A competitive firm has the following short run cost function: C ( q ) = q 3-8 q 2 + 30 q + 5 . a. Find MC, AC, and AVC and sketch them on a graph. The functions can be calculated as follows: MC = ∂ C ∂ q = 3 q 2-16 q + 30 AC = C q = q 2-8 q + 30 + 5 q AVC = VC q = q 2-8 q + 30 Graphically, all three cost functions are u-shaped in that cost declines initially as q increases, and then cost increases as q increases. Average variable cost is below average cost. Marginal cost will be initially below AVC and will then increase to hit AVC at its minimum point. MC will be initially below AC and will also hit AC at its minimum point. b. At what range of prices will the firm supply zero output? The firm will find it profitable to produce in the short run as long as price is greater than or equal to average variable cost. If price is less than average
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