You are considering buying a new house that costs $300K. With probability 0.2 the roof will have to be replaced immediately. With probability 0.5 it will have to be replaced in 10 years. Otherwise it will last 20 years. A new roof costs $20K and will last 20 years. An alternate house costs $310K, but has just had a new roof put in. You have a discount rate of 10%. You are indifferent between the houses, so you want the house with the lowest expected cost.
a. If you are risk neutral, what is the value of information on the state of the roof?
b. If you have utility ln (w) and current wealth equal to $500K, what is the value of information on the state of the roof?