These two stories by Kurt Vonnegut were written almost a decade apart but they are definitely connected. The Big Trip Up Yonder, published in Galaxy Science Fiction January 1954 is a comical yet scary description of what over population was going to do to society after aging was conquered and a simple daily dose of "anti-gerosone" would keep you forever the same age. Would Gramps EVER take 'That Big Trip Up Yonder', or would his hordes of descendants be stuck with him forever in a tiny apartment!?
2 B R 0 2 B, published in Worlds of If, January 1962 takes this basic situation many years into the future and a solution has been found. The population of the US has dropped from 40 billion to 40 million. Not what everyone would call a pretty solution, but nevertheless a solution to the population problem. I believe this is the type of story it is best to listen to, not describe, so enjoy.