Relative Deprivation, Envy and Economic Inequality

Abstract

The purpose of this paper is to develop an economic measure of relative deprivation and explore its relationship to envy and economic inequality. Although the Gini coefficient has been interpreted as an index of relative deprivation, it will be shown that its magnitude fails to satisfy the most important property required of an index of relative deprivation. Though inequality gives rise to discontent, a common index of inequality is unable to reflect the actual degree of discontent in the society whereas a properly constructed measure of relative deprivation should be capable of doing so. Frequent attempts to demonstrate that the Gini coefficient is a measure of relative deprivation may be due to the much quoted statement by one of the famous exponents of relative deprivation, Runciman (1966), who wrote, 'The magnitude of a relative deprivation is the extent of the difference between the desired situation and that of the person desiring it.' This is a clear indication that Runciman conceives relative deprivation as a linear function of the difference between two situations. On the other hand Runciman talks about the curvilinear relationship between inequality and grievance in connection with the main finding of Stouffer et a]. (1949) which seems to have been completely ignored in economic literature.The plan of this paper is as follows. In the introductory section we discuss the concepts of relative deprivation, envy and fairness and their relationship to economic inequality. In Section I1 the importance of the concept of the reference group as the context of relative deprivation is briefly discussed. In the third

Proximity-sensitive individual deprivation measures

“…The indices of Chakravarty and Chattopadhyay (1994) and of Podder (1996) are special cases of the class D U , where U : R + → R + is an increasing and strictly concave utility function. This class of measures was suggested by Hey and Lambert (1980) and the individual index corresponding to any such U is defined by letting, for all (y;…”

“…Chakravarty and Chattopadhyay (1994) employ a power function U with a positive power, whereas Podder (1996) suggests to use a logarithmic utility function U .…”

“…Contributions that are close to our own as far as the feasibility issue is concerned include those of Paul (1991), Chakravarty and Chattopadhyay (1994), Podder (1996) and Esposito (2010). Among these, Esposito (2010) is the only one that provides a characterization of the individual deprivation index that is being proposed.…”

A new class of deprivation-based generalized Gini indices

“…Correspondence to: Kai-yuen Tsui (1979,1983). Clarifying and extending his pioneering studies is the subject of the papers by Hey and Lambert (1980), Chakravarty and Chakraborty (1984), Berrebi and Silber (1985), Paul (1991) and Podder (1996) among others.…”

“…Taking a cue from Runciman (1966), it is common in the literature to define relative deprivation of a person with income x relative to a richer person with income y as y − x , while a person is not deprived with respect to those poorer than her. To be exact, let x ↑ = (x (1) , x (2) , · · · , x (N ) ) such that 0 < x (1) ≤ x (2) ≤ · · · ≤ x (N ) be a vector of positive income levels and π = (π 1 , π 2 , · · · , π N ) be a vector of positive numbers such that π i is the number of persons with income level x (i ) .…”