The social welfare implications, decomposability, and geometry of the Sen family of poverty indices Kuan Xu and Lars Osberg Department of Economics, Dalhousie University Abstract. In this paper, we propose a unified framework for the Sen indices of poverty inten- sity that shows an explicit connection between the indices and the common underlying social evaluation function. We also identify the common multiplicative decomposition of the indi- ces that allows simple and similar geometric interpretations and easy numerical computa- tion. JEL Classification: C000, H000, O150 Implications en termes de bien-être collectif, décomposabilité et géométrie de la famille d’indices de pauvreté à la Sen. Dans ce mémoire, les auteurs proposent un cadre d’analyse intégré des indices d’intensité de pauvreté à la Sen qui souligne la relation explicite entre ces indices et la fonction sociale d’évaluation commune qui les soustend. Les auteurs identifient aussi la décomposition multiplicative commune de ces indices qui permet d’en donner des interprétations géométriques simples et idoines et de faire des calculs numériques faciles. 1. Introduction Since Sen proposed an axiomatic approach to poverty research and an index of poverty intensity in 1976, poverty measurement has become an active research agenda. A vast theoretical literature has developed over the years, 1 and applications We would like to thank GordonAnderson, Charles Beach, Satya R. Chakravarty, Russell David- son, Donald Hester, Michael Hoy, James MacKinnon,YangYao, Ling Zhu, seminar participants at the ChineseAcademy of Social Sciences, Dalhousie University, Peking University, Queen’s Uni- versity, and the Canadian Economics Association Annual Meeting, and three anonymous referees for their helpful comments on our work. Kuan Xu would like to thank Dalhousie University and Lars Osberg would like to thank SSHRC for financial assistance: Email: Kuan.Xu@Dal.Ca and Lars.Osberg@Dal.Ca 1 See Zheng ~1997! and Foster and Sen in Sen ~1997!, and the references therein, for recent com- prehensive surveys. Canadian Journal of Economics 0 Revue canadienne d’Economique, Vol. 35, No. 1 February 0 février 2002. Printed in Canada 0 Imprimé au Canada 0008-4085 0 02 0 138–152 0  Canadian Economics Association