Should public sectors be complements of private sectors?

This paper discusses competition between high-quality private service providers that maximize their own profits and a low-quality public service provider that maximizes social surplus. There are two heterogeneous consumer groups: those who demand only high-quality services and those who care little whether services are highor low-quality. The setting reflects the fact that some consumers feel dissatisfaction with public service providers. We show that, under certain conditions, social welfare is smaller when there is a public service provider than when there is not. The result holds even though the efficiency of the public service is equal to that of the private services.