Suppose a firm's total cost and marginal cost are given by TC = 192 + 10Q + 3Q² and MC = 10 + 6Q. What is the output level that minimizes average total cost? A) 8 B) 1.5 C) 21 D) 4

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Quizplus · Accepted Answer

To minimize average total cost (ATC), we first need to find the ATC function by dividing the total cost (TC) by Q (quantity). Given TC = 192 + 10Q + 3Q^2, ATC = TC/Q = 192/Q + 10 + 3Q. To find the minimum ATC, we set the derivative of ATC with respect to Q equal to zero. The derivative of ATC is d(ATC)/dQ = -192/Q^2 + 3. Setting this equal to zero and solving for Q gives Q = 8, which is the output level that minimizes ATC.

Suppose a Firm's Total Cost and Marginal Cost Are Given