A friend's comment that for most people, a lot of 15,000 to 20,000 square feet is about all we could put to use (for a home), got me thinking. That's 0.33 to 0.46 acre. Certainly some of us need more, particularly if we are market farming or are growing all our own food. Many of us live on far less land, particularly in or near cities. In Manhattan, a lot 25' wide and 100' deep, or 0.57 acres, is standard, and might bring $7 million or more; it might house a single family, quite generously, in 3 or more stories.
At 2.5 persons per household, 0.33 acre average lot size works out to 2.5*3*640 = 4800 people per square mile. To accommodate all 300 million of us would require a circle with a radius of 141 miles. (Calculation: 300,000,000, divided by 4,800, divided by pi; take the square root.) That's a circle whose opposite edges are in
- Los Angeles and Las Vegas (272 miles); or
- Pittsburgh and Cincinnati (285 miles); or
- Albany and Buffalo (288 miles); or
- Chicago and Cincinnati (291 miles); or
- Philadelphia and Pittsburgh (297 miles); or
- St. Louis and Nashville (304 miles); or
- New Orleans and Montgomery (310 miles); or
- Boston and Philadelphia (317 miles); or
- Atlanta and Charleston (SC) (320 miles).
A 0.50 acre lot size works out to 2.5*2*640 = 3200 people per square mile. To accommodate all 300 million of us at that density would require a circle with a radius of 173 miles. That's a circle whose opposite edges are in
- New Orleans and Birmingham (339 miles); or
- Kansas City and Oklahoma City (343 miles); or
- New Orleans and Houston (346 miles); or
- Chicago and Columbus (351 miles); or
- Baltimore and Cleveland (361 miles); or
- New York and Pittsburgh (362 miles); or
- Albany and Washington D.C. (366 miles); or
- Los Angeles and Phoenix (372 miles); or
- Atlanta and Memphis (387 miles); or
- Minneapolis and Chicago (403 miles).
If we were all content with a single-family home on that Manhattan 25x100 lot, the calculation would be 2.5x17x640 = 27,200 people per square more. To accommodate all 300 million of us would of require a circle with a radius of 105 miles ... diameter of 210 miles. No we haven't even talked about any multi-family housing! This is all single-family.
Not everyone wants as much as 0.33 acres. If we return to the 0.33 acre assumption per family, but assume that half of the single-person households would prefer 0.05 acres, and that 25% of the remainder of households would prefer 0.10 acres.
1-person households represent about 52 million people. If half of those households would choose to live on 0.05 acres, and the other half would still want to be on .33 acre, the "central core" of 26 million people would live on 26 million*.05 acres/640 = 2,031 square miles; that's a radius of 25.4 miles. If the rest of us, 248 million, chose to live at .33 acre per household, with an average household size of 3.0 (pulled from thin air!) that would be 248 million, divided by 3 per household equals 83 million hh at .33 acre is 42,800 square miles; add that to the 2,031 sq miles occupied by the .05 acre group. That's 44,831 square miles. Divide by 3.14, and take the square root: the circle would need to have a radius of 119 miles. A 240-mile circle would be the area between Dallas and Houston (239 miles), or Chicago and Detroit (275 miles), or St. Louis and Indianapolis (244 miles) or St. Louis and Kansas City (244 miles).
Of course none of these calculations allows any room for places to work, so let's say that we need to devote, say, 30% of our land to places that would employ us (and simultaneously provide for our shopping needs). Let's further say that beyond that we need to allow 20% more for streets, railroads, parks, rivers, airports, schools. That 44,831 square miles grows to just about 70,000 square miles.
So how big an area is that? Divide it by pi (3.14) ... 22,300 and take the square root: 149 miles. That's a 300 mile circle, to contain all 300 million of us!
And if, instead of a single urban area 300 miles across, we instead looked at 50 cities, they would need to be 1,400 square miles each, with a radius of 21 miles (and a population of 6 million people each).
Some of us don't care about being within a commuting distance of what a city has to offer, and prefer to live in the wide open spaces. That's fine, as long as they cover the costs themselves. And they shouldn't be asked to pay for the infrastructure of the cities, except to the extent that they make use of them.