Suppose that an individual has a utility function U(c) = c 1=2 : They have 400 dollars. With probability 0.1 they get sick, which results in complete loss of their wealth (their wealth becomes 0. a. What is their expected wealth? What is their expected utility? How much would they being willing to pay for insurance which would fully cover the cost of being sick if they become ill? b. Now suppose there is a second individual who has the same wealth, and gets sick to a similar degree (loses all of their money if they get sick), but who gets sick with probability .5. What is their expected wealth? What is their expected utility? How much would they being willing to pay for insurance which would fully cover the cost of being sick if they become ill? c. Suppose an insurance company can’t tell the deference between individuals 1 and individual 2. What is the expected cost of insuring individual 1 (hint: how much wealth does the insurance company expect to lose)? The expected cost of insuring individual 2? If the insurance company believes that 75 percent of the population is like individual 1 and 25 percent are like individual 2, what is the expected cost of insurance if both of them buy it? (hint: just use the law of expected value one more time) d. If the insurance company offers the averaged plan at cost (which you just calculated), are both individuals willing to purchase the plan? Is this an example of adverse selection, or moral hazard, or neither? Is the equilibrium a pooling equilibrium or separating equilibrium?