Market size and fare-free public transit in theory

Studies of fare-free public transit claim it is most convenient in small communities, because their transit systems tend to have lower farebox recovery ratios and more available capacity. This paper offers a rationale for these tendencies by working through a static model of a bus route with boarding/alighting delays, crowding and elastic demand that scales with a “market size” parameter. Due to externalities passengers impose, ridership arises as an equilibrium outcome given a certain market size and the agency’s choice of fare and fleet size. When the fare and fleet size are chosen to satisfy the First- and Second-Order Conditions for maximizing social surplus, the farebox recovery ratio, number of passengers on each bus and the rate passengers board each bus are all smaller in smaller markets. An extension explores capacity choice. • A model of a homogeneous bus route where the demand function scales with market size. • Derives the equilibrium and welfare-maximizing fare and fleet size for a given market size. • Comparative statics show how the equilibrium/optimum change with market size. • Smaller markets should have lower farebox recovery ratios and capacity utilization.