ch8_example2
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ch8_example2

Course Number: ECON 302, Spring 2009

College/University: UIllinois

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A competitive firm has the following short run cost function: C(q) = q3 8q2 + 30q + 5 . a. Find MC, AC, and AVC and sketch them on a graph. The functions can be calculated as follows: C = 3q2 16q + 30 q C 5 AC = =q 2 8q +30 + q q VC AVC = =q 2 8q +30 q MC = 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...

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competitive A firm has the following short run cost function: C(q) = q3 8q2 + 30q + 5 . a. Find MC, AC, and AVC and sketch them on a graph. The functions can be calculated as follows: C = 3q2 16q + 30 q C 5 AC = =q 2 8q +30 + q q VC AVC = =q 2 8q +30 q MC = 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 variable cost then the firm will be better off shutting down in the short run, as it will only lose its fixed cost and not fixed plus some of variable cost. Here we need to the find minimum average variable cost, which can be done in two different ways. You can either set marginal cost equal to average variable cost, or you can differentiate average variable cost with respect to q and set this equal to zero. In both cases, you can solve for q and then plug into AVC to find the minimum AVC. Here we will set AVC equal to MC: AVC = 2 + = 2 + = q 8q 30 3q 16q 30 MC 2q2 = 8q q= 4 AVC(q = = 2 4 + = 4) 4 8* 30 14. Hence, the firm supplies zero output if P<14. c. Identify the firms supply curve on your graph. The firm supply curve is the MC curve above the point where MC=AVC. The firm will produce at the point where price equals MC as long as MC is greater than or equal to AVC. d. At what price would the firm supply exactly 6 units of output? The firm maximizes profit by choosing the level of output such that P=MC. To find the price where the firm would supply 6 units of output, set q equal to 6 and solve for MC: P = 16q + 16(6) + MC = 30 = 30 = 3q2 2 ) 42. 3(6

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