .In this case we discuss whether the Gini-coefficient of wealth distribution decreases when income per capital increases. We get the conclusion as follows :if the social security capital is unchanged when income per capital increases ,Gini-coefficient increases fast .But if the social security capital is increases with the increasing of income per capital ,Gini-coefficient increases slow then gap between the rich and the poor could reach a reasonable level.