Subsidizing and pricing private toll roads with noncontractible service quality: A relational contract approach

• Some of the private operator’s performance elements cannot be perfectly measured.
• We use noncontractible service quality to capture these performance elements.
• To improve service quality, the government needs a self-enforcing subsidy design.
• We use relational contract approach to derive the optimal subsidy and toll price.
• Some implications for practice are derived from model results.

In private toll roads, some elements of the private operator’s performance are noncontractible. As a result, the government cannot motivate the private operator to improve them through a formal contract but through a self-enforcing contract that both parties are unwilling to deviate unilaterally. In this paper, we use noncontractible service quality to capture these performance elements. By employing a relational contract approach, we aim to investigate the optimal subsidy plan to provide incentives for quality improvement. We show that government subsidy is feasible in quality improvement when the discount factor is sufficiently high and marginal cost of public funds is sufficiently small. Under feasible government subsidy, we have demonstrated the optimal subsidy plans in different scenarios. Moreover, some comparative statics are presented. Based on the derived subsidy plans, we further investigate the optimal toll price. We find that the optimal toll price generates zero surplus for the private operator and positive surplus for consumers. We then make two extensions of our model to re-investigate the government’s optimal decisions on subsidy plan and toll price when her decision sequence is changed and when government compensation is present upon termination of the relationship. Some implications for practice have been derived from our model results.