A contagious illness is spreading in Freedonia. Fortunately, government scientists have just discov- ered an effective vaccine. Given current raw material prices, it costs $10 to produce each dose of vaccine. Assume that Freedonia has 100 citizens, and that the demand for vaccine in the first time period is as follows: Q = 100 - where P is vaccine price and y is disease prevalence. 2.1 Assume a competitive vaccine manufacturing market and a disease prevalence of 15% (y = 0.15). How many citizens demand the vaccine this period? 2.2 After this initial round of vaccinations, demand for the vaccine plummets because many citizens have been vaccinated and do not need another vaccine. Among the unvaccinated population, demand is now: Q = 75 - P The outbreak has slowed down considerably but the prevalence is still rising. Now assume y = 0.2. How many unvaccinated citizens will demand vaccine this period? 2.3 The demand for vaccine in the third period is as follows: Q = 40. Because of the success of the vaccination campaign, disease prevalence is now 10%. How many unvaccinated citizens demand vaccine this period? 2.4 What does the price need to be for everyone to vaccinate?