By Satya R. Chakravarty
ISBN-10: 364275502X
ISBN-13: 9783642755026
ISBN-10: 3642755046
ISBN-13: 9783642755040
In this publication we're occupied with source of revenue profile established moral social index numbers. a moral index is designed from an specific social assessment functionality with a particular objective in brain. for instance, a moral relative inequality index determines the fraction of overall source of revenue which may be kept with none welfare loss if society distri buted earning both. moral indices distinction with descriptive indices that are de rived with out utilizing any suggestion of social welfare. remember the fact that, moral indices aren't intended to supplant descriptive indices, particularly they're developed with diversified goals. we commence bankruptcy 1 with a proper dialogue at the proposal of a social overview functionality. frequently physique of this bankruptcy we think of the matter of rating source of revenue profiles utilizing a social evaluate functionality. In bankruptcy 2 we set approximately interpreting adjust local techniques to the size of inequality. In bankruptcy three we concentration our recognition at the Gini index, the main often used index of inequality, and its extensions. In bankruptcy four we formulate the idea of a moral distance functionality that measures welfare of 1 inhabitants relative to a different. bankruptcy five is dedicated to quantifications and discussions of other definitions of relative deprivation recommend through Runci man(1966).
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A similar result for absolute indices can be established using a dominance relation involving the absolute LC (Moyes(1987) and Chakravarty(1989». We can also focus our attention on fixed population, arbitrary mean income case. In such a case the domain of definition of the inequality index is Dn, where n E IN is fixed. 2 (Fields and Fei 1978, Foster 1985) Let x and y be two distributions of income over a given population size n, that is x, y E Dn. Then the following statements are equivalent: (i) In(x) > In(y) for all relative inequality indices In: Dn --+ 1R1 that satisfy PD and 1M.
3 (Foster 1985) Let x, y E Dc be arbitrary. Then the following statements are equivalent: (i) I(x) > I(y) where I: Dc 'L --+ 1R1 is any inequality index that satisfies 1M, PD and PP. (ii) y x. 1 and hence omitted. It is now evident that for any two income profiles x and y of a given total over 37 a given population size, x 'L y if and only if x is regarded as less unequal than y by any inequality index satisfying 1M and PD. 2 the former is also equivalent to the requirement that x is regarded as better than y by any strictly S--concave SEF.
Symmetry of W implies symmetry of QAD about the ray of equality xl = x2. Thus, the points Q and D represent two distributions of the total income 2· A(X) (denoted by OM = ON). By similarity of triangles OAxf and OBA(x), the AKS index now becomes 1- OA/OB. 27) two functions of incomes appear in a ratio form, it is intuitively reasonable to inteFpret 13 as a relative index. However, in general, 13 is not a relative index. 2, suppose that the distribution y = (cx l , cx 2), where c > 0, is obtained from the distribution x = (Xl' x2) denoted by Q by raising or decreasing incomes proportionally.
Ethical Social Index Numbers by Satya R. Chakravarty
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