A firm in a competitive market has the following cost structure: What is the lowest price at which this firm might choose to operate?

Question

A firm in a competitive market has the following cost structure:  What is the lowest price at which this firm might choose to operate?

Quizplus · Accepted Answer

To determine the lowest price at which the firm might choose to operate, we need to find the minimum point of the average variable cost curve (AVC). From the cost structure, we can calculate the AVC as follows:
AVC = VC/Q = (2Q+110)/Q = 2+110/Q
To find the minimum point of this curve, we need to take the derivative with respect to Q and set it equal to zero:
dAVC/dQ = -110/Q^2 = 0
Q = sqrt(110) ≈ 10.5
Plugging this value of Q back into the AVC equation, we get:
AVC = 2+110/10.5 ≈ $12.10
Therefore, the lowest price that covers variable costs and allows the firm to stay in business is slightly above $12 per unit. However, since the question only gives us whole numbers as answer choices, the best choice is B ($3), which at least covers some of the fixed costs and contributes to reducing the overall losses of the firm.

A Firm in a Competitive Market Has the Following Cost