If he thinks the chances of low, medium, and high compliance are 20%, 30%, and 50% respectively, and he uses the Expected Value criterion, how many new workers will he hire

Question Completion:

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

Investment                       Compliance

                               Low   Medium   High

1                                50         50        50

2                              100         60        20

3                              150         70      - 10

Chances of             20%       30%    50%

He will hire 1 new worker.

Explanation:

a) Data and Calculations:

Investment                       Compliance

                               Low   Medium   High    Expected Net Revenue

1                                50         50        50                 $50

2                              100         60        20                 $48

3                              150         70      - 10                  $46

Expected net revenue:

With 1 worker, expected values = 50*20% + 50*30% + 50*50% = 50

With 2 workers, expected values = 100*20% + 60*30% + 20*50% = 48

With 3 workers, expected values = 150*20% + 70*30% + -10*50% = 46

b) By hiring only 1 new worker, the expected net revenue is maximized at $50 instead of $48 and $46 with 2 and 3 workers respectively.  The expected values are obtained by weighing the outcomes with the probabilities of the events occurring, and then totaling each option.  The option that yields the greatest revenue is chosen.