Suppose a furniture manufacturer is producing in the short run (with its existin

Question

Suppose a furniture 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 (L) Pairs of shoes (Q)
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) Indicate the points that delineate the three stages of production.
(c) Does this production function exhibit diminishing returns to labour? Explain.
(d) Explain intuitively what might cause the marginal product of labour to become negative.

Explanation / Answer

The marginal product of labor is the additional amount of output from one more unit of labor. In this case, how many more shoes an additional worker produces. Average product of labor is simply output/labor, how many shoes/how many workers

Workers Pairs of Shoes Marginal Product Average Product
1 10 - 10
2 18 8 9
3 24 6 8
4 28 4 7
5 30 2 6
6 28 -2 4.66
7 25 -3 3.57

b) In stage 1, there is output per input increases at an increasing rate, that is the marginal product is increasing. This does not occur in this production function. In stage 2 output increases at a decreasing rate, that is marginal and average product is decreasing. This occurs from 1 Worker up to 5 workers. Stage 3 is where additional inputs cause output to decline, and marginal product decreasees. In this production function, this occurs at the 6th worker

c) This production function exhibits diminishing returns to labor, since each worker contributes less to the total product than the previous one; tht is marginal product is always decreasing

d) With too many workers, there are not enough machines for each of them to use, so there are delays while the workers wait for machines to become available. Additionally, the size of the plant may be too small, and a large number of workers means they get in each others way. These are some reasons why marginal product may become negative.

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