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Chapter 1Figure It Out 8.2

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Cardboard boxes are produced in a perfectly competitive market. Each identical firm has a short-run total cost curve of TC = 3Q3 – 18Q2 + 30Q + 50, where Q is measured in thousands of boxes per week. The firm’s associated marginal cost curve is MC = 9Q2 – 36Q + 30.

Which expression represents the firm’s average variable cost?

A.
B.
C.
D.

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      What level of output would a firm in the cardboard box industry choose if it wanted to minimize its average variable cost of production?

      To minimize average variable cost, the firm should produce units of output.

      When AVC is at its minimum, MC = AVC. Substitute the expressions for MC and AVC to find that 9Q2 – 36Q + 30 = 3Q2 – 18Q + 30. Solve for Q to find that, when MC and AVC are equal (and AVC is it its minimum), Q = 3. For further review, see section “Average and Marginal Costs”.
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          Calculate the price below which a firm in the market will not produce any output in the short run (the shut-down price).

          The shut-down price is $

          The firm should stop production if the price it receives for its cardboard boxes is insufficient to cover its average variable costs. The firm’s average variable costs are AVC = 3Q2 – 18Q + 30; they are minimized at output level Q = 3. Substitute 3 for Q in the formula for average variable cost to find the lowest possible AVC which is $3. So, if the price is below $3, the firm will not, at any output level, be able to cover its variable costs and it should shut down. For further review, see section “Profit Maximization in a Perfectly Competitive Market.”
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