Question

1. Use the following production function to answer the questions below where labor is measured in workers per day, capital is measured in sewing machines available per day, and output is measured in jeans per day.

                                                                        Labor

                                                1        2      3       4       5       6       7       8

                        Capital

                              1                 15     34     44     48     50     51     51     47

                              2                 20     46     64     72     78     81     82     80

                              3                 21     50     73     83     92     99   103   103

Suppose a firm had three sewing machines and could vary only the amount of labor input.

a. Graph the production function for jeans given three sewing machines.

b. Compute and graph the marginal product curve on a separate diagram.

c. What amount of labor is associated with the point of diminishing returns?

d. After the point of diminishing returns is reached, is total output still increasing when marginal product begins
    to diminish? In other words, does diminishing returns imply diminishing output? Explain your answer.  

e. When total output stops increasing, what is the value of marginal product?

Answer 1

a. This graph plots labor and the associated output at a fixed capital of 3 sewing machines.

b. The Marginal Product at each level of Labor employed.

c. From 3 laborers the diminishing returns starts. ( before that MP was 29 and then it fell to 23)

d. In a production function there are 3 stages : increasing at an increasing rate , increasing at a decreasing rate and decreasing.

Here, when the diminishing returns is reached at labor (3), the output is still increasing but at a diminishing rate. Hence, it can be seen that the output is still increasing but with an additional labor hired the increase in marginal product is lesser than before, hence, falling.

After a point, an additional unit of labor will result in decreased output. Here, the marginal product will be below zero or a negative number. In this case it is likely to be after labor (8). Since, at labor 7 and 8 the output is constant.

e. Here total output stops increasing from labor(8) as it is the same as when in was labor (7). At this point MP will be 0. As an additional unit of labor did not increase or decrease the output. After this point, the output will fall and MP will be negative.

Labor	Output	MP
1	21
2	50	29	Increasing at an Increasing rate
3	73	23 ( point of change)	Increasing at a decreasing rate
4	83	10	Increasing at a decreasing rate
5	92	9	Increasing at a decreasing rate
6	99	7	Increasing at a decreasing rate
7	103	4	Increasing at a decreasing rate
8	103	0	Constant returns