Instead of the artificial resources procured from taxing other citizens of different states, independent states would be forced to make wise fiscal decisions to encourage economic growth.
If this is impossible or simply not done, then the population of that state will decrease as citizens move to other places with higher standards of living. This equillibrium will over time help to even things out.
But also remember that with the elimination of the income tax, economies of each state will grow at a much greater rate than before, so chances are all states will be better off in the long run.
