In a utopian world of free markets with the non aggression principle at play, there would not be 'overpopulation per square acre' as you called it.
If we really did run out of farmland (completely plausible), people would start building upwards (or underground hydro-gardens)
They already have greenhouses which are multiple stories. Imagine clusters of skyscrapers that only take up a few city blocks being the equivalent of several dozen acres of dense vegetation that can be harvested more than once a year.
Coupled with free market green/renewable energy, there would almost be no limit of how many people this earth could sustain.
The only limit I can imagine would be to how much space the natural ecosystem can survive in (as in not cementing over the whole world, extincting every species)
Alas, this is only plausible in a utopian type society where government didn't milk the productivity from the people to the point where we still have fossil fuel driven cars for the last century. You'd think technology would have advanced at least a little bit.
In this current paradigm? I see the world starving and choking on our pollution once we hit that critical 'mass'. That is if there is no real progression of the technologies I mentioned.
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