Do you assume normal distribution of income? Because income is Pareto distributed, and shifting the median changes other parameters quite unusually. For your c

Do you assume normal distribution of income? Because income is Pareto distributed, and shifting the median changes other parameters quite unusually. For your convenience: US Gini index is ~41%, and, correspondingly, the alpha parameter of Lomax (Pareto type II) distribution is ~1.71. If you plug the median in [1], and try to run any income redistribution scenarios, it doesn't work. [1] https://en.wikipedia.org/wiki/Lomax_distribution https://en.wikipedia.org/wiki/Lomax_distribution