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Problem 14.1 - Resource demand

Problem:

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?

Problem 14.2 - Optimal combination of resources

Problem:

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?