Inequality indicators and distinguishability in economics

Money has a material counterpart, such as banknotes or coins, and an ideal expression, monetary units. In the latter case, it is boson-like: individual incomes have no a priori limit, and their units are not distinguishable from each other in economic processes. Individuals, on the other hand, usually occupy one job at a time which makes them akin to fermions. We apply to individual incomes down-to-earth statistical calculations, similar to those for quantum particles, and obtain expressions for the cumulative distribution function, probability density and Lorenz function resulting from the simultaneous use of both statistics. They provide extremely good fits to corresponding data on French income distributions. On this basis, we propose a new entropic inequality indicator.