Market size and fare-free public transit in theory

Abstract

Studies of fare-free public transit claim it is most convenient in small communities, because small bus agencies tend to have lower farebox recovery ratios and passenger loads. This paper presents a static model of a bus route with passenger delays, crowding and elastic demand that scales with a ``market size'' parameter. 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. Although the First-Order Conditions on fare suggest that the optimal fare should be strictly positive, we demonstrate that a zero fare may nonetheless be optimal if there are ``zero-price discontinuities,'' such as fare collection costs and other factors.

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