社会福利函数与收入不平等的度量——一个罗尔斯主义视角

Social Welfare Function and Measurement of Income Inequality:A Rawlsian Perspective

本文试图从现代社会选择理论的视角探讨收入分配问题,并利用社会福利泛函方法重新解释了AKS不平等度量。文章指出并证明了:在标准福利主义假设下,如果一个社会福利函数满足凹性、连续性、匿名性、单调性和规范齐次性,且其所对应的代表性效用函数是一个严格递增的凹函数,则必定存在一个相应的AKS不平等指数;进一步利用纳什和罗尔斯主义社会福利函数,分别构建了纳什-阿金森指数和罗尔斯主义AKS指数,后者独立于代表性效用函数的正单调变换,且放松了凹性假设;最后,对我国地区收入差距、城镇居民收入差距和农村居民收入差距分别进行了不同指数的测算与比较。

The problem of income distribution is discussed from the viewpoint of modern social choice theory, and the traditional AKS measure of income inequality is reinterpreted under the framework of social welfare functional. It shows that for any social welfare function satisfying formal welfarism, concavity, continuity, anonymity, monotonicity, and normative homogeneity, if its representative utility function is concave and strictly increasing, then there must be a corresponding AKS index. Furthermore, based on Nash and Rawlsian social welfare functions, Nash-Atkinson index and Rawls-AKS index are proposed respectively; the later is independent from positive monotone transformation of the representative utility function, whose concavity is then relaxed. Finally, calculations of regional, urban, and rural income inequality in China are also implemented.