Chapter 1. Figure It Out 8.2
1.1 Screen 1 of 3
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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.
Question
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1.2 Screen 2 of 3
What level of output would a firm in the cardboard box industry choose if it wanted to minimize its average variable cost of production?
Question
To minimize average variable cost, the firm should produce 607M7xmPORU= 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”.
1.3 Screen 3 of 3
Calculate the price below which a firm in the market will not produce any output in the short run (the shut-down price).
Question
The shut-down price is $ Q1FdPC+1WRw=
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.”