Inequality foundations of concentration measures: An application to the Hannah-Kay indices

The aim of this paper is to provide a connection between concentration and inequality. In particular, we show that the general entropy inequality indices are, among inequality measures, those consistent with the whole set of Hannah-Kay concentration indices. We isolate the inequality component underlying concentration measures, obtaining an explicit additive decomposition of the change in concentration into the change in its two components, i.e., inequality and the number of firms. This relationship proves to be valid for the whole set of Hannah-Kay concentration indices, and embodies as particular cases some others previously found in the literature. We are particularly grateful to Emilio Cerdá for helpful comments on the mathematical formulation of the paper. The second author also acknowledges support through the European Commission Project #ERBCHRXCT980248.