Based upon the following data, what is the expected value of perfect information
ID: 2383191 • Letter: B
Question
Based upon the following data, what is the expected value of perfect information, assuming the probability of the state of nature that favors location A occurring is 0.50, the probability of the state of nature that favors location B occurring is 0.30, and the probability of the state of nature that favors neither location A nor location B occurring is 0.20.
Payoff Matrix
State of Nature Favors Alternative A
State of Nature Favors Alternative B
State of Nature Favors Neither Alternative A nor Alternative B
Alternative A
$88
($5)
($5)
Alternative B
($8)
$156
($8)
Alternatives A and B
$80
$151
($13)
Neither Alternative A
nor Alternative B
$0
$0
$0
Note: The values in the preceding table are shown in millions of dollars.
State of Nature Favors Alternative A
State of Nature Favors Alternative B
State of Nature Favors Neither Alternative A nor Alternative B
Alternative A
$88
($5)
($5)
Alternative B
($8)
$156
($8)
Alternatives A and B
$80
$151
($13)
Neither Alternative A
nor Alternative B
$0
$0
$0
Explanation / Answer
Alternative A - (88 * .50 ) - (5 * .30 )- (5*.20)
= 44 -1.5 - 1
= $ 41.50
Alternative B- ( -8 *.50 ) +(156 *.30)- (8*.20)
= - 4 + 46.8 - 1.6
= $ 41.20
Alternative A and B = (80*.50 )+(151*.30 )- (13*.20)
= 40 + 45.3 - 2.6
=$ 82.70
neither alternative A nor B - $0
I would recommend for alternative B -as it has a least payoff ($ 41.20).In alternative neither A nor B ,payoff is 0 because you will not go either for any alternative.
so altenrative B should be selected.expected value of perfect information is $ 41.20 million.
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