1. Problem: Resource demand
Suppose a firm's short-run total product schedule is given in the table below. It sells its output in a competitive market for $1.50 per unit.
|
Labor
|
Total Product
|
Marginal Product
|
Marginal Revenue Product
|
|
0
|
0
|
|
|
|
1
|
8
|
|
|
|
2
|
18
|
|
|
|
3
|
29
|
|
|
|
4
|
39
|
|
|
|
5
|
47
|
|
|
|
6
|
52
|
|
|
|
7
|
53
|
|
|
|
8
|
53
|
|
|
a. What is the marginal product of the first worker?
b. What is the marginal revenue product of the first worker?
c. Fill in the rest of the table. How many workers will this firm hire at a wage of $7?
d. If the wage rises to $9, how will the firm adjust its employment?
e. Alternatively, suppose the firm sells its output according to the following demand schedule:
|
Labor
|
Total Product
|
Product Price
|
Total Revenue
|
Marginal Revenue Product
|
|
0
|
0
|
----
|
|
|
|
1
|
8
|
$3.50
|
|
|
|
2
|
18
|
2.80
|
|
|
|
3
|
29
|
2.30
|
|
|
|
4
|
39
|
1.90
|
|
|
|
5
|
47
|
1.65
|
|
|
|
6
|
52
|
1.50
|
|
|
|
7
|
53
|
1.40
|
|
|
f. Fill in the remaining two columns of the table. How many workers will be hired at a wage of $7?
2. Problem: Optimal combination of resources
Suppose a firm's marginal product of capital and marginal product of labor schedules are as shown in the table below. The firm hires both capital and labor competitively for $4 and $8, respectively. Its output is sold in a competitive market for $.50 per unit.
|
Capital
|
MP of Capital
|
Labor
|
MP of Labor
|
|
0
|
|
0
|
|
|
1
|
10
|
1
|
28
|
|
2
|
9
|
2
|
30
|
|
3
|
8
|
3
|
24
|
|
4
|
7
|
4
|
20
|
|
5
|
6
|
5
|
16
|
|
6
|
5
|
6
|
12
|
|
7
|
4
|
7
|
8
|
|
8
|
3
|
8
|
4
|
a. Suppose the firm is currently using 4 units of capital and 4 units of labor. Is the corresponding output being produced at least cost? How do you know?
b. What combination of labor and capital should the firm use to maximize its profit?
c. If the marginal product of each resource does not depend on the quantity of the other resource, what output level corresponds to the input combination you just found? Does this combination produce this output level at least cost?Problem:Labor markets: competition and monopsony
Suppose a firm hiring from a competitive labor market has the marginal revenue product schedule as given in the first two columns of the table below:
3. Problem: Suppose a firm hiring from a competitive labor market has the marginal revenue product schedule as given in the first two columns of the table below:
|
Labor
|
Marginal Revenue Product
|
Wage Rate
|
Total Labor Cost
|
Marginal Labor Cost
|
|
0
|
$ 0
|
|
|
|
|
1
|
20
|
$ 6
|
|
|
|
2
|
24
|
8
|
|
|
|
3
|
28
|
10
|
|
|
|
4
|
24
|
12
|
|
|
|
5
|
18
|
14
|
|
|
|
6
|
12
|
16
|
|
|
|
7
|
6
|
18
|
|
|
a. If this firm can hire labor competitively at a wage of $16, how many workers will it hire?
Alternatively, suppose the firm has monopsony power such that it must pay $6 to hire the first worker and must increase the wage rate by $2 to attract each successive worker, as shown in the third column of the table above.
b. What is the total labor cost of hiring one worker? Of two workers? What is the marginal labor cost of the second worker?
c. What is the total labor cost of hiring three workers? What is the marginal labor cost of the third worker? Fill in the remainder of the final two columns.
d. What level of employment maximizes this firm's profit?
e. What wage rate will the firm pay to attract the profit-maximizing number of workers? Compare this outcome with that in part a.