Problem
A consumer with vN-M utility function U(x) = log(x) 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 x dollars in case of an accident, he must pay rx dollars for insurance to the company up front.
1. Assume r = 0.25. How much insurance does he buy?
2. Assume now that the insurance company is a monopolist that wants to maximize expected profits. What price would the monopolist charge this consumer?