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.

The rules of Ramsey pricing should be adjusted where the regulated firm is not selling to consumers or to perfectly competitive industries. Some rail charges should be below Ramsey prices.