Question

Philip Musa can build either a large video rental section or a small one in his Birmingham drugstore. He can also gather additional information or simply do nothing. If he gathers additional​ information, the results could suggest either a favorable or an unfavorable​ market, but it would cost him ​$4 comma 000 to gather the information. Musa believes that there is a​ 50-50 chance that the information will be favorable. If the rental market is​ favorable, Musa will earn ​$14 comma 000 with a large section or ​$6 comma 000 with a small. With an unfavorable​ video-rental market,​ however, Musa could lose ​$21 comma 000 with a large section or ​$12 comma 000 with a small section. Without gathering additional​ information, Musa estimates that the probability of a favorable rental market is 0.8. A favorable report from the study would increase the probability of a favorable rental market to 0.9. ​Furthermore, an unfavorable report from the additional information would decrease the probability of a favorable rental market to 0.3. Of​ course, Musa could ignore these numbers and do nothing. What is your advice to​ Musa? Choose the correct decision tree below.

Answer 1

Answer:

The expected payoff is $ 6200

Explanation:

With more information

For favorable outcome,

EV of large = 0.9 × 10000 + 0.1 × (-29000) = 6100

EV of small = 0.9 × 1000 + 0.1 × (-14000) = -500

EV of nothing = -4000

Max EV of node 2 (favorable) = MAX (6100, -500, -4000)   = 6100

For unfavorable outcome,

EV of large = 0.3 × 10000 + 0.7 × (-29000) = -17300

EV of small = 0.3 × 1000 + 0.7 × (-14000) = -9500

EV of nothing = -4000

Max EV of node 3 (unfavorable) = MAX (-17300, -9500, -4000)  = -4000

EV of more information = 0.5 × 6100 + 0.5 × (-4000) = 1050

With no information

EV of large = 0.8 × 14000 + 0.2 × (-25000) = 6200

EV of small = 0.8 × 5000 + 0.2 × (-10000) = 2000

EV of nothing = 0

Max EV of node 4 = MAX(6200, 2000, 0)  = 6200

EV of node 4 is the maximum. Therefore,  Philip Musa should not gather more information, and build a large video section . The expected payoff is $ 6200