中文摘要
城市公共交通系统的补贴通常以规模经济和次优因素（例如作为替代选择的道路定价过低）为依据。我们构建了一个公共交通线路模型，其中存在用户之间（车内拥挤）、用户与车辆之间（上下车延误）以及车辆之间（拥堵）的摩擦。我们推导了利润最大化和福利最大化的供给方案。我们证明，当需求超过第一个阈值时，系统进入拥堵状态，服务频率随之下降。当需求超过第二个阈值时，服务质量的严重恶化会使公共交通线路在规模不经济的状态下运营，因而应征收庇古税而非给予补贴。这一有悖于莫林（Mohring，1972）经典法则的发现，在存在不收费的道路替代选择、且交通网络结构保持不变的条件下依然成立。我们利用伦敦皮卡迪利线的数据估计该模型，发现早高峰期间存在显著的规模不经济：在观察到的服务质量供给水平下，其规模不经济总计为每次出行−1.49英镑（最优水平下为每次出行−0.61英镑）。这些结果对当前针对最繁忙公共交通线路的补贴政策提出了质疑。
Abstract
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.