Problem 13-19 (Algorithmic) Hale\'s TV Productions is considering producing a pi
ID: 419615 • 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 $200,000. Hale's decision alternatives and profits (in thousands of dollars) are as follows State of Nature Reject, Si -150 200 1 Year, S2 2 Years, S3 Decision Alternative Produce pilot, d Sell to competitor, d2 150 450 200 200 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 $45,000, 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: P(SIF) = 0.05 P(S21F) = 0.28 P(S3lF)-0.67 P(S1IU) 0.47 P(S2lU) 0.32 PS3W) = 0.21 P(F) 0.63 P(U)-0.37Explanation / Answer
b. If an agency is not used, the EV is
for d1 = -150x0.2+150x0.3+ 450x0.5 =240
For d2 = 200
Hence the decision is to produce.
e. EV of agency's information
Favorable scenario with d1 = -150x0.05+150x0.28+ 450x0.67 = -7.5+42+301.5 =336
Favourable scenario with d2 = 200
Hence favorable scenario with d1 is acceptable
Unfavorable scenario with d1 =-150x.47+150x0.32+450x0.21 = 213
Unfavorable scenario with d2 = 200
Hence unfavorable sceanrio with d1 is acceptable
EV with agency = 336x0.63+213x0.37 =211.68+144.84 = 356.52
Since $45000 need to be paid to the agency, the net EV = 356520-45000 = 311520
Which is more than EV without agency. Hence paying $45000 t the agency is justified.
The maximum that can be paid to the agency is 356520-240000 = 116520
EV with perfect information with / without agency = 450
(b) EV of PI without agency = 450- 240 = 210 thousands
EV of PI with agency = 450000-311520 = 138480
= $138 thousand