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. After the formulation of theoretical models we also carry out an empirical analysis where choice of frequency and vehicle size are analysed with special attention paid to the level of occupancy rates. It appears that average occupancy rates are low in rail transport. As a result the frequency and vehicle size response of the railway company appears to be 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% and an increase of vehicle size of about 0.15% ). This has important implications for the environmental costs of railway firms. Given the low occupancy rate, an additional passenger does not lead to a proportional increase in capacity so that the marginal costs are lower than the average costs.