This paper studies the provision of, and demand for, a public service when a private alternative is available. We link the concept of adequate resources for a public service to the availability of a private alternative, rather than to the public service's ability to meet total demand. We also consider a situation where only part of the population has access to the state service (as is, for instance, the case with subsidised housing) and formalize the concept of the poverty trap, which occurs when access to the public service is of an all or nothing type.