The Maryland Department of Public Health wants to avert a possible West Nile Virus epidemic. There is a new vaccine that can provide effective protection. The supply curve for the vaccine (measured in millions of doses) is given by the following equation: QS =0.10+0.02P, where P is the price per vaccine dose in U.S. dollars. In deciding whether to have a shot, each person considers the personal benefit of not getting the virus. The total private demand for shots is given by the following demand function: QP =0.80-0.02P. But each person who gets a shot reduces the chance that other, non-vaccinated individuals will get the virus. When this benefit is included, the demand function for society is QSOC=0.90-0.02P. NOTE: QS , QP , and QSOC are measured in millions of doses and P is measured in U.S. dollars.

a. What is the market equilibrium using the private demand function (please provide detailed, step by step solution) ?