> If you had to feed 100M people with a nutritionally complete diet forever, how small of an area could you manage to generate the food?
I don't know the answer for centralized food production, but for local food production based on what I know about self-sufficiency and homesteading, my back of the napkin math goes like this:
Minimum food production area for family of 4 (2 adults, 2 kids) based on diet:
1/2 acre for vegetables/chickens
2-3 acres for dairy products
5 acres for grains/nuts
10 acres for meat
Plus 2-3 acres timber for heating
That's ~ 20 acres per family, working all day, almost every day to produce food and heat.
That is still assuming you would be able to use modern technology (tractors/implements etc.) instead of manual labor and do this in a moderate hardiness zone, probably 5-9. There is a reason in the 1800s homestead land grants were up to 160 acres.
From a US perspective: The US has roughly 900 million acres of farm land. If everyone would homestead (unrealistic), and every family would be relocated to a productive area (unrealistic), this land could support 45 million homesteads.
> and leaving ethics off the table (Soylent Green, etc)?
I expect this to be an unrealistic scenario as well. IMHO people will start roaming for food and stealing from those who produce it, instead of patiently waiting for their government handout of whatever astronaut food was stored.