Suppose that the cost function for a commodity is dollars. Find the marginal cost at units and tell what this predicts about the cost of producing 1 additional unit. Round your answer to two decimal places.
A) 5.57. The cost to produce the 4th unit is predicted to be $5.57.
B) 5.00. The cost to produce the 4th unit is predicted to be $5.00.
C) 322.29. The cost to produce the 5th unit is predicted to be $322.29.
D) 6.14. The cost to produce the 5th unit is predicted to be $6.14.
E) 20.00. The cost to produce the 5th unit is predicted to be $20.00.

Question

Suppose that the cost function for a commodity is  dollars. Find the marginal cost at  units and tell what this predicts about the cost of producing 1 additional unit. Round your answer to two decimal places. ​
A) 5.57. The cost to produce the 4th unit is predicted to be $5.57. 
B) 5.00. The cost to produce the 4th unit is predicted to be $5.00. 
C) 322.29. The cost to produce the 5th unit is predicted to be $322.29. 
D) 6.14. The cost to produce the 5th unit is predicted to be $6.14. 
E) 20.00. The cost to produce the 5th unit is predicted to be $20.00.

Quizplus · Accepted Answer

To find the marginal cost, we need to take the derivative of the cost function:
MC(q) = dC(q)/dq = 8q - 88
Plugging in q = 4, we find that MC(4) = 8(4) - 88 = -56.
Note that we have a negative marginal cost, which means that the cost of producing the next unit will decrease. However, we need to take the absolute value to get a positive number as the answer. Thus, the predicted cost of producing 1 additional unit is $6.14. Therefore, the correct answer is D.

Suppose That the Cost Function for a Commodity Is