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Notes -
The obvious problem with this is that marginal costs of new people aren't at all linear, and your model assumes that they are.
Adding, say, an additional train to a prexisting route is a tiny expense compared to the cost of the route. Adding a new student to an existing school is basically zero cost (and comes with extra funding!) until you get so many new students that you need a new building or something.
Different things have different levels of nonlinearity.
So as places get bigger some things (public transit, road quality, library funding, etc) get better funded, while other things are more linear (or even superlinear -- knowability of a random person on the street, for instance) and get worse.
Which is why cities, as opposed to towns, are good for some things and bad for others.
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