Isaac Asimov's Daneel Olivaw series of books had the overpopulated Earth alright, but it also had spacer colonies on distant planets that very much kept their populations at a sensible level and were magnificently wealthy in comparison because of it (and robots).
there's a short story, which i think is Asimov's, about a probe reaching earth. and it only detects two life forms in a fully automated planetary extraction mechanism. And those two are forever occupied trying to struggle the remaining half from one another.