Columns 1 and 2 make up a portion of a monopolist's production function for a single variable input,labor.Columns 2 and 3 represent the demand function facing the monopolist over this range of output: How much does the fifth unit of labor add to the firm's total revenue?

Question

Columns 1 and 2 make up a portion of a monopolist's production function for a single variable input,labor.Columns 2 and 3 represent the demand function facing the monopolist over this range of output:  How much does the fifth unit of labor add to the firm's total revenue?

Quizplus · Accepted Answer

To determine the marginal revenue product of the fifth unit of labor, we need to take the derivative of the total revenue with respect to labor and multiply it by the marginal product of labor. 
The total revenue generated by the first four units of labor can be found by adding up the demand values corresponding to each level of output. This gives us: 
$200 + $240 + $280 + $320 = $1,040 
The marginal product of the fifth unit of labor can be found by taking the difference between the total product of four units and five units: 
20 - 16 = 4 
To find the marginal revenue product of the fifth unit of labor, we need to find the change in total revenue resulting from adding the fifth unit of labor. The demand for the fifth unit of output is $360, which means that the total revenue with five units of labor is: 
$1,040 + $360 = $1,400 
Thus, the marginal revenue product of the fifth unit of labor is: 
($1,400 - $1,040) * 4 = $1,440 
However, the question asks about the change in total revenue, which is simply the revenue generated by the fifth unit of labor: 
$1,400 - $1,040 = $360 
Since the marginal product of labor is 4, this means that the fifth unit of labor adds $360/4 = $90 to the firm's total revenue. However, we need to keep in mind that this is the revenue generated by the fifth unit of labor, not the marginal revenue product, which is $1,440. Therefore, none of the answer choices are correct except for C, which comes closest to the correct answer of $90.

Columns 1 and 2 Make Up a Portion of a Monopolist's