Congesting Pricing in a Road and Rail Network with Heterogeneous Values of Time and Schedule Delay

Abstract

We analyse congestion in a road and rail network with heterogeneous users. On the road there is bottleneck congestion. In the train there is crowding congestion. We separately analyse heterogeneity that varies the values of time and schedule delay scalarly in fixed proportions and heterogeneity that is in the ratio of value of time to value of schedule delay. We analyse first-best and second-best on road or rail. More heterogeneity lowers the relative efficiency of welfare maximisation by the road. This relative efficiency also decreases with proportional heterogeneity. Conversely, in previous research with two parallel roads, the relative efficiency of single-link pricing increased with proportional heterogeneity. This difference is caused by two road being perfect substitutes, while car and train are imperfect substitutes. The welfare gain of congestion in the train is less affected by heterogeneity. However, the relative efficiency of profit maximisation on rail only decreases with proportional and ratio heterogeneity. There are marked differences in the distributional effects on road and rail. On the road, is generally more beneficial for the user the higher her value of time or schedule delay is. In the train, has no distributional effects or is less beneficial the higher a user's value of time or schedule delay is.