Honestly, running out of food is not going to as large of a problem as say water or cheap energy.
And half of that is because humans insist on turning deserts into Las freakin Vegas.
The Malthusian Vice has been disproven for food, but it is closer to truth when it comes to cheap energy. After all, if we stopped eating meat, we'd increase our caloric production by double, triple, quadruple. Get protein from eggs. I'm just saying, we could support such numbers.
And just ask Tokyo citizens about how much space humans *REALLY* need...
But then again, these alternatives are not particularly NICE. Our population probably won't crash, but it may become unpleasant.