Ask exploding heads

Doing some research, it looks like potatoes are one of the most energy dense foods you can grow at 17.8 million calories per irrigated acre. A regular human diet of about 2000 calories per day would work out to about 730,000 calories per year. This means that if you used every mm of that area to grow potatoes, you'd come up short, about 356,000 calories per year. And you'd need to find water, and so on and so forth, I think it'd be a challenge.

On the other hand, the US has about 1.6 Billion acres of land that's presently used for grazing cattle, forests, farming and so on, so if you gave 8 billion people a fair share of each, you'd give everyone 0.2 acres about 800m3. At that point, each individual person on earth would likely have enough land to grow food, have a place to live, maybe have some light (or heavy) industry.

Incidentally, the federal government owns about 640 million acres (2.6 million km2) of land in the United States, about 28% of the total land area of 2.27 billion acres (9.2 million km2). That could be enough to provide 0.08 acres (Approx 3000 square feet) to everyone on earth, and if you assume (incorrectly) that all that land is fertile enough to grow potatoes with irrigation, that area could likely just barely feed and house everyone and also give a bit of space for a fallow field.