Social welfare rankings of income distributions A new parametric concept of intermediate inequality

This paper installs a new concept of intermediate inequality, which we refer to as η-inequality equivalence, in the notable form of equivalence of the Lorenz partial ordering and social welfare dominance. The η-inequality equivalence is a parameterized generalization of Krtscha’s (1994) non-linear compromise between the relative and absolute inequality views. For each η ∈ 0,1], we place a class of social evaluation functions satisfying the S-concavity as well as the property that an increase in incomes while leaving η-inequality intact raises welfare. We prove that one income distribution dominates another for all social evaluation functions in iff the former has a higher mean and a higher η-Lorenz curve. We prove also that the class is strictly increasing in the sense of inclusion as η decreases.I am grateful to Kiyoshi Kuga for his helpful comments and suggestions. I am also grateful to an anonymous referee and an associate editor for many valuable comments and suggestions that have much improved the paper. A previous version of this paper was presented at the annual meeting of the Japanese Economic Association, October 7, 2001, Tokyo, Japan. I wish to thank Takashi Toyoda for his helpful comments and suggestions at the meeting. This research was supported in part by the Ministry of Education, Culture, Sports, Science and Technology in Japan (Grant-in-aid for Scientific Research No.12630032).