Philip Musa can build either a large video rental section or

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 $ 3,000 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 $ 15,000 with a large section or $ 5,000 with a small. With an unfavorable video- rental market, however, Musa could lose $ 20,000 with a large section or $ 10,000 with a small section. Without gathering additional information, Musa estimates that the probability of a favorable rental market is .7. A favorable report from the study would increase the probability of a favorable rental market to .9. Furthermore, an unfavorable report from the additional information would decrease the probability of a favorable rental market to .4. Of course, Musa could ignore these numbers and do nothing. What is your advice to Musa?

Solution

there can be 4 cases.

1) Musa gather additional information and do large rental

2) Musa gather additiona info and do small rental

3) Musa dosnt gather any info and do large rental

4) Musa doesnt gather any info and do small rental

let X be the random variable denoting his profit.

case 1)

probability of favourable rental is 0.9. so probability of unfavourable rental is 0.1.

for favourable he earns $15,000 and for unfabourable he losses $20,000 for large rental.

X:                $15,000         -$20,000

P[X=x]:          0.9                   0.1

so estimated profit E[X]=0.9*15000-0.1*20000=$11,500

but there is $3000 to gather info.

so actual estimated profit is $11500-$3000=$8500

case 2)

probability of favourable rental is 0.9. so probability of unfavourable rental is 0.1.

for favourable he earns $5,000 and for unfabourable he losses $10,000 for small rental.

X:                $5,000         -$10,000

P[X=x]:          0.9                   0.1

so estimated profit E[X]=0.9*5000-0.1*10000=$3,500

but there is $3000 to gather info.

so actual estimated profit is $3500-$3000=$500

case 3)

probability of favourable rental is 0.7. so probability of unfavourable rental is 0.3.

for favourable he earns $15,000 and for unfabourable he losses $20,000 for large rental.

X:                $15,000         -$20,000

P[X=x]:          0.7                   0.3

so estimated profit E[X]=0.7*15000-0.3*20000=$4,500

case 4)

probability of favourable rental is 0.7. so probability of unfavourable rental is 0.3.

for favourable he earns $5,000 and for unfabourable he losses $10,000 for small rental.

X:                $5,000         -$10,000

P[X=x]:          0.7                   0.3

so estimated profit E[X]=0.7*5000-0.3*10000=$500

so estimated profit is large for case 1)

so it advisable for musa to gather additional info and start large video rental.