Well either way they're paid with real estate taxes. So the question is should someone on two acres be paying four times as much as someone on a half acre. Or the same as a 16 unit apartment building?
Cost proportional to area doesn't even make sense for utilities or roads (average distance only goes up as the square root), never mind straightforward per-resident costs such as public school or trash disposal.
I said "trash disposal" for a reason. Rather than handwave that things cost "more" with area, the sane way to analyze it is in terms of their growth. Rather than talking in terms of lot area, it's clearer to discuss in terms of single dimension distance between houses (lot area ~= L^2), holding population constant.
Schools/hospitals/trash disposal/wastewater treatment - heavily proportional to population, with a negligible increase per area due to convenience - O(1).
Distribution (telecom, electric, trash hauling, water, sewer) - Picture a square town with a single N-S route and one E-W route per row of lots - O(L)
General transportation - The average distance between any two points also goes up linearly - O(L)
Roads themselves - probably the closest thing proportional to area, but that's not even true as in less dense areas it's easier to drive further in the wrong direction (say further east before being able to cut north). O(L^1.5) ? In the absolute worse this is O(L^2), but what else is?
Note that based on lot sizes I'm basically talking about denser or less dense suburbs here. Suburbs are their own hellhole regardless of density, but I've seen many developments with neighbors right on top of one another in areas that are otherwise more spread out. Despite the increased density, those developments are straight residential (no stores, restaurants, or even parks to walk to), and thus gain little from the increased density besides the developer packing in the maximum number of economic rent streams.
And tying this back to Georgism - what does that look like if you're a neighbor to one of these developments? The town increases their valuation to pay for the per-resident cost. Then it declares that your land is worth a similar amount. So you're either stuck paying the same real estate taxes as a multiple family development, or selling your house so another development can be built.
Your argument about costs ignores the key fact that rural areas are far less productive than urban areas, and so cannot afford even the same per-capita rates as urban areas.
As for the land value economics of multi-family development in rural areas: it just isn't that important IMO.
However your described scenario seems like a great way for the rural area to become economically relevant by gradually building up a functional amount of density.
I don't see how this "productivity" you're talking about is relevant to my point. The page you link is talking about the large scale urban-rural balance, not analyzing the gradient in a given region.
Cities themselves are obviously centers of commerce and concentrations of wealth - but it's nonsensical to extrapolate this feature as applying to slightly denser suburbs. If someone lives in the suburbs and commutes into the city to work, then all their "productivity" happens in the city. And obviously the more workers you can fit into a given area, the more work gets done (cf factory housing).
Furthermore, cities are inherently more interconnected and thus the activities there are more legible to the system, whereas rural work is less so - eg a couple working full time plus and hiring maids/contractors/etc to take care of their home creates a lot more cashflow than a rural couple DIYing.
In rural areas though the whole point is that the land isn't very valuable, so the land tax will correspondingly be very low, so feel free to do economically inefficient things like having a giant house in those areas - the cost of your building will probably be far more than the cost of your land, so in practice you're not paying 4x more.
All the services still have to be paid for though. So unless tax districts get much larger such that each one includes a regional city, the rural/suburban taxes would still have to be significant.
> Well either way they're paid with real estate taxes.
Not necessarily. They could well be paid for by any other taxes. Income taxes, etc. There's no rule to state that certain taxes have to pay for certain expenses.
