On the Benefit of Privatization in a Mixed Duopoly Service System

We consider a mixed duopoly service system with two service providers (SPs): one private and the other public. The public SP’s objective is welfare maximization, whereas the private SP is profit driven. Customers are heterogeneous in terms of their quality tastes and choose from three options, namely, joining the private queue, joining the public queue, and balking (or taking an outside option). We first consider the scenario where the private SP provides a premium service and the public SP provides a regular service. Paradoxically, we find that although the public SP’s objective is welfare maximization, welfare in the system can be less than that obtained with only profit-seeking private SPs. We further demonstrate that the maximum social welfare is achieved by partially privatizing the public SP, that is, by including both welfare and profit maximization as arguments in its objective function. In extreme cases in which the public SP’s capacity is very small, fully privatizing the public SP can be socially desirable. We then consider the alternate setting where the public SP provides a premium service and the private SP provides a regular service and obtain similar conclusions. These findings, however, rely on the assumption that an outside option exists for balking customers, and one should be cautious in generalizing to no-balking situations.