Question

An agency is having problems with personal phone calls made during working hours. Each minute of a personal call costs the agency $0.25 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)

# of operators total mins of personal calls per hour

0 685

1 585

2 500

3 430

4 380

5 345

6 320

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

b. If operators are paid $17.25 an hour, how many operators should the agency hire?

c. Assume that the cost of personal calls temporarily falls to $0.21 in wasted wages. If the operator wage is still $17.25/hour, how many operators should the agency hire now?

d. Assume a change in the operator labor market results in operator wages falling dramatically to $8.75 an hour; with the cost of personal calls going back to the original $0.25 per minute, how would this affect the number of operators the agency should optimally hire?

Answer 1

a)

Savings in personal calls at the addition of first operator=(685-585)=100 minutes/hour

Cost of a call (wasted wages)=$0.25 per minute

Savings due to first operator=100*0.25=$25

Agency can pay a maximum of $25 as wages to first operator.

b) We can calculate savings in wage wasted due to personal calls with the help of operator added as under

# of operators	Total minutes of personal calls per hour	Marginal Product of operator	Hourly Savings @$0.25 per minute	Wage rate, $/hr
0	685
1	585	100	25.00	17.25
2	500	85	21.25	17.25
3	430	70	17.50	17.25
4	380	50	12.50	17.25
5	345	35	8.75	17.25
6	320	25	6.25	17.25

We find that savings per hour is higher than the wage rate till 3rd operator. After that savings are less than wage rate. There is effectively no saving by adding 4th operator.

Agency should hire 3 operators.

c)

We get the following observations in this case

# of operators	Total minutes of personal calls per hour	Marginal Product of operator	Hourly Savings @$0.21 per minute	Wage rate, $/hr
0	685
1	585	100	21.00	17.25
2	500	85	17.85	17.25
3	430	70	14.70	17.25
4	380	50	10.50	17.25
5	345	35	7.35	17.25
6	320	25	5.25	17.25

We find that savings per hour is higher than the wage rate till 2nd operator. After that savings are less than wage rate. There is effectively no saving by adding 3rd operator.

Agency should hire 2 operators.

d)

We get the following observations in this case

# of operators	Toal minutes of personal calls per hour	Marginal Product of operator	Hourly Savings @$0.25 per minute	Wage rate, $/hr
0	685
1	585	100	25.00	8.75
2	500	85	21.25	8.75
3	430	70	17.50	8.75
4	380	50	12.50	8.75
5	345	35	8.75	8.75
6	320	25	6.25	8.75

We find that savings per hour is higher than or equal to the wage rate till 5th operator. After that savings are less than wage rate. There is effectively no saving by adding 6th operator.

Agency should hire 5 operators.