This paper characterizes the class of inequality measures that are multiplicatively decomposable, meaning they can be expressed as a product of within-group and between-group inequality components, with weights summing to one. Remarkably, this corresponds to the class of inequality measures that is additively decomposable in subgroups, so that that total inequality can be written as the weighted sum of inequalities within groups. The proposed measures satisfy standard axioms in inequality measurement, including scale and population independence, the Pigou-Dalton transfer principle, and—for reasonable parameter values—the transfer sensitivity principle. We illustrate the properties of the new class using data on global income inequality and inequality within the United States.

Keywords: Inequality, Decomposition, Pigou-Dalton Transfer

JEL Classification: D31, D63, O15