Problem_Set_5_Solutions

# Problem_Set_5_Solutions - q where AC/q =-F/q 2-b + 2 q = 0...

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ECON W3211.002 Intermediate Microeconomics Problem Set 5 Due Wednesday, November 3, 2010 1. For each of the following cost functions, ﬁnd the average ﬁxed cost, marginal cost, average variable cost, and average cost. (a) C = 10 + 10 q i. AFC = 10 /q ii. MC = 10 iii. AV C = 10 iv. AC = 10+10 q q (b) C = 10 + q 2 i. AFC = 10 /q ii. MC = 2 q iii. AV C = q iv. AC = 10+ q 2 q (c) C = 10 + 10 q - 4 q 2 + q 3 i. AFC = 10 /q ii. MC = 10 - 8 q + 3 q 2 iii. AV C = 10 - 4 q + q 2 iv. AC = 10 q + 10 - 4 q + q 2 2. A ﬁrm’s cost curve is C = F + 10 q - bq 2 + q 3 , where b > 0 . (a) For what values of b are cost, average cost, and average variable cost positive? (From now on, assume that all these measures of cost are positive at every output level.) i. C is positive when b < F +10 q + q 3 q 2 . ii. AC is positive when b < F/q +10+ q 2 q . iii. AVC is positive when b < 10+ q 2 q . (b) What is the shape of the AC curve? At what output level is the AC minimized? i. AC is an upward facing parabola. It is minimized at the level of

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Unformatted text preview: q where AC/q =-F/q 2-b + 2 q = 0 . (c) At what output levels does the MC curve cross the AC and the AVC curves? i. MC crosses AC at q such that-F/q-bq-2 q 2 = 0 . ii. MC crosses AVC when q = b 2 or, trivially, when q = 0 . (d) Use calculus to show that the MC curve must cross the AVC at its minimum point. 1 i. In the current problem, we can conrm this result by observing that AV C q =-b + 2 q = 0 only when q = b 2 . 3. Each rm in a competitive market has a cost function of C = 16 + q 2 . The market demand function is Q = 24-p . Determine the long-run equilibrium price, quantity per rm, market quantity, and number of rms. (a) p * LR = 8 (b) q * LR = 4 (c) Q * LR = 16 (d) N * LR = 4 2...
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## This note was uploaded on 10/03/2011 for the course ECON W3211 taught by Professor Elmes during the Fall '09 term at Columbia.

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Problem_Set_5_Solutions - q where AC/q =-F/q 2-b + 2 q = 0...

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