Second-best Monopoly Pricing in a Congested Service System

<div> Problem definition: We study pricing and regulation in a congested service system operated by a profit-maximizing monopolist, where access to a privately owned service can be priced while a public alternative remains free. This setting arises naturally in markets that combine private and public provision, such as transportation networks with tolled lanes and free roads or healthcare systems with private and public service tiers. Such environments are inherently "second best": pricing decisions at the private service affect not only paying customers but also congestion experienced by users of the free alternative, while institutional or legal constraints limit the ability to price the public channel. This interdependence creates a central regulatory challenge: how should access be controlled when monopoly pricing in one part of the system generates spillover congestion elsewhere? </div> <div> Methodology/results: We develop a stylized model in which strategic customers choose, based on price and waiting costs, between two M/M/1 queues: a priced server operated by a revenue-maximizing monopolist and a free alternative. We characterize equilibrium outcomes under monopoly pricing and compare them with both the socially optimal allocation and the unregulated, free access case. Monopoly pricing distorts system performance by restricting access to the priced server and shifting congestion to the free server, exploiting cross-server congestion spillovers. As a result, monopoly pricing can lead to higher social cost not only relative to the social optimum but even compared to unregulated access, and the inefficiency gap can become arbitrarily large. We then introduce a simple regulatory mechanism—the q-control mechanism—that requires a fixed fraction q of customers to be admitted at a regulated price. This mechanism reshapes the monopolist’s incentives by limiting its ability to extract revenue through congestion spillovers. We characterize how the optimal choice of q depends on system parameters and show that the mechanism can mitigate monopoly distortions and even restore the first-best outcome. <br> Managerial implications: Our findings highlight the key limitations of relying on monopoly pricing to manage congestion in second-best service systems with mixed public–private provision, where pricing tools are institutionally constrained. When pricing power is concentrated in the hands of a single operator, tolls may be used not only to ration access but also to shift <br> congestion toward unpriced alternatives, worsening overall performance. Rather than regulating prices directly or subsidizing capacity, regulators can improve efficiency by shaping the composition of demand. In particular, price concessions—often introduced for equity—can also serve as an operational tool: guaranteeing a fraction of users access at regulated terms can discipline monopoly incentives, reduce congestion spillovers, and improve system performance. </div>