Income inequality measures and the middle class

¹ Peoples’ Friendship University of Russia (RUDN University), Miklukho-Maklaya Street, 6, 117198 Moscow, Russian Federation
² All-Russian correspondence multidisciplinary school, B-234 Vorob'evy Gory, MGU, 119234 Moscow, Russian Federation

^* Corresponding author: pavlov_oi@rudn.ru

Abstract

We study how the presence of the middle class in the sense of Gevorgyan-Malykhin affects the value of income inequality measures including the Gini coefficient J and the Hoover index H. It is proved that in the presence of the middle class (1) $J \leqslant \frac{1}{2}\frac{{L'\left( 0 \right)}}{2}$J≤12L′(0)2 (where L is the Lorenz function), (2) $H \leqslant \frac{1}{2}$H≤12, (3) the longest vertical distance between the diagonal and the Lorenz curve (which is equal to H) is attained at ${z_0} < \frac{3}{4}$z0<34 A tight upper bound for P90/P10 ratio is found assuming L′(0)>0. Tight upper and lower bounds for the differential deviation in terms of the Gini coefficient are found as well.