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An agency is having problems with personal phone calls made during working hours
An agency is having problems with personal phone calls made during working hours. Each minute of a personal call costs the agency $0.11 in wasted wages. The agency decides to hire operators to monitor calls in order to attain the optimal number of personal calls (minimize total cost of personal calls).
| Number of Operators | Total Minutes of Personal Calls (per hour) |
|---|---|
| 0 | 1200 |
| 1 | 975 |
| 2 | 825 |
| 3 | 725 |
| 4 | 650 |
| 5 | 600 |
| 6 | 570 |
A. What is the most the agency would be willing to pay the first operator?
B. If operators are paid $10.75 an hour, how many operators should the agency hire?
Expert Solution
| Number of Operators | Total Minutes of Personal Calls (per hour) | Marginal Product of Operator (reduction in minutes of personal calls) | Marginal Value Added ($) |
|---|---|---|---|
| 0 | 1200 | - | - |
| 1 | 975 | 225 | 24.75 |
| 2 | 825 | 150 | 16.5 |
| 3 | 725 | 100 | 11 |
| 4 | 650 | 75 | 8.25 |
| 5 | 600 | 50 | 5.5 |
| 6 | 570 | 30 | 3.3 |
A. $24.75
As shown above, the first operator reduced the amount of personal calls by 225 minutes per hour which is adds a value of $0.11*225=$24.75 and this is the maximum they would be willing to pay.
B: 3 Operators
The company will hire any operator until they add less value than their wage. In this case, the first three operators all add more value than $10.75 an hour but any further hiring does not. This means the firm will only hire 3 operators.
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