The aim of this paper is to ascertain the optimum costs and levels of service for public transport. Assuming that a welfare maximizing Public Transport Authority in practice makes decisions about both prices and frequency of service well ahead of their implementation, this paper analyzes the joint optimization of prices and service frequency. The Authority is assumed to deal with the welfare of public transport only, without any concern with environmental or modal split issues etc. The conclusions reached are as follows: (1) In the absence of a budget constraint the optimal prices of public transport are, on average, above operator marginal cost, but below average variable cost. (2) Contrary to what might be expected, optimal high-frequency services should typically be subsidized more than optimal low-frequency services, given that there is no minimum frequency constraints. (3) In urban public transportation there may be one low- frequency/ low-subsidy-per-passenger local optimum and one high-frequency/ high-subsidy-per-passenger local optimum, one of which if global. (4) On services where all passengers have the same ideal departure time, the optimal subsidy is zero, given neither a budget nor a minimum frequency constraint. (5) A budget constraint tends to push optimal prices upwards and a minimum frequency constraint to push optimal prices downwards, compared to the situation without constraints. These are the main findings in this paper, which deals with the joint determination of prices and frequency for public transport. The partly new and more general results in this paper are due to a more detailed specification of the demand function and some fundamental aspects not previously taken into account, e.g., the impact of variable values of time, discontinuity in passenger behaviour with respect to frequency and several passenger groups.
Abstract