Abstract
We provide a survey of the Kolkata index of social inequality, focusing in particular on income inequality. Based on the observation that inequality functions (such as the Lorenz function), giving the measures of income or wealth against that of the population, to be generally nonlinear, we show that the fixed point (like Kolkata index k) of such a nonlinear function (or related, like the complementary Lorenz function) offer better measure of inequality than the average quantities (like Gini index). Indeed the Kolkata index can be viewed as a generalized Hirsch index for a normalized inequality function and gives the fraction k of the total wealth possessed by the rich 1−k fraction of the population. We analyze the structures of the inequality indices for both continuous and discrete income distributions. We also compare the Kolkata index to some other measures like the Gini coefficient and the Pietra index. Lastly, we provide some empirical studies which illustrate the differences between the Kolkata index and the Gini coefficient.
Highlights
Inequality in a society can broadly be categorized as inequality of condition or inequality of opportunity
For all income distributions used till the previous section we found that given any F, the value of the normalized k index is no more than the value of the Pietra index and the value of the Pietra index is no more than the value of the Gini index
Apart from capturing the essential character of the nonlinear Lorenz function, gives us a very tangible one, giving that (1 − k) fraction of the population possess k fraction of the total wealth in the society
Summary
Inequality in a society can broadly be categorized as inequality of condition or inequality of opportunity. A tool that is indispensable in measuring income and wealth inequality is the Lorenz function and its graphical representation, the Lorenz curve (see Ref. 6). The pioneering work in this approach is Ref. 12 which suggested that there is an underlying notion of social welfare associated with any measure of income inequality. It is this concept with which we should be concerned. Each Lorenz function is associated with a real number and these numbers are used to compare inequality across different income distributions. This is a descriptive approach where we quantify the difference in inequality between pairs of distributions (see Ref. 13).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
