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Solutions to Problems
Chapter 14
1a. The wage rate is $6 an hour. The wage rate adjusts to make the quantity of labour demanded equal to the quantity supplied
(see figure 1).
1b. The number of pickers hired is 400 a day. At a wage rate of $6 an hour, 400 pickers a day are hired (see figure 1).
1c. The income received is $2,400 an hour.
Income = wage rate multiplied by the number of pickers
= $6x400
= $2,400 an hour
Figure 1
Figure 2
3a. Marginal product of labour is the increase in total product that results from hiring one additional student. The marginal
product of labour schedule for Wanda’s fish shop is shown in table 1 and the marginal product of labour curve (MP) derived
from this schedule is shown in figure 3.
40
35
30
25
AP
20
15
MP
10
Dollars per hour per student
Wanda’s fish shop – Problems 3, 5 & 7
45
25
20
15
10
MRP
MRP/
5
5
0
0
0
2
4
6
8
Number of students
0
2
4
6
8
Number of students
figure 3
3b. Marginal revenue product of labour is the increase in total revenue that results from hiring one additional student. The
marginal revenue product schedule for Wanda’s fish shop is shown in table 1 and the marginal revenue product curve
(MRP) derived from this schedule is shown in figure 3.
3c. Wanda’s demand for labour curve is the same as the downward sloping section of the marginal revenue product curve MRP
in figure 3.
3d. Wanda hires 7 students.
Wanda hires the number of students that makes the marginal revenue product equals to the wage rate of $7.50 an hour.
When Wanda increases the number of students from 6 to 7, marginal product is 15 kilograms of fish an hour, which Wanda
sells for 50 cents a kilogram. Marginal revenue product is $7.50—the same as the wage rate (see table 1).
Table 1  Problems 3&7
Fish sells for $0.50 per kilogram
Number of
students
Q
(Kgs per hour)
AP
(Q/L)
1
20
20.00
MP
(dQ/dL)
ARP
$(PxAP)
MRP
$(PxMP)
10.00
2
50
25.00
30
12.50
15.00
3
90
30.00
40
15.00
20.00
4
120
30.00
30
15.00
15.00
5
145
29.00
25
14.50
12.50
6
165
27.50
20
13.75
10.00
7
180
25.71
15
12.86
7.50
8
190
23.75
10
11.88
5.00
5a. Marginal product does not change (see table 3).
5b. Marginal revenue product decreases.
The new marginal revenue product schedule for Wanda’s fish shop is shown in table 3 and the marginal revenue product
curve (MRP/) derived from this schedule is shown in figure 3.
5c. Wanda's demand for labour decreases, and her demand for labour curve shifts leftward from MRP to MRP / in figure 3.
Wanda is willing to pay the students their marginal revenue product, and the fall in the price of fish has lowered their
marginal revenue product.
5d. Wanda will employ 5 students.
At the wage rate of $7.50, the number of students Wanda hires decreases as the demand for labour curve shifts leftward. The
fifth student adds $8.33 to revenue and will be employed. The sixth student adds $6.67 to revenue, less than his wage and
will not be employed (see table 3).
Table 3  Problem 5
The wage rate is $7.50
Fish sells for $0.50
per kilogram
MP
MRP
(dQ/dL)
$(PxMP)
Fish sells for $0.3333
per kilogram
MP
MRP
(dQ/dL)
$(PxMP)
Number of
students
Q
(Kgs per hour)
1
20
2
50
30
15.00
30
10.00
3
90
40
20.00
40
13.33
4
120
30
15.00
30
10.00
5
145
25
12.50
25
8.33
6
165
20
10.00
20
6.67
7
180
15
7.50
15
5.00
8
190
10
5.00
10
3.33
7a. Marginal revenue product does not change because there has been no change in the price of fish or the marginal product of
labour (see table 1).
7b. Wanda's demand for labour remains the same because marginal revenue product has not changed.
7c. Wanda will hire fewer students. At the wage rate of $10 an hour, Wanda hires the number of students that makes marginal
revenue product equal to $10 an hour. Wanda now hires 6 students—down from 7. The marginal product that results when
Wanda hires the sixth student is 20 kilograms of fish an hour, and Wanda sells this fish for 50 cents a kilogram. Marginal
revenue product of the sixth student is $10 an hour (see table 1).
9.
Wanda maximizes her profit when marginal revenue product equals the wage rate and when marginal revenue equals
marginal cost.
When the wage rate is $7.50 an hour, Wanda hires 7 students.
Marginal revenue product
= marginal product x price
= 15 x $0.50
= $7.50 an hour = wage rate.
Marginal revenue = price
= 50 cents.
Marginal cost
= Wage rate  marginal product
= $7.50  15
= 50 cents = marginal revenue.
So when Wanda hires 7 students, marginal revenue equals marginal cost and profit is maximized (see table 5.
Table 5  Problem 9
Fish sells for $0.50 per kilogram
L
(students)
Q
(Kgs per hour)
1
20
Wage rate is $7.50 per hour
MR
(price)
TVC
(LxW)
MC
(dTVC/dQ)
MRP
$(PxMP)
7.50
2
50
0.50
3
90
0.50
22.50
0.19
20.00
4
120
0.50
30.00
0.25
15.00
5
145
0.50
37.50
0.30
12.50
6
165
0.50
45.00
0.38
10.00
7
180
0.50
7.50
8
190
0.75
5.00
0.50
0.50
15.00
0.25
15.00
52.50
60.00
11. Venus installs two production lines.
The cost of the first production line is $1 million. The net present value is $1,097,052 so Venus buys the production line.
The cost of the second production line is $1 million. The net present value is $1,041,270 so Venus buys the production line.
The cost of the third production line is $1 million. The net present value is $985,488 so Venus does not buy the production
line.
Table 7  Problem 11
Interest rate 5%
Net Present
Value
Plant 1
Plant 2
Plant 3
97,052
41,270
-14,512
Cost
1,000,000
1,000,000
1,000,000
Present Value of
marginal revenue
product
Present Value of
year 1 income
Present Value of
year 2 income
1,097,052
590,000/1.05 =
561,905
590,000/1.052 =
535,147
1,041,270
560,000/1.05 =
533,333
560,000/1.052 =
507,936
985,488
530,000/1.05 =
504,762
530,000/1.052
=480,725
13. To answer this problem, we need to know the interest rate and the price that Greg expects next year. If he expects the
price to rise by a bigger percentage than the interest rate, he pumps none and waits for the higher price. If he expects
the price to rise by a smaller percentage than the interest rate, he pumps it all now. If he expects the price to rise by a
percentage equal to the interest rate, he doesn't mind how much he pumps.
14. Income of $2,400 a day is divided between opportunity cost and economic rent. Economic rent is the area above the
supply curve below the wage rate (see figure 1).