Suppose a firm's total cost curve is TC = Q³

Question

Suppose a firm's total cost curve is TC = Q³ - Q² + Q + 10. Using calculus, the quantity that minimizes average variable cost for the firm is Q = ____. A) 1 B) 0.75 C) 0.5 D) 0.25

Quizplus · Accepted Answer

The average variable cost (AVC) is derived from the total cost (TC) equation minus any fixed costs. Given the TC equation, the fixed cost is 10, so the variable cost (VC) equation is everything else: VC = Q³ - Q² + Q. The AVC is then VC/Q, which simplifies to the terms in VC that depend on Q, since the other terms are constants or cancel out. To minimize AVC, we take the derivative of AVC with respect to Q, set it equal to zero, and solve for Q. The derivative of AVC with respect to Q (d(AVC)/dQ) simplifies to a constant plus 1 (since the derivative of Q with respect to Q is 1), indicating that the AVC curve is a linear function of Q. Without the specific constants, we can't perform exact calculus, but the question seems to imply a specific solution. Given the options and assuming a typical U-shaped AVC curve, the minimum point would be where the derivative equals zero. However, without the specific function details provided in the question, the correct answer relies on understanding that the minimization of AVC typically occurs at a point where Q > 0, assuming the constants lead to a meaningful AVC curve. Given the options and the nature of AVC curves, a common assumption is that the minimum AVC occurs at a positive quantity of Q, making 0.5 a reasonable choice based on typical economic theory and the structure of AVC curves.

Suppose a Firm's Total Cost Curve Is TC = Q3