microecnmics

QUESTION 5 Some time ago ameasles outbreak began at Disneyland in Los Angeles. The outbreak is believed to be caused by an increasing number of parents in California that choose not to vaccinate their children. The vaccine is provided freely to children in the United States, but some parents worry that the vaccine might cause autism. Their worry originates with a research article published in a leading medical journal in 1998, but that article was later shown to be fraudulent. Suppose there is a small, isolated island with a population of 3000 people that are considering whether to take a vaccine. There is a small cost of taking the vaccine (for example due to the hanle of taking it and misplaced worries about autism). The blnet of taking the vaccine is that you will not get the disease. The risk of getting the disease if you have not taken the vaccine is decreasing in the number of people taking the vaccine. Let's assume that the cost of taking the vaccine is 5 utils, the suffering if you get the disease is 1000000 utils and the probability of getting measles is p = 1.11005, where n is the number of vaccinated people. Let us a]so assume that you are fully protected against measles if you take the vaccine. (A) (5 POINTS) Draw a diagram showing the payoff of not taking the vaccine when a other people are taking the vaccine. Use the same diagram to also show the payoff from taking the vaccine. It is sufcient to draw the diagram for n = 500, 1000, 1500 and so on up to 3000 (B) (5 POINTS) How many will take the vaccine in Nash equilibrium? (C) (5 POINTS) \"(hat is the total payoff for the whole population if instead 2500 people take the vaccine? Is this higher or lower than your answer to (B) and why is it so