Second Best Decision Making of Railway Operators: How to fix Fares, Frequency and Vehicle Size

Railway networks are characterised by variations in demand on different links. Optimal strategies therefore call for a differentiated treatment of fares, frequencies and vehicle sizes in various links. However, for several reasons, railway operators may apply uniform levels for these decision variables. In this paper we investigate the welfare losses implied by uniform setting of fares per km, frequencies or vehicle sizes. This is done within the context of a model with uniform cost structures, uniform price elasticities, uniform demand levels across the day, but with demand levels that vary across segments of the network. We demonstrate that the largest welfare loss results when frequencies are made uniform across links. Welfare losses due to making vehicle size and price per km uniform across links are smaller. We further find that when capacity, represented by frequency and vehicle size, is set at its optimal level at the various network segments, the contribution of price differentiation to social welfare is very limited. These results suggest that where differentiated prices are important to address issues like congestion and directional asymmetries in demand, differentiated supply in terms of vehicle size and in particular frequences are the preferred way of addressing demand variations on different segments in a network.