Because values of time and passenger behaviour depend on the level of frequency it is found that: (1) in urban public transport there may be one low-deficit local optimum and one high-deficit local optimum, one of which is global; (2) contrary to what might be expected, optimal financial deficit per passenger is typically larger for high frequency services than for low-frequency services; (3) the optimal off-peak may exceed the optimal peak price.

The authors derive the Ramsey pricing rule in the presence of externality costs. They find that it is based, not on social marginal costs, but on the sum of marginal private costs and a fraction of marginal externality costs. Thus the Ramsey quantity rule does not hold.

Pricing rules are derived under different objectives for schemes including travelcards and ordinary tickets. To calculate the effects on revenue of different combinations of fares it is necessary to know the distribution of the population in terms of trip behaviour.