改进的收入空间法及其在中等收入人口度量中的应用

提出了衡量社会分配公平的局部公平指数D(p)=((L'(p))/((L"(p))),给出了其确切的经济学解释.同时定义了分别对应穷人和富人的Gini指数G_1,G_2,在此基础上建立了改进的收入空间法,用于确定中等收入人口范围:(1-1/2D(1-G_1))m,(1+1/2D(1-G_2))m],其中m为中位收入.模型对2013全国研究生数学建模竞赛E题的收入分配数据进行定量研究,得出的结论与经济学的原理"两极分化时中等收入人口降低,中问隆起时中等收入人口升高"相符合,这体现了模型的准确性与可靠性.

An Improved Income Space Method and Its Application in the Measurement of the Middle Income Population

In this paper,we give the concept of local fairness index D(p) =(L'(p))/(L"(p)),which measures the fairness of the income distribution,and provide its economic explanation.Meanwhile,we define the Gini Indexes G_1,G_2 for the poor and the rich respectively.From these,we establish the improved income space method and get the range of the middle income population explicitly:(1-1/2D(1- G_1))m,(1 +1/2D(1- G_2))m].Here,m is the median of the income.Based on this model,we analyze the income distribution data provided in Problem E in the National Graduate Mathematical Contest in Modeling in 2013 and obtain some satisfactory results.Our results accord with a economic principle,that is,"The middle income population decreases when polarization is high and increases when the middle part of the income curve is higher than other parts." This reveals the accuracy and reliability of our model.