Choice of frequency and vehicle size in rail transport – implications for marginal external costs

Frequency of services and vehicle size are important policy instruments of railway companies. Extending Mohring's basic ‘square root model’ for frequencies, we arrive at more general formulations for frequency, vehicle size and price under alternative regimes of welfare and profit optimisation. It appears that in the more refined models the frequency response of railway companies with respect to changes in passenger volumes is not far removed from the standard square root result. Analysis of empirical data for the Netherlands shows that the responsiveness of the Dutch railway company in terms of frequency and train size to an increase in demand is low. It is estimated that an increase in the number of passengers of 1% leads to an increase in the supply of capacity of about 0.5% (a frequency increase of about 0.35% to 0.40% and an increase of vehicle size of about 0.10%). This has important implications for the environmental costs of the railway company. An additional passenger does not lead to a proportional increase in capacity so that the marginal costs are lower than the average costs. It is further demonstrated that policies of keeping frequency and train size constant during the peak and off-peak have adverse effects on the environmental performance of railways.