Ben owns a home in "tornado alley" in Oklahoma that is worth $100,000. In any given year, he knows that there is a 1% chance his home will be hit by a tornado. If it is, his home will be completely destroyed.
Ben's certainty equivalent of his uncertain prospect is $98,000.
a. Graph Ben's utility of wealth function and the expected value of his uncertain prospect. Label his expected utility and his certainty equivalent.
b. What is the maximum Ben will be willing to pay to insure his house? Explain.
c. Ben's town in Oklahoma is home to 999 other families, each of whom owns a $100,000 home that has a 1% chance of being destroyed and each of whom has preferences identical to Ben's. The local insurance company is considering offering tornado insurance to the residents of the town. It has determined that its administrative costs in providing such insurance would be $1,200 per policy.
How many policies will be sold? At what price? Explain.