不公平度量指标的可分解性研究(英文)

A Note on Decomposable Measures of Inequality

研究了不公平度量指标的可分解性.证明了在对称性、齐次性和塞尔(Theil)可分解性假设下,连续性和庇古-多尔顿条件(Pigou-Dalton condition)等价.进一步证明了满足对称性、齐次性和一般塞尔可分性,并且在完全平均分配时取零的不公平度量指标只有三种形式.推广了已有的一些结果,并且去掉了可微性假设,其意义在于不公平度量指标的可微性没有合理的经济学解释.

This paper is devoted to the investigation on the decomposable inequality measures. It is proved that under the assumptions of symmetry, homogeneity, and Theil decomposability, the condition of continuity and Pigou-Dalton principle are equivalent. It is also shown that there are only three kinds of ine- quality measures which take the value zero exactly at points of complete equality and satisfy the eonditions of symmetry, continuity, homogeneity, and general Theil decomposability. Some results of this paper are the extensions of well known results, but we get rid of the assumption of differentiability, which （i. e. secondorder differentiability） carries little economic meaning.