5. Health Insurance Consider a society with three types of individuals according to their lifestyle: healthy, average and unhealthy. The probability of getting sick in a year of each type is, respectively: 0.05, 0.25 and 0.75. Assume that each individual starts with income equal to Y = $10. Assume that if individuals get sick they automatically go to a hospital and get cured. The marginal cost for medical treatment is $4. The utility of each type is given by: U(Y) = 0.0572 Where 7 is your disposable income. Then, if you don't get sick your utility is u(= 10) = 5, but if you have to pay, say $5 for the hospital visit your utility isu(Y 105 = 5) = 3.75. The utility of not getting medical treatment is equal to 0, thus, if the expected utility is negative it is better for the consumer to not get medical treatment (is a good idea to figure out now for what price range will that be true for each consumer type). (a) Assume that the market for health care is perfectly competitive and there is no health insurance. Assume that there is a single individual of each type. Find the price for health care and the expected utility of each type. (b) Assume now that the market for health care is characterized by a monopoly and that there is a single consumer of each type. Find the optimal price of the monopolist and determine if all consumers get health care when they get sick. (c) Assume that now the population distribution is: 100 healthy, 200 average and 150 unhealthy. How will your answers for part (a) and (b) change