Inequality and Negative Income

This paper deals with some problems in the measurement of inequality when negative incomes are allowed. A helpful axiom is defined, called the Greatest Gets More axiom. Using this axiom it can be shown that the properties of some inequality measures depend on whether there are negative incomes or not. In this paper for the intermediate measures of Eichhorn and the centrist measures of Kolm a threshold value is given above which the Greatest Gets More axiom holds. Furthermore, a simple proof is given for the fact that there exists no function which fulfills the three axioms Pigou-Dalton, homogeneity and additive invariance when the data contain negative incomes.