The Lorenz curve and Gini coefficient are typically used to measure inequality. A different way to measure inequality is introduced here: I = CN, the product of concentration and number of units. The resultant index can be interpreted with reference to an inequality base where one unit owns all and the rest nothing. This inequality index also integrates the measurement of inequality, concentration, and diversification into one system, where diversification is measured as the inverse of concentration. I = CN accommodates various measures of concentration, including the Herfindahl-Hirschman and Tideman-Hall indexes. The Tideman-Hall concentration index also provides indexes of concentration, diversification and inequality as functions of Gini. As one application, the inequality index can be used to provide an index of economic development.
Fred Foldvary. "The Measurement of Inequality, Concentration, and Diversification." Journal of Interesting Economics (2001).