The optimal size of an urban area is a controversial topic. We take optimal urban size to be that which minimizes net costs of city size, with larger cities first having various economies of scale (e.g. waste pickup) then later diseconomies of scale (e.g. pollution, congestion)

We show here that the usual textbook declaration that there is no such thing as a "supply curve" for a monopoly can be confusing for students and is at least somewhat misleading. The perfect competition case corresponds to a "one-parameter" demand curve facing the firm; varying that parameter...