Artha Vijnana: Journal of The Gokhale Institute of Politics and Economics

Gurupada Chakrabarty ¹

Affiliations
1 National Council of Applied Economic Research, Parisila Bhawan, 11-Indraprastha Estate, New Delhi 110002, IN

Abstract

In the history of development of ideas about measurement of income inequality three measures viz., Relative Mean Deviation R, Relative Mean Difference D and Gini coefficient G played significant roles. Equivalence of D and G is well-known. This paper looks into the relationship among these three measures and the Lorenz curve to demonstrate that D and G are really generalizations of the primitive measure R.

Full Text

     

Gurupada Chakrabarty ¹

Affiliations
1 National Council of Applied Economic Research, New Delhi - 110002, IN

Abstract

Welfare judgement on income distribution has often been made on the basis of weighted sum of individual incomes, the weights being based on some notion of relative deprivation. In a recent contribution to this Journal, Chakrabarty (1995) proposed a set of weights leading to a Social Welfare Function (SWF) based on Theil's entropy measure, not normalised. This paper proposes two more sets of weights leading to a pair of SWFs with similar properties and interpretations. Properties of a new measure of inequality derived from these SWFs are also scrutinised.

Full Text

     

Gurupada Chakrabarty

Abstract

Chakravarty (1982) derived a Social Welfare Function based on a set of axioms conforming to widely shared views on measurement of welfare. The Social Welfare Function turned out to be a decreasing function of normatised Theil's Entropy Measure and an increasing function of the mean income. Theil's measure T as such, has a number of desirable properties and conforms to the Principle of Population Replication. The normalised measure (T/log n), however, fails to do so. By altering one of the assumptions in his set up an alternative Social Welfare Function has been derived. This Social Welfare Function is a negative transformation of Theil's measure as such, not normalised, and has some Interesting properties and Interpretations different from those of Chakravarty (1982).

Full Text

     

Gurupada Chakrabarty

Abstract

In the discussions of the size distribution of income reference is frequently made to summary measures of inequality. Many alternative measures of inequality have been proposed from time to time motivated by certain theoretical considerations or, more appropriately, theoretical intuitions. Gini Coefficient is one of the oldest of such measures proposed. All of these measures are reasonable but arbitrary from the point of view of their welfare implications.

Full Text