The Economics of Crowding in Public Transport

We analyze trip-timing decisions of public transit users who trade off crowding costs and disutility from traveling early or late. Considering fixed and then endogenous demand, we derive the equilibrium distribution of users across trains for three fare regimes: no fare, an optimal uniform fare, and an optimal train-dependent fare that supports the social optimum. We also derive the optimal number of trains and train capacity, and compare them across fare regimes. Finally we calibrate the model to a segment of the Paris RER A mass transit system and estimate the potential welfare gains from train-dependent fares.