Question: Deciding to Play Golf the Value of Information The probability that it will rain on any given day is 0.25, and the probability is independent from day to day. You are trying to decide whether or not to make a tee time tomorrow to play golf. This requires a commitment on your part of turning down, say, movie tickets in favor of playing golf. If you accept the tickets, you also make the commitment not to go golfing. There is a weather forecast that signals whether it will rain tomorrow or not. There is a 0.2 probability of receiving a "rainy" forecast. There is a 0.75 probability that it rains when there is a rainy forecast and a 0.125 probability of rain when there is a "sunny" forecast. Assume you are risk neutral.
You place the following monetary values on the potential outcomes a sunny day at the golf course ($100), a rainy day at the movies ($20), a rainy day at home (-$20), and a sunny day at the movies ($0)
a. If you have no weather forecast, evaluate the expected value of planning to golf and planning to go to the movies.
b. What is the value of perfect information about tomorrows weather?
c. What is the optimal decision when you observe each type of forecast ("rainy" and sunny")?
d. Taking into account the optimal decisions from part (c), what is the value of the information communicated by the forecast?