Mathematical Social Sciences 6 (1983) 307-3 I3 North-Holland 307 zyxwvutsr A NEW PNDEX OF POVERTY Satya R. CHAKRAVARTY Indian Statistical Institute, Calcutta 700 055. India Communicated by A. Sen Received 7 September 1982 Revised 25 July 1983 This paper introduces index of poverty’. a new index of poverty. The index satisfies all the axioms for ‘a good Key words: Measurement of poverty; a new index based on the ‘uuility gaps’ of the poor. zyxwvutsrqpon 1. Introduction In measuring the incidence of poverty the most widely used statistic is the propor- tion of population that falls below the poverty line. But this index does not reflect the intensity of poverty suffered by the poor. As an alternative, the aggregate value of the difference between the incomes of the poor and the poverty line has been con- sidered. This index is insensitive to transfers of income among the poor so long as nobody crosses the poverty line as a result of such transfers. In his pioneering paper Sen (1976) introduced a superior (ordinal) index of poverty. Alternatives and varia- tions of Sen’s index have been proposed in the literature (see Section 4 for a discus- sion). But almost all of the existing indices have one or more shortcomings. This paper introduces a new poverty index that avoids many of the shortcomings of other indices. Moreover, the index possesses some attractive properties, e.g. at- taching greater weight to transfers lower down the income scale and decom- posability. 2. Axioms for a good index of poverty With a population of size irl,the distribution of incomes is represented by a vector y=(yi,yz, . . . . u,), where y+OVi= 1,2, . . . . n. We assume that the incomes are ar- ranged in non-decreasing order, i.e. yl~yz~... siv,q(sn) is the number of the poor who have income below the poverty line 2 (given exogenously). A poverty index P which is assumed to be a non-negative scalar function of y and t should satisfy the following properties: 0165-48%/83/$3.00 0 1983, Elsevicr Science Publishers B.V. (North-Holland1