Problem: Hale's TV Productions has acquired a script for a pilot episode of a new television show. A competitor has heard of the script, and offered Hale $100,000 for the script and rights to the series concept.
If Hale decides to produce the pilot and market the series themselves, they'll face after-tax production costs of $100,000. If they then fail to sell the series to a network (s1), they'll not earn anything from the pilot. However, if a network offers them a one-year (s2) or two-year (s3) contract, they'll net a profit on their investment.
The payoff table (profit in $1000s) for Hale's TV Production follows:
|
|
States of Nature
|
|
s1
|
s2
|
s3
|
|
Decision Alternatives
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Produce Pilot
|
d1
|
-100
|
50
|
150
|
|
Sell to Competitor
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d2
|
100
|
100
|
100
|
|
Probability of States of Nature
|
0.2
|
0.3
|
0.5
|
For a consulting fee of $5000, an agency will review the plans for the comedy series and indicate the overall chance of a favorable network reaction to the series. Assume that the agency review will result in a faorable (F)or an Unfavorable (U) review, and that the following probabilities are relevant.
P(F) = .3, P(s1| F)=0.09 P(S1| U) = 0.45
P(U)=0.31 P(S2| F) =0.26, P(S2| U) = 0.39
P(S3| F) 0.65 P(S3| U) = 0.16
A. Construct a decision tree from this problem
B. What is the recommended decision if the agency opinion is not used? What is the expected Value?
C. What is the expected value of the perfect information”
D. What is Hale’s optimal decision strategy assuming the agency’s information is used?
E. What is the expected value of the agency’s information?
F. Is the agency’s information worth $5000 fee? What is the maximum that Hale should be willing to pay for the information?
G. What is the recommend decision?