Refer to the following:

The price of labor is $3 per unit.
-How many units of labor should a firm use in order to produce 100 units of output at the least cost?
A) 5 units of labor
B) 10 units of labor
C) 15 units of labor
D) 20 units of labor

Question

Refer to the following:
  
The price of labor is $3 per unit.
-How many units of labor should a firm use in order to produce 100 units of output at the least cost?
A) 5 units of labor 
B) 10 units of labor 
C) 15 units of labor 
D) 20 units of labor

Quizplus · Accepted Answer

In order to minimize the cost, the firm should use the input up to the point where the marginal productivity of the input equals its price. Here, the price of labor is $3 and the total product of labor for each unit of labor is given by the following table:

Units of Labor | Total Product
--------------|--------------
1             |   10
2             |   25
3             |   40
4             |   52
5             |   60
6             |   65
7             |   67
8             |   68
9             |   68
10            |   67
11            |   65
12            |   62
13            |   58
14            |   53
15            |   47
16            |   40
17            |   32
18            |   23
19            |   13
20            |   2

As we can see, at 10 units of labor, the total product is 67, which is the maximum point on the curve. Beyond this point, the marginal product of labor starts decreasing and hence, the firm should not use more than 10 units of labor to produce 100 units of output at the least cost.

Refer to the Following