Proposition 4. At the social optimum: (a) the road charge is set as a
toll extracting from each suburban commuter the external cost he
imposes on all other suburban commuters (Pigouvian taxation); (b-i)
the public transit system is invested in until the sum of the marginal
benefits of all users of it is equal to the marginal cost of creating it
(Samuelson’s rule), and (b-ii) the bridges (roads) are invested in until
the sum of the congestion cost savings of all suburban commuters
equals the marginal cost of suburban land (Samuelson’s rule); (c-i)
the aggregate Pigouvian tolls completely pay for the land used for the
bridges; and if the planner optimizes the city’s population, then (c-ii)
the aggregate differential rent from the core’s land market completely
pays for the public transit system (Henry George Theorem).