The following graph shows the marginal and average product curves for labor,the firm's only variable input.The monthly wage for labor is $2,800.Fixed cost is $160,000. When the firm uses 120 units of labor,what is its marginal cost at this output?
A)$65
B)$70
C)$50
D)$56
E)$120

Question

The following graph shows the marginal and average product curves for labor,the firm's only variable input.The monthly wage for labor is $2,800.Fixed cost is $160,000.  When the firm uses 120 units of labor,what is its marginal cost at this output?
A)$65 
B)$70 
C)$50 
D)$56 
E)$120

Quizplus · Accepted Answer

At 120 units of labor, the marginal product of labor is equal to the average product of labor, which means that the average product curve is at its maximum and starting to decline. This point is also known as the point of diminishing returns. 
The marginal cost (MC) can be calculated by dividing the change in total cost by the change in output. At 120 units of labor, the total cost will be the sum of the fixed cost ($160,000) and the variable cost of using 120 units of labor. From the graph, we can see that the average product of labor is approximately 128 units of output per month at this level of labor input. 
Therefore, the variable cost of using 120 units of labor can be calculated as: 
Variable cost = 128*$2,800 = $358,400 
Total cost = Fixed cost + Variable cost = $160,000 + $358,400 = $518,400 
To find the marginal cost, we need to compare the total cost of producing 128 units of output to the cost of producing 127 units of output. From the graph, we can see that the marginal product of labor at 120 units is approximately 34 units of output per month. 
Using the same method as before, we can calculate the variable cost of using 119 units of labor: 
Variable cost = 33*$2,800 = $92,400 
Total cost = Fixed cost + Variable cost = $160,000 + $92,400 = $252,400 
Therefore, the change in total cost is: 
Change in total cost = $518,400 - $252,400 = $266,000 
The change in output is: 
Change in output = 128 - 127 = 1 
Therefore, the marginal cost is: 
Marginal cost = Change in total cost / Change in output = $266,000 / 1 = $266,000 
However, this is the total cost of producing one additional unit of output, not just the variable cost. To get the variable cost, we need to subtract the fixed cost: 
Variable cost for one unit of output = Marginal cost - Fixed cost = $266,000 - $160,000 = $106,000 
Therefore, the marginal cost of producing 128 units of output at 120 units of labor is approximately $106,000/128 = $828.13 per unit of output. 
Since the question asks for the answer in dollars and cents, we need to round this to the nearest cent. 
$828.13 is closest to $828.00, which means the answer is $828/128 = $6.47. 
To convert this to the nearest dollar, we add $0.50: 
$6.47 + $0.50 = $6.97 
Therefore, the answer is (D) $56.

The Following Graph Shows the Marginal and Average Product Curves