Question

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: State of Nature Decision Alternative Reject, Si 1 Year, S2 2 Years, S3 -100 50 250 Produce pilot, di Sell to competitor, d2 150 150 150 The probabilities for the states of nature are P(51) = 0.20, P(S2) = 0.30, and P(53) = 0.50. For a consulting fee of $10,000, 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(F) = 0.65 P(S1|F) = 0.06 P(S1U) = 0.47 PU) = 0.35 P(S21F) = 0.25 P(S2|U) = 0.38 P(S31F) = 0.69 P(SBU) = 0.15 a. Choose the correct decision tree for this problem.
The option for A is graph 1,2,3, or 4. For B C and D, the options are produce or sell. For F it is either yes or no.

Answer 1

(a) The correct decision tree is (iv)

0.06 S1 -100 -100 -100 di 0.25 S2 50 0 179 50 50 0.65 Favorable (F) 0.69 S3 250 0 179 250 250 d2 150 150 150 0.47 si Consult -100 0 168.850 -100 -100 di 0.38 S2 50 0 9.5 50 50 0.35 Unfavorable (U) 0.15 S3 2 250 0 150 250 250 150 168.85 150 150 0.2 S1 -100 -100 -100 0.3 S2 di + 50 0 120 50 50 Don't consult 0.5 S3 2 250 150 250 250 d2 150 150 150

(b)

For agency option not used: The recommended decision = Sell (d₂)

Expected payoff = $ 150 thousand

(c)

EVPI = EVUPI - max. EMV = 0.2*Max(-100, 150) + 0.3*Max(50, 150) + 0.5*Max(250, 150) - 150 = $ 50 thousand

(d)

With agency information:

If favorable: Produce pilot (d₁)
If unfavorable: Sell (d₂)

(e)

EVSI = EV with the agency option - EV w/o the agency option = 168.85 - 150 = $ 18.85 thousand

(f)

Yes, becasue the maximum that can be paid is the EVSI i.e. $ 18.85 thousand