Question

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 $5 and $8, respectively. This assignment will be graded out of 6 points with 2 points possible for each question.

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	9	4

1. 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?

2. Consider your answer to the question above. Generally speaking, what would a firm need to do in order to move towards producing at the least cost?

3. What is the least-cost combination of labor and capital?

Answer 1

From the table, you need to calculate the ratio of marginal product of a factor and the price of the factor and follow the equimarginal principle. We know that optimum mix of two inputs involve MPL/MPK = PL/PK or MPL/PL = MPK/PK. For an optimum mix, it should be ensured that MPL/PL = MPK/PK.

Capital	MP of Capital	(MP/$) for capital	Labor	MP of Labor	(MP/$) for labor
0			0
1	10	2	1	28	3.5
2	9	1.8	2	30	3.75
3	8	1.6	3	24	3
4	7	1.4	4	20	2.5
5	6	1.2	5	16	2
6	5	1	6	12	1.5
7	4	0.8	7	8	1
8	3	0.6	9	4	0.5

1. Suppose the firm is currently using 4 units of capital and 4 units of labor. At this level we see that MPL/PL = 2.5

and MPK/PK = 1.4. Clearly MPL/PL > MPK/PK and so the corresponding output is not being produced at least cost.

For the least cost combination, more labor and less capital should be used.

2. As mentioned, a firm needs to use the more productive factor and reduce the usage of less productive factor in

order to move towards producing at the least cost. Here MPL/PL > MPK/PK and so labor is more productive than

capital. Least cost combination requires the use of more labor as it is more productive and less capital as it is less

productive.

3. What is the least-cost combination of labor and capital?

There are two combinations where MPL/PL = MPK/PK . These include K = 1, L = 5 and K = 6, L = 7. Out of these,

the least cost combination is K = 1, L = 5.