ABC inc. must make a decision on its current capacity for next year. ABC is cons
ID: 442752 • Letter: A
Question
ABC inc. must make a decision on its current capacity for next year. ABC is considering three alternatives. For each alternative, estimated profits (in $000s) based on next year's demand are shown in the table below. ABC Inc. estimates that the probability of high demand is 0.7 and the probability of low demand is 0.3.
Next year's demand
Alternative High Low
A1: Expand $192 $97
A2: Subcontract $175 $125
A3: Do Nothing $147 $120
Suppose there is a clairvoyant who can predict the demand perfectly (the clairvoyant's prediction is always correct). You want to know how much this clairvoyant's prediction worth. In order to do so, you need to first calculate parts a and b.
1a. Calculate the expected value with perfect information.
1b. Calculate the value without perfect information.
1c. Calculate the expected value of perfect information.
Explanation / Answer
1) a)
Demand High Low
Expand $192 $97
Subcontract $175 $125
Do Nothing $147 $120
Selecting the maximum outcome = $192 * $0.70 + $125 * 0.30
Expected value with perfect information=$134.40 +$37.50
=$171.90
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1b) Expand = $192* 0.7= 134.40 + $97 * 0.3 =$29.10 =$163.50
Subcontract $175*0.7 = $122.50 + $125*0.30=$37.50 = $160
Do Nothing $147 * 0.70= $102.90 + $120 * 0.30=$36 =$138.90
Selecting the maximum for combined value =$163.50
Expected Value without perfect information is $163.50
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1C) Expected value of perfect information =Expected value with perfect information - Expected Value without perfect information
Expected value of perfect information = $171.90 - $163.50=$8.40
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