3. There is a town with 100 identical residents with initial wealth of $1000 and a utility function u = vwealth. Every person owns a car and there is a proba- bility p = .2 that a person's car will need a costly repair in a given year. If a person needs a repair, they must pay $500 to fix it. (a) What is the maximum amount that a person would be willing to pay to insure their self against the cost of repairing their car? (b) Suppose a single company exists to offer these insurance policies. What price do they charge? What are their expected profits? (c) Bonus: What is the probability that the insurance company incurs a loss in a given year