4. Consider an insurance market with two types of people; healthy and sick. Both have wealth $10,000, and face a possible loss of $8,400, and have utility U(c) = ve. Healthy people have a probability p, = .20 of suffering this loss, while sick people have a probablety p, = .40. (a) Calculate the certainty equivalent for the lottery each type of person faces. 5 points. (b) Calculate the most each time of person would pay for full insur- ance. 5 points. (c) Calculate the actuarially fair price for each type of person. 5 points. (d) If insurance companies can tell these types of people apart, what prices should they charge? 5 points. Suppose insurance companies cannot tell these types of people apart, but know that proportion A = .90 of the population is healthy, while 1 - A = .10 is sick. (a) Is a pooling equilibrium possible? 5 points. Suppose there is a third type of person, who is very sick, and will incur the loss with certainty p = 1. (a) Calculate the most this person would pay for full insurance. 5 points. (b) Calculate the actuarial fair price for this type of person. 5 points. Suppose there is proportion of very sick people, were is small. There are therefore A(1- ) = .9(1- ) healthy people, (1 -A) (1 - ) = .1(1 - ) sick people, and very sick people