Diseconomies of scale and subsidies in urban public transportation

Subsidization of urban public transportation systems is often motivated by economies of scale and second-best considerations such as an underpriced road alternative. We model a public transit line subject to frictions between users (in-vehicle crowding), users and vehicles (boarding and alighting delays), and vehicles (congestion). We derive the profit- and welfare-maximizing provisions of supply. We show that if demand exceeds a first threshold, the system enters a congested regime and service frequency decreases. Beyond a second threshold, the strong deterioration of service quality causes the transit line to operate under diseconomies of scale, calling for a Pigouvian tax instead of a subsidy. This finding, which goes against Mohring's classical rule (1972), holds with an untolled road alternative, provided that the network structure remains constant. We estimate the model for the London Piccadilly line and find evidence of substantial diseconomies of scale during the morning peak, adding up to −1.49 £/trip for the observed provision of service quality (-0.61 £/trip at optimum). These results question current subsidy policies for the busiest transit lines.