Figure out Davids optimal decision strategy etc. by calculating the following (5 pts each subpart. Make sure to show your work and give explanations for decisions to get full credit. OK to show work on tree- just indicate where relevant that thats where the work is below.):

1. EV at node 10.

2. EV at node 11

3. What decision should David make at node 5? Explain your answer or no credit.

4. EV at node 6

5. EV at node 7

6. What decision should David make at node 3? Explain your answer or no credit.

7. EV at node 8

8. EV at node 9

1. What decision should David make at node 4? Explain your answer or no credit.

10. What is the EV at node 2?

11. What decision should David make at node 1? Explain or no credit.

50. What is the EV without SI?

1000. What is the EV with SI?

14. What is the EV of SI?

• Without taking the cost of hiring a consultant into account, what should Davids decision strategy be?

16. Suppose the consultant will charge $25,000 for his report. In this case would David still make the same decision at node 1 as he had earlier? Explain your answer or no credit.

17. What is Davids optimal decision strategy taking the cost of hiring a consultant into account?

18. What is the EV WITHOUT PI?

19. What is the EV WITH PI?

20. What is the EV OF PI?

21. What is the efficiency of the sample information in Davids case?

3. David's rich aunt died and left him a sizable inheritance. He thought about keeping her portfolio of investments just as she had left it since she ended up so rich, but he realized that as an old lady, she invested in more conservative instruments as she got older. David is young and optimistic, so he thought he might try a more aggressive portfolio, particularly investing in new technologies. His decision alternatives at this point are to keep the portfolio as is (D1), or to invest more aggressively (D2), even though that has greater risk. He developed the following payoff table (in $1000s), with S1 and 52 the state of new technological developments being strong (S1) or weak (S2) in the coming year. David decided that the probability of new technological developments being strong this year was 0.6. D1 D2 S1 150 500 S2 200 -100 After some thought, David thought that his business background wasn't specific enough in the tech area for him to make meaningful decisions, so he considers hiring a consultant with expertise in the tech area to help him out. To decide if he should hire the consultant - or not-he developed the following decision tree after doing some research on the consultant's past recommendations (and of course using Bayes' rule). (Favorable report means favorable to a more aggressive portfolio Profit Payoff s1 F 0.87_ 150 D1 S2F 0.13 200 Favorable report issued P(F) =0.68 S1 F 0.87 S2F 0.13 Hire Consultant si lu 0.16 D1 S2U 0.84 Unfavorable report issued PU) = 0.324 siu 0.16 500 S2U 0.84 0.6 Do not hire consultant 0.6 500 0.4 -100 3. David's rich aunt died and left him a sizable inheritance. He thought about keeping her portfolio of investments just as she had left it since she ended up so rich, but he realized that as an old lady, she invested in more conservative instruments as she got older. David is young and optimistic, so he thought he might try a more aggressive portfolio, particularly investing in new technologies. His decision alternatives at this point are to keep the portfolio as is (D1), or to invest more aggressively (D2), even though that has greater risk. He developed the following payoff table (in $1000s), with S1 and 52 the state of new technological developments being strong (S1) or weak (S2) in the coming year. David decided that the probability of new technological developments being strong this year was 0.6. D1 D2 S1 150 500 S2 200 -100 After some thought, David thought that his business background wasn't specific enough in the tech area for him to make meaningful decisions, so he considers hiring a consultant with expertise in the tech area to help him out. To decide if he should hire the consultant - or not-he developed the following decision tree after doing some research on the consultant's past recommendations (and of course using Bayes' rule). (Favorable report means favorable to a more aggressive portfolio Profit Payoff s1 F 0.87_ 150 D1 S2F 0.13 200 Favorable report issued P(F) =0.68 S1 F 0.87 S2F 0.13 Hire Consultant si lu 0.16 D1 S2U 0.84 Unfavorable report issued PU) = 0.324 siu 0.16 500 S2U 0.84 0.6 Do not hire consultant 0.6 500 0.4 -100