Private health care as a supplement to a public health system with waiting time for treatment

We consider an economy where most of the health care is publicly provided, and where there is waiting time for several types of treatments. Private health care without waiting time is an option for the patients in the public health queue. We show the effects of a tax (positive or negative) on private health care, and derive the socially optimal tax/subsidy. Finally, we discuss how the size of the tax might affect the political support for a high quality public health system.