Question: A consumer with vN-M utility function U(r) = log(r) and initial wealth W-$500,000 faces a probability p = 0.2 of incurring a monetary loss

A consumer with vN-M utility function U(r) = log(r) and initial wealth

A consumer with vN-M utility function U(r) = log(r) 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 r for each dollar of coverage. That is, if he wants to get back z dollars in case of an accident, he must pay rz 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 profits. In particular, she sets a price r and the consumer pays rr dollars for r dollars coverage, as before. What price would the monopolist charge this consumer? (c) Now suppose the monopolist offers an insurance policy (P, r) to the consumer with a dollars of coverage for a total price of P. What insurance policy will the monopolist choose to maximize expected profits?

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