There are 250 people on an island. Each person can be vaccinated against smallpox at no cost. Receiving the vaccine entails a 1 percent chance of serious illness; serious illness inflicts a cost 5. Given that 11 persons are vaccinated, the probability of an outbreak of smallpox is 1 - (M250). In an outbreak of smallpox, every individual who is not vaccinated catches smallpox and suffers the cost 6, while every person who is vaccinated does not catch the disease. a) What is the socially optimal (from the utilitarian viewpoint) number of individual that should receive the vaccine? How large is the probability of an outbreak of smallpox? b) If left to their own devices, how many people will choose to receive the vaccine? How large is the probability of an outbreak of smallpox? What is the social cost of an outbreak? c) Is government intervention justified in the case of infectious diseases? Discuss