Inequality curve and inequality index based on the ratios between lower and upper arithmetic means

A new inequaliy curve I(p) based on the ratio between the lower mean M(p) and the upper mean M+(p) is proposed. By averaging I(p) the new inequality index I is obtained. The index I satisfies the usual properties required to an inequality measure. Being U(p) = 1 - I(p) a ratio between two arithmetic means, the meaning of I(p) is very straightforward. The index I is related to the Gini index R and the Bonferroni index B by the relation: R ≤ B ≤I. In section 6 the curves I(p) and the Lorenz curve L(p) for the N = 14026 personal incomes, regarding the Bank of Italy survey on the household expenditure, are reported.