QUESTION 2 Value of information

Jim is thinking about producing a new type of electric razor for men. If the market were favourable he would get a return of $100,000, but if the market were unfavourable he would lose $60,000. Jim estimates the probability of a favourable market is 0.5.
(a) What should Jerry do? Show calculations. A friend would charge him $5,000 for some market research providing one of two signals, that the market is favourable or unfavourable. His friend’s past record is such that 70% of the time he would correctly provide a favourable market prediction and 20% of the time he would incorrectly provide a favourable market prediction.
(b)Revise the prior probabilities in light of his friend’s track record.
(c)What is the posterior probability of a good market given that his friend has provided an unfavourable market prediction?
(d)What is the expected net gain or loss from engaging his friend to conduct the market research? Should his friend be engaged? Why?