Problem 13-19 (Algorithmic) Hale\'s TV Productions is considering producing a pi
ID: 418778 • Letter: P
Question
Problem 13-19 (Algorithmic)
Hale's TV Productions is considering producing a pilot for a comedy series in the hope of selling it to a major television network. The network may decide to reject the series, but it may also decide to purchase the rights to the series for either one or two years. At this point in time, Hale may either produce the pilot and wait for the network's decision or transfer the rights for the pilot and series to a competitor for $150,000. Hale's decision alternatives and profits (in thousands of dollars) are as follows:
The probabilities for the states of nature are P(S1) = 0.20, P(S2) = 0.30, and P(S3) = 0.50. For a consulting fee of $5,000, an agency will review the plans for the comedy series and indicate the overall chances of a favorable network reaction to the series. Assume that the agency review will result in a favorable (F) or an unfavorable (U) review and that the following probabilities are relevant:
Choose the correct decision tree for this problem.
What is the recommended decision if the agency opinion is not used? What is the expected value? Enter your answer in thousands of dollars.
Recommended decision
Expected Value = $ thousands.
What is the expected value of perfect information? Enter your answer in thousands of dollars.
EVPI = $ thousands.
What is Hale's optimal decision strategy assuming the agency's information is used?
If Favorable
If Unfavorable
What is the expected value of the agency's information? Round your answer to two decimal places. Enter your answer in thousands of dollars.
EVSI = $ thousands.
Is the agency's information worth the $5,000 fee? What is the maximum that Hale should be willing to pay for the information?
Decision
Hale should pay no more than $ thousands. Round your answer to two decimal places. Enter your answer in thousands of dollars.
What is the recommended decision?
Explanation / Answer
The correct decision tree is (iv).
First the company will take decision whether to use agency or not. (decision node 1)
IF agency is used, then there are two outcomes/events favorable and unfavorable (event node 2). If the result of favorable the producer can decide whether to produce or sell (decision node 3). For any of these decision, the state of nature will be rejected, purchased fo 1 year or 2 years(event node 6, 7). Similarly, is the case if the result are unfavorable.
IF agency is not used, the producer can decide whether to produce or sell (decision node 5). For any of these decision, the state of nature will be rejected, purchased fo 1 year or 2 years (event node 10, 11).
The calulation of expected value at nodes are as follows:
Chance node No.
Agency Favorable
Prob.
0.08
0.28
0.64
Conditional Payoff
Event
S1
S2
S3
S1
S2
S3
EMV
6
d1
-100
50
250
-8
14
160
166
7
d2
150
150
150
12
42
96
150
Chance node No.
Agency result Unfavorable
Prob.
0.45
0.33
0.22
Conditional Payoff
Event
S1
S2
S3
S1
S2
S3
EMV
8
d1
-100
50
250
-45
16.5
55
26.5
9
d2
150
150
150
67.5
49.5
33
150
Chance Nodes
No Agency
Prob.
0.2
0.3
0.5
S1
S2
S3
Conditional Payoff
EMV
10
d1
-100
50
250
-20
15
125
120
11
d2
150
150
150
30
45
75
150
Calculating of EMV at Decision Nodes 3, 4, and 5
Decision Nodes
EMV
Decision
3
= Max EMV (6,7)
= Max (166, 150)
= 166
d1
4
=Max EMV (8, 9)
= Max (26.5, 150)
= 150
d2
5
=Max EMV (10, 11)
= Max (120, 150)
= 150
d2
Calculating of EMV at Chance Node 2
EMV = 0.67 x EMV(3) + 0.33 x EMV (4) = 0.67 x 166 + 0.33 x 150 = 160.7
Calculating EMV at decision node 1
EMV = Max EMV (2, 5) = Max (160.7, 150) = 160.7
Decision: Consider Agency information and if the results are favorable consider decision d1 (produce). But if results are unfavorable consider decision d2 (sell to competitor)
What is the recommended decision if the agency opinion is not used? What is the expected value?
Recommended decision: d2 (sell) (decision node 5)
Expected Value = $150 thousands.
What is Hale's optimal decision strategy assuming the agency's information is used?
If Favorable, decision - d1: produce (decision node 3)
If Unfavorable, decision - d2: sell (decision node 4)
What is the expected value of the agency's information? Round your answer to two decimal places. Enter your answer in thousands of dollars.
EVSI = EV of decision using agency – EV of decision not using agency
EVSI = 160.7 – 150 = 10.7
EVSI = $ 10.7 thousands = $10,700
Is the agency's information worth the $20,000 fee? What is the maximum that Hale should be willing to pay for the information?
Decision (yes/no): No (fee is more than EVPI of using agency)
Hale should pay no more than $ 10.7 thousands.
What is the recommended decision?
no agency; produce the pilot
Chance node No.
Agency Favorable
Prob.
0.08
0.28
0.64
Conditional Payoff
Event
S1
S2
S3
S1
S2
S3
EMV
6
d1
-100
50
250
-8
14
160
166
7
d2
150
150
150
12
42
96
150