Much of the information was off the top of my head, and needs a point of clarification.
With 20" of rain, 5,000 s.f / person is required (4,000 is growing space, 1,000 is paths, etc.)
With 10" of rain ~10,000 s.f. / person is required - 1/2 with crop, half sloped to divert rainwater to the crop.
2,000 calories per day for 365 days is 730,000 calories
Crops for one person in 4,000 s.f growing space:
2,400 s.f. "carbon & calorie crops" grains, fava beans, sunflowers, filbers, raisins.
e.g. Quinoa yield 13 lbs / 100 s.f. @ 1500 Cal / lb = 468,000 Cal + 936 lbs dry biomass for compost
1,200 s.f. "high-calorie root crops" potatoes, burdock, sweet potatoes, garlic, parsnips, salsify
e.g. Sweet Potatoes yield 164 lbs / 100 s.f. @ 375 cal /lb = 738,000 Cal
400 s.f. "vegetable and cash crops" salad crops, etc., mixed to provide non-caloric nutrition
e.g. cabbage yield 191 lbs / 100 s.f. @ 98 cal / lb = 74,982 cal
Total caloric yield = 1,280,000 or 3,500 a day from a 5,000 s.f. plot @ 20" of rain a year, with yields from 'intermediate' soils and skills. Even bad soils would be 'intermediate' after a few years of this method. Actual caloric yields would vary, as several species in each category should be grown, yields and caloric content should be similar.
None of this is to say that I think that population growth shouldn't be controlled by education and opportunities to work. Living at the limit of available resources is much less comfortable than living well beneath it. The 5 Billion hectare of agricultural land is from the Statistics Division, Food and Agriculture Organization of the United Nations (FAO)
link. It includes 1.5 Bn Ha under permanent crops and arable land. This would support 15 billion people. There are also 3.5 Bn Ha of permanent pastures, at least some of which could be converted tp cropland. Total agricultural lands represent 37% of the world's land area.
Again, the point i'd like to make is that we humans have more than enough resources to survive.
I think I'm in the minority on DU, in that i believe in free markets. I beleive the failure of modern capitalism & even market socialism is the particular concepts of ownership we have, and a failure to recognize the commons. Specifically, I think that natural resources can not be legitimately owned, but must be 'rented' from the rest of us. There are variety of good reasons for this view, a few include: "No one created it, no one can own it.", "Search back long enough, and all titles are based on theft", "It was a gift of
"
Attempting to assign access to natural resources by government fiat would result in inequities as well: who gets their 40 acres in lower manhattan, and who gets theirs in eastern Wyoming? Renting them from the rest of us allows market forces to work in assigning the best uses to the best lands, while limiting income from those lands to actual productivity (as the location value was paid in rent).
Similar economic forces would work for the allocation of groundwater, surface water, atmospheric pollution, fishing rights, timber rights, drilling rights, mining rights, broadcast rights, airway rights, and orbit rights.
A glaring example of the effects of not doing this is shown by water rights out west. Hereditary (allodial) water rights given to farmers allow them to grow lettuce and other water-intensive crops in the middle of a desert, when millions of folks downstream need (and are willing to pay) for water. The farmers then stop farming, and make small (sometimes large) fortunes leasing their water rights to downstream users, profiting not off of their labor and investment, but rather off of a government license.
Another examples would be (you'll like this NNadir) coal plants 'grandfathered' into pollution rules. The correct procedure would be to auction the right to pollute out, preferably at the world level. A maximum output of CO2 could established, and companies would have to bid on permits. This way the revenue goes the general welfare, rather than to historical polluters, as it does in current tradeable permit schemes.