Patrick Bateman is considering four alternatives Friday night. The payoff for ea
ID: 2906551 • Letter: P
Question
Patrick Bateman is considering four alternatives Friday night. The payoff for each opportunity will depend on economic conditions, and are represented in the payoff table below.
Poor
Average
Good
Excellent
Return videotapes
50
25
40
25
Dinner at Dorsia
80
300
20
10
Pick up friends in his limo
100
15
25
50
Design new business cards
25
75
-50
30
If the probabilities of each economic condition are 0.50, 0.15, 0.20, and 0.15, respectively, what is the EXPECT VALUE OF PERFECT INFORMATION?
Poor
Average
Good
Excellent
Return videotapes
50
25
40
25
Dinner at Dorsia
80
300
20
10
Pick up friends in his limo
100
15
25
50
Design new business cards
25
75
-50
30
Explanation / Answer
here expected value of Return videotapes
=E(Return videotapes)=50*0.5+25*0.15+40*0.2+25*0.15=40.5
E(Dinner at Dorsia)=80*0.5+300*0.15+20*0.2+10*0.15 =90.5
E(Pick up friends in his limo)=100*0.5+15*0.15+25*0.2+50*0.15=64.75
E(Design new business cards)=25*0.5+75*0.15+(-50)*0.2+30*0.15=18.25
therfore expected value without perfect information=max(40.5,90.5,64.75,18.25)=90.5
expected value with perfect information=0.5*100+0.15*300+0.2*40+0.15*50=110.5
therefore EXPECTED VALUE OF PERFECT INFORMATION
=expected value with perfect information-expected value without perfect information=110.5-90.5=20