The issue of income distribution is gaining momentum in current economic debate. Many scholars have recently emphasized the role played by income inequality and functional income distribution in shaping major macroeconomics trends of modern capitalist economies (see Piketty, 2014). For this reason, it is of utmost importance to be in possession of the right methodological tools to bridge the gap between theory and reality. Although much has been written about the measurement of income dispersion across people, little attention has been paid to the measurement of income composition across people.The present work provides a novel methodological framework to tackle this issue. First of all, a new index of income sources polarization will be introduced, together with its mathematical properties. In addition to that, it will be shown how the same methodology can be employed to evaluate the extent to which savings and consumptions are polarized across the population. Second of all, a new instrument called "Dual-Polarization Box" will be presented. The latter allows for a joint analysis of the two polarization issues (the one of income sources, and that of saving and consumption). Indeed, the box displays all possible combination of the two indexes for a given society at a point in time. According to their position in the box, societies can thus be classified as Classical Capitalism, or Representative Agent Capitalism. Third of all, an empirical investigation for the cases of the US and France during the 20th century will be undertaken, and the results discussed.