According to Hans Rosling, if birthrates develop everywhere similarly, population will max out at around 10Bn within the next decades, and should then stay stable for a while. 10Bn to reach a somewhat comfortable living standard seems quite a stretch for the home planet based on current (mostly non-renewable) technologies. And a high enough standard is also necessary for the birth rates to stabilize, so it's not like keeping whole continents in poverty would help anyone.