[ebBPxIai]

I'm not sure whether I fully understood what you mean.
Equal distribution and appropriate distribution contradict themselves. As far as I understood, Rawls was talking about appropriate distribution only, not equal distribution. He did mention social and economic inequalities as part of society. But that they have to be so arranged that this imbalance is justified (= justice), that even the least-advantaged member can benefit from it in the end.
I hope I didn't get you wrong.