An agency is having problems with personal phone calls made during working hours
ID: 1163167 • Letter: A
Question
An agency is having problems with personal phone calls made during working hours. Each minute of a personal call costs the agency $0.15 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
1260
1
1090
2
950
3
830
4
730
5
640
6
570
What is the most the agency would be willing to pay the first operator?
If operators are paid $15 an hour, how many operators should the agency hire?
Assume that the cost of personal calls temporarily rises to $0.125 in wasted wages. If the operator wage is still $15/hour, how many operators should the agency hire now?
Assume a change in the operator labor market results in operator wages falling to $13 an hour; with the cost of personal calls back at the original $0.15 per minute, how would this affect the number of operators the agency should optimally hire? (I.e., what is the new optimal number in this scenario?)
Number of Operators
Total minutes of personal calls
(per hour)
0
1260
1
1090
2
950
3
830
4
730
5
640
6
570
Explanation / Answer
The most the agency would be willing to pay the first operator = (1260- 1090) * 0.15 = $25.5
If operators are paid $15 an hour, the agency should hire the number of operators at which the Marginal benefit from hiring an operator is equal to Marginal Cost ($15)
Hence, at number of operators = 4 we get MB= (830-730) * 0.15 = $15 =MC
Thus, hire 4 operators.
When the cost changes to $0.125 then at number of operators = 3 we get MB = (950-830) * 0.125 = $15 = MC
Thus, hire 3 operators.
Now MC =$13.
So, in this case 5 operators will be hired because MB = (730-640) *0.15 = $13.5
Since, this is closest to MC=$13 and we cannot employ a fraction of an operator, hence 5.
Thus hire 5 operators
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