A consumer with vNM utility function U (as) = log(:c) and initial wealth W = $500, 000 faces a probability p = 0.2 of incurring a monetary loss of d = $200, 000 in an accident. An insurance company offers him insurance at a price 7" for each dollar of coverage. That is, if he wants to get back 3: dollars in case of an accident, he must pay r3: dollars for insurance to the company up front. (a) Assume r = 0.25. How much insurance does he buy? (b) Assume now that the insurance company is a monopolist that wants to maximize expected prots. What price would the monopolist charge this consumer? (c) Now suppose the monopolist oers an insurance policy (13,33) to the consumer with :5 dollars of coverage for a total price of P. What insurance policy will the monopolist choose to maximize expected prots