We will explain in some detail why so different conclusions can
be obtained. Fig. 1 plots the consumer surplus(CS)(see Eq. (3)),
producer surplus(PS)(see Eq. (4)) and total social benefits
(CSþPS) as a function of the number of trains in the initial
situation without investment.All benefits are compared to the
reference situation with n¼4 trains/h.
The CS increases with the number of trains up to 5 trains/h,
driven by declining waiting time.Above 5 trains/h,the CS declines
with increasing number of trains because the travel time increases
due to capacity constraints.ThePSh as a maximum at 3.5 trains/h;
fare revenues increases lower than operating costs after that point.
Total benefits PSþCS attain a maximum at 4 trains/h.We can note
in passing that the profit-maximizing optimum is different from
the social optimum;a commercial operator trying to maximize
profits will run fewer trains than what is socially optimal.Thisis
one of the arguments for society providing,regulating or subsidizing public transport.