3. Optimum in the core–periphery model with public transit
and road congestion
So far, the transport infrastructure for public transit and roads
was sunk in place. Hence, the cost or capacity of that infrastruc-
ture was not treated. How should that infrastructure be optimally
sized and optimally priced and what optimal level of urban
population should it support? We need to first embellish the
model a bit, adding important features in a simple way.
We will assume that travel in the core occurs by means of a public
transit infrastructure that costs k units of income to supply, and that
each worker who uses this infrastructure incurs a private cost c(k) to
travel in the core with c 0 (k)o0, c 00 (k)40 (see Fig. 4). That is, a higher
investment in public transit lowers the private cost of mobility within
the core. For road transportation, we assume that the bridges from
the suburbs to the core, require A units of suburban land to make, and
at the unit opportunity cost of r, the bridges will cost rA.
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The