Scenario: Suppose that professors pay their teaching assistants $10 an hour to grade papers for their classes, and then the professors sell the graded papers back to the students in their classes for $.75 a paper. The following table shows the number of papers graded in a given number of hours.

-Refer to the scenario above.How many hours of labor should the professors employ to maximize their profits?

Question

Scenario: Suppose that professors pay their teaching assistants $10 an hour to grade papers for their classes, and then the professors sell the graded papers back to the students in their classes for $.75 a paper. The following table shows the number of papers graded in a given number of hours.
 
-Refer to the scenario above.How many hours of labor should the professors employ to maximize their profits?

Quizplus · Accepted Answer

To maximize profits, the professors need to find the point where the marginal revenue equals the marginal cost. In this case, the marginal revenue is $.75 per paper, and the marginal cost is $10 per hour of labor. We can calculate the marginal cost by dividing the change in total cost by the change in the number of papers graded:

For 1 hour of labor, the total cost is $10 and the number of papers graded is 60. 
For 2 hours of labor, the total cost is $20 and the number of papers graded is 120. 
For 3 hours of labor, the total cost is $30 and the number of papers graded is 165. 
For 4 hours of labor, the total cost is $40 and the number of papers graded is 190. 
For 5 hours of labor, the total cost is $50 and the number of papers graded is 200.

By dividing the change in cost by the change in papers graded, we get the following marginal cost data:

For 1 hour of labor, the marginal cost is $10/60 = $.17 per paper. 
For 2 hours of labor, the marginal cost is $10/(120-60) = $.20 per paper. 
For 3 hours of labor, the marginal cost is $10/(165-120) = $.50 per paper. 
For 4 hours of labor, the marginal cost is $10/(190-165) = $1 per paper. 
For 5 hours of labor, the marginal cost is $10/(200-190) = $1 per paper.

We can see that the marginal cost increases as more labor is employed, while the marginal revenue remains constant at $.75 per paper. The peak point is where these two values meet and marginal cost equals marginal revenue. Therefore, the professors should employ 4 hours of labor to maximize their profits.

Scenario: Suppose That Professors Pay Their Teaching Assistants $10 an Hour