Very few children are born. The few that are quickly build up massive wealth worsening the conditions of their pare ts generation. Very quickly no more children are born as they would not have a better quality of life. The human race dies out within a couple of generations.
I think this is the right track: only children who will have a better quality of life can be born, therefore... no children are born. Ever. Because without new poor children, the rich children who would have had a better quality of life can't either.