My answer is the Human Cube.
Picture a manufactured module (would actually come in several sizes to accommodate larger or smaller families). It would internally be sorta like a double wide, except the windows would be LCD panels showing images of the outdoors. At both ends are doors opening into a built in section of hallway. Sprinkle in an occasional common module. Now stack them like Lego's with the utilities all interlocking as you stack them. Allow 50'x50' (much larger than that double wide) and you can fit 10k units per square mile. Stack them 10 layers deep and you have 100k units per square mile. There are around 124 million families in the US, so we'll need to cover around 1240 or so square miles. That "sounds" like a lot, but it's only 35 miles on a side. That's barely a ranch out west.
Ok, it would wind up a bit larger because that just the residential. We'd need some recreation space, commercial space, etc and there would need to be a way to extract failing units for replacement, etc. But basically, the entire population of the United States "could" easily fit into a space smaller than Rhode Island.
And there'd be no snow to shovel, rain to flood the basement, etc.
High Density farms nearby would grow/raise the food - it wouldn't even need to be that soylent stuff.
Of course, Europe would need one of their own. Asia and India would probably need several each... But pretty soon the entire world would be living within these self contained communities.
I think I've made my point. Modern problems. Modern solutions.
You're welcome. I'll be solving prison overpopulation next week. (spoiler, it'll be a variation on these modules, but without doors...)