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.
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.
