question archive The local operations manger for the IRS must decide whether to hire 1, 2, or 3 temporary workers

The local operations manger for the IRS must decide whether to hire 1, 2, or 3 temporary workers

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The local operations manger for the IRS must decide whether to hire 1, 2, or 3 temporary workers. He estimates that net revenues (in thousands) will vary with how well taxpayers comply with the new tax code.

# of workers Low Compliance Medium Compliance High Compliance
1 50 50 50
2 100 60 20
3 150 70 -10

1. If he uses the maximin criterion, how many new workers will he hire?

2. If he uses the minimax regret criteria, how many workers will he hire?

3.If he thinks the chances of low, medium, and high compliance are 20%, 30%, and %50%, resepectively, what are the expected net revenue for the number of workers he will decide to hire?

4. If he thinks the chances of low, medium, and high compliance are 20%, 30%, and 50%, respectively, what is the expected value of perfect information?

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Answer:

1.

# of workers Low Compliance Medium Compliance High Compliance Maximin
1 50 50 50 50
2 100 60 20 20
3 150 70 -10 -10

Using the maximin criteria, he will hire 1 worker.

2.

# of workers Low Compliance Medium Compliance High Compliance Minimax
1 50 50 50 50
2 100 60 20 100
3 150 70 -10 150

Using the minimax regret criteria , he will hire 1 worker.

3.

# of workers Low Compliance Medium Compliance High Compliance EV
1 50 50 50 50
2 100 60 20 48
3 150 70 -10 46
Probabilities 0.2 0.3 0.5  

The expected net revenue will be 50.

4.

# of workers Low Compliance Medium Compliance High Compliance
1 50 50 50
2 100 60 20
3 150 70 -10
Probabilities 0.2 0.3 0.5

EVwPI = 0.2*150+0.3*70+0.5*50= 76.

EVPI = EVwPI - EVwoPI = 76 - 50 = 26

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