If the total cost function is TC = Q3 - 6Q2 + 14Q + 75, would you expect the bottom of the ATC curve to be greater than, less than, or equal to 3?
What will be an ideal response?
Greater than 3. MC intersects AVC at its minimum so the answer can be obtained by taking the first derivative of the AVC which is Q2 - 6Q + 14 and setting it equal to zero. The derivative is 2Q - 6 so 2Q - 6 = 0 and Q = 3. Therefore, the marginal cost curve is below the ATC at an output of 3 so the quantity will increase beyond 3 as the marginal cost approaches the ATC curve where that curve is minimized. Alternatively, the answer could be found by dividing the TC equation by Q to get ATC and then setting the first derivative of the result equal to zero and solving for Q.
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