Question

Suppose a chair manufacturer is producing in the short-run (with its existing plant and equipment). The manufacturer has observed the following levels of production corresponding to different numbers of workers:

Number of workers	Number of chairs
1	10
2	18
3	24
4	28
5	30
6	28
7	25

a. Calculate the marginal and average product of labor for this production function.

b. Does this production function exhibit diminishing returns to labor? Explain.

c. Explain intuitively what might cause the marginal product of labor to become negative.

Short answer

a. The marginal and average product of labor is computed in the following table.

Number of workers	Number of chairs	Marginal product	Average product
1	10	10	10
2	18	8	9
3	24	6	8
4	28	4	7
5	30	2	6
6	28	-2	4.67
7	25	-3	3.57

b. Yes, the production function shows diminishing returns to labor.

c. The marginal product of labor would become negative if the existing plant becomes overcrowded with workers.

Step-by-step solution

The explanation for part (a)

The marginal product of labor refers to the addition in output due to the employment of one extra worker.

MPL for 2nd worker, in this case, is computed below.

MPL₂ = chairs produced by 2 workers - chairs produced by 1 worker

= 18 - 10 = 8

The average product of labor refers to the output produced per unit of a worker.

APL for 2nd worker is computed below.

$APL=\frac{no.ofchairsproduced}{no.ofworkers}=\frac{18}{2}=9$

Following the above procedures, the marginal and average products of labor are computed below.

Number of workers	Number of chairs	Marginal product	Average product
1	10	10	10
2	18	8	9
3	24	6	8
4	28	4	7
5	30	2	6
6	28	-2	4.67
7	25	-3	3.57

The explanation for part (b)

The above table shows that the marginal product of labor decreases with an increase in labor employment. So the production function exhibits diminishing returns to labor.

The explanation for part (c)

The marginal product of labor will become negative if the fixed inputs become overcrowded with variable inputs. In other words, if there is no idle equipment or the existing plant becomes congested with the workers. Then the efficiency or the productivity of the additional workers would fall.