Analyzing the optimization of subsidies for PPP urban rail transit projects: A choice between passenger demand, vehicle kilometer, or an improved efficiency-oriented framework

Prior to designing detailed subsidy contract terms for public-private partnerships (PPPs), local governments often face the challenge of selecting the basic modes of a subsidy (in this case, passenger demand subsidy or vehicle-kilometer subsidy). However, most studies do not discuss the reasons for choosing a particular mode or its applicability. This paper addresses this gap by constructing Stackelberg game models to analyze the characteristics of two subsidy modes: vehicle-kilometer subsidy and passenger demand subsidy. Four situations derived from these two subsidy modes are then modeled and analyzed, exploring the relationships among parameters and clarifying the strategies of local governments. Additionally, a comparison is made between the two subsidy modes to demonstrate the optimal utilization of subsidies. Based on this analysis, an efficiency-oriented subsidy framework is proposed to overcome the shortcomings of existing subsidies and provide new insights into subsidy design for PPPs. The results indicate that the vehicle-kilometer subsidy loses its incentive or regulatory effects on the private sector when the vehicle-kilometer is predetermined. Furthermore, the subsidy mode, the local government's goals, and financial stress will influence key parameters (price and vehicle-kilometer); further, the preference of both parties for subsidy modes is closely related to price. The proposed efficiency-oriented subsidy framework offers significant advantages in reducing prices, increasing consumer surplus and efficiency, conserving social resources, and strengthening cost control. This paper contributes to the literature by emphasizing the importance of selecting appropriate subsidy modes, exploring the differences between two common modes, and further providing a novel and effective subsidy mode. Further, this paper can also guide mutual parties to optimize their strategies and enhance the overall efficiency and performance in PPP urban rail transit projects.