For the payoff table below, the decision maker will use P(s1) = .15, P(s2) = .5, and P(s3) = .35.
s1 s2 s3
d1 -5000 1000 10,000
d2 -15,000 -2000 40,000
a. (15 pts) What alternative would be chosen according to expected value?
First you have to figure out the expected monetary value so you would do the following calculations…
D1=(.15*-5000)+(.5*1000)+(.35*10000)=3500
D2=(.15*-15000)+(.5*-2000)+(.35*40000)=10,750
If you choose the best alternative with the highest expected value or payout, the answer would be d2.
b. (10 pts) For a lottery having a payoff of 40,000 with probability p and -15,000 with probability (1-p), the decision maker expressed the following indifference probabilities.
Payoff Probability
10,000 .85
1000 .60
-2000 .53
-5000 .50
Let U(40,000) = 10 and U(-15,000) = 0 and find the utility value for each payoff.
The formula for finding the utility value of a certain payoff is U(M)=[p*(max payoff]+[(1-p)*U(min payoff)]
So we start with 10,000…
U(10,000)=[.85*10]+[(1-.85)*0] which is equal to 8.5
If we do this for all the different payoffs we will get the following utility values:
The Utility value of 10,000 would be 8.5
The Utility Value of 1,000 would be 6
The Utility Value of -2,000 would be 5.3
The Utility Value of -5,000 would be 5
(15 pts) What alternative would be chosen according to expected utility?
The alternative that would be chosen according to expected utility is the utility value of 10,000, which is 8.5.