A terrible disease called fictitia is ravaging the woebegone nation of Pcoria. Fortunately, government scientists have just discovered the formula for an effective vaccine. Given current raw material prices, it costs $ 10 to produce each dose of vaccine.

Assume that Pcoria has 100 citizens, and that the demand for vaccine in the first time period is

where P is vaccine price and γ is disease prevalence.

a. Assume a competitive vaccine manufacturing market and a disease prevalence of 20% (γ = 0.2). How many citizens demand the vaccine this period?

b. 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

The fictitia outbreak has slowed down considerably but the prevalence is still rising.

Now assume γ = 0.25. How many unvaccinated citizens will demand vaccine this period?

c. The demand for vaccine in the third period Q = 40 − P/γ. Because of the success of the vaccination campaign, disease prevalence is now 10%. How many unvaccinated citizens demand vaccine this period?

d. What does the price need to be for everyone to vaccinate?

e. The Pcorian parliament appropriates funds for a vaccine subsidy in an attempt to wipe out fictitia once and for all. If they subsidize manufacturers by the full production cost of the vaccine, what price will consumers face? Will everyone decide to vaccinate?

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Q=100- P Y