Question

An agency is having problems with personal phone calls made during working hours. Each minute of a personal call costs the agency $0.10 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	795
1	678
2	566
3	457
4	356
5	264
6	176

a.   What is the most the agency would be willing to pay the first operator?

b.   If operators are paid $9.10 an hour, how many operators should the agency hire?

c.   Assume that the cost of personal calls falls to $0.09 in wasted wages. If the operator wage is still $9.10/hour, how many operators should the agency hire now?

d.   Assume a change in the operator labor market results in operator wages rising to $9.70 an hour; with the cost of personal calls at $0.09 per minute, how would this affect the number of operators the agency should optimally hire?

Answer 1

a)

Number of Operators	Total minutes of personal calls (per hour)	Marginal Saving in personal calls on additional operator, MP	Marginal Saving, MP*waste wage per call ($0.10)
0	795
1	678	117	11.7
2	566	112	11.2
3	457	109	10.9
4	356	101	10.1
5	264	92	9.2
6	176	88	8.8

Maximum wage that can be paid to first operator=Marginal saving of first operator=$11.7 per hour.

b)Agency would increase operators as long as Marginal Saving of operator is higher than or equal to wage rate ($9.10), Marginal Saving is higher than wage rate till 5th operator. After that marginal saving is less than wage rate. So, optimal number of operators is 5.

Agency would hire 5 operators.

d)

Number of Operators	Total minutes of personal calls (per hour)	Marginal Savings in personal calls on additional operator, MP	Marginal Saving, MP*waste wage per call ($0.09)
0	795
1	678	117	10.53
2	566	112	10.08
3	457	109	9.81
4	356	101	9.09
5	264	92	8.28
6	176	88	7.92

Agency would increase operators as long as Marginal Saving of operator is higher than or equal to wage rate ($9.10), Marginal Saving is higher than wage rate till 3rd operator. After that marginal saving is less than wage rate. So, optimal number of operators is 3.

Agency would hire 3 operators.

d)

Refer to table in part c

Agency would increase operators as long as Marginal Saving of operator is higher than or equal to wage rate ($9.70), Marginal Saving is higher than wage rate till 3rd operator. After that marginal saving is less than wage rate. So, optimal number of operators is 3.

Agency would hire 3 operators.