It depends on what you mean by "balanced diet" (are you going to require meat?) but let's just work an example with sweet potatoes, which are pretty nutritionally packed and can be ludicrously productive.
Let's say you planted just one acre over with sweet potatoes; you could grow roughly 5 tons of usable roots, about 10,000 kcal/day. Swap some of that area out for other crops for nutrient balance and you'd still have a huge excess for one person, even accounting for a farmer's caloric needs. You might also end up hating sweet potatoes after a year, but that's why you specialize in a few calorie crops and then trade with others for what you need.
Anyway, it seems to me that an acre would be more than enough for a whole family.
I keep bees, for instance, and my hives produce about 50-100lbs of honey per year. It's not super nutritious, but it's low effort per lb. Ten hives could produce a lot of raw calories. But it's also a skill, and you can kill your bees if you aren't careful.
The point I'm making is that, we're all bringing different skills and backgrounds. I've grown potatoes but never at the scale of an acre. I don't know what challenges that brings.
More to the point, how is everyone in a big city going to find that space?
I think this generally holds for living in cities. Since residence is basically vertical, it gets progressively harder to also grow and raise food vertically also. All the space is already taken. And all the space that isn't housing is infrastructure (roads, sewers, cables) that would all have to be ripped out in order to plant enough to sustain the city.
So the food production moves away from the city, and away from the people who need the food. The OP is right to wonder: what happens if the supply lines from the countryside are cut? That would be a huge disaster, and whenever this has happened throughout history, it was a huge disaster. E.g. when Greece was occupied by the Axis, in the 1940's, the people in Athens died in droves of famine while the people in the countryside, well, they subsisted. In fact, anecdotally, my friend's grandma told her there was no other time they were so fat in their lives because they ate all they had everyday, just because they didn't know if they would have any more food tomorrow. But the countryside had food to eat while the city was left with scraps. btw this was originally caused by the Nazis who requisitioned crops to feed their war effort, assholes.
in the greater Athens–Piraeus area alone, some 40,000 people died of starvation, and by the end of the Occupation "it was estimated that the total population of Greece [...] was 300,000 less than it should have been because of famine or malnutrition" (P. Voglis).[24]
https://en.wikipedia.org/wiki/Axis_occupation_of_Greece#Econ...
(When I'm tired, I write too much :P)
Cities have other benefits, though -- access to materials, labor, community, rapid healthcare. Gotta make your tradeoffs.
The above is true with some qualifications. You will need decent soil and plentiful clean water. And a power source to pump the water. And fertility which you will have to bring in. The compost you make won't do it. A way to control pests, (ya ya muh organic, but we are trying to survive here). So some pesticides. Sprayers. More then one, they break. Maybe some herbicides as well so you don't burn so many calories hoeing. Some mechanical help like a rototiller will make this much more possible. Fuel oil and parts for that. Some fencing and trellising. Bird netting. A way to preserve harvests like canning, drying or freezing.
Most importantly (and most people will lack this rendering half an acre vs 5 acres moot for practical purposes) you will need a fair amount of expertise to pull it off. Generally from experience. And it will be a lot of work and mostly unforgiving of mistakes.
Source: I mostly made it up, but I am an agronomist and long time gardener. It's probably roughly right though.
I'd assume even with massive supply chain disruptions, books still exist (and perhaps even libraries) and you can still ask other people for advice or even band together, division of labour is still a thing and useful.
You can either organise that as some kind of cooperative, or just like we organise companies today.
Well I don’t, but if you need some help I suppose you can use my profile for contact information. This could be delicate for both our families. KIDDING I’m pretty sure you meant fertilizer there.
And yes, your half acre number is much much closer to accurate.
Check out “The Market Gardener” by Jean Martin Fortier. The quoted statement is a myth. Farms historically were nowhere near as large as today and we able to provide a balanced diet to those literally on the same block (think “in-fill market gardens”)
If it's one year’s output of that land to feed that person for a year, then it's just 5 acres for a person (and you can drop of then “for a year”, since the output period matches the consumption period.)
(Their server seems to be slow tonight, check out this for a summary of their system: https://web.archive.org/web/20210411002519/http://growbioint... )
Normal greenhouses are much simpler, more efficient and have been in use for decades. They make full use of the sun.