to a Luce Question 1 (50p) invest $100,000 rest rate Nick Young decides to invest $100,000 primarily in the stock market. The returns from investing in pharmaceutical stocks and agriculture stocks are given in the table below. In addition, Nick also considers about putting his money in a certificate of deposit (CD) at an interest rate of 8% regardless of market scenarios. Nick estimates that the probabilities of a favorable market: a neutral market: and an unfavorable market are 4:3:3. Favorable Neutral Unfavorable Pharmaceutical stocks 13,000 10,000 -1,000 Agriculture stocks 11,000 8,000 -1,000 Now, Nick is considering paying $500 for a stock market newsletter. These types of letters could predict whether the market would be Good or Poor, and the probability of a Good: Poor indication is 48:52. Then, based on these predictions, Nick could make better investment decisions. Given a favorable market, the probability of a Good: Poor indication from the newsletter is 75:25. On the other hand, the probability of a Good: Poor newsletter is 2:8 given a neutral market scenario. The probabilities of a Good: Poor newsletter is 4:6 given an unfavorable market scenario. (a) Define the alternatives and states of nature for this problem. (10p) (b) What decision would Nick make if he wanted to minimize his expected regret? (15p) (c) Construct a decision tree to help analyze this problem. What should Nick invest in? (20p) (d) If the cost of a market newsletter increases to $750, will Nick change his decision? (5p) 84 wvorable OA utal -0,5 wable matket = 0,3 live = I nature =?