Gini coefficients and median / mean income ratio Simple question: If the GINI coefficient (market incomes) goes up, is it a necessary feature that the mean income rises relative to the median?
No, since you can change the Gini coefficient by altering the distribution of incomes in the top half (keeping the total the same) without changing the mean or median income; you can also change the Gini coefficient by altering the distribution of incomes in the bottom half without changing the mean or median income.

Compare the Gini coefficients of {2,2,2,2,2,6,10,10,10,10,10} and of {1,1,1,1,6,6,6,6,6,6,26}: the former will have a Gini index of about 0.33 while the latter will have a Gini index of about 0.46 though the mean and median do not change (6 each)