Interactions inequality-polarization: an impossibility result

Recent literature stresses the multidimensional nature of income distribution. Two of the most relevant components are inequality and polarization. In this paper, we prove the impossibility of keeping simultaneously constant these two aspects whenever the distribution of incomes changes. Distributional change could originate from any economic policy or simply from economic growth. Hence, our result implies an effective restriction for policymakers that they cannot avoid and should not ignore. Our proof embodies a general view of polarization that includes the Wolfson and the Esteban and Ray approaches. The paper also develops other links for the case of controlling only one variable and deducing the implications for the other variable.