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solution_to_hw8

solution_to_hw8 - Professor Faingold Solution prepared by...

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Unformatted text preview: Professor Faingold Solution prepared by Zhentao Shi 1 Economics 121b: Intermediate Microeconomics Solution to Problem Set 8 April 17, 2011 1. (a) A's demand function is x A = 1 . 5- . 1 p , and B's demand function is x B = 4- . 2 p . The market demand function is x = ( 4- . 2 p, if 15 < p ≤ 20 (1 . 5- . 1 p ) + (4- . 2 p ) , if ≤ p ≤ 15 = ( 4- . 2 p, if 15 < p ≤ 20 5 . 5- . 3 p, if ≤ p ≤ 15 The corresponding market inverse demand function is p = ( 1 3 (55- 10 x ) , if 1 ≤ x ≤ 5 . 5 20- 5 x, if < x ≤ 1 The revenue function R ( x ) = p ( x ) × x = ( 1 3 (55- 10 x ) x, if 1 ≤ x ≤ 5 . 5 (20- 5 x ) x, if < x ≤ 1 The marginal revenue function MR = d R ( x ) d x = ( 1 3 (55- 20 x ) , if 1 ≤ x ≤ 5 . 5 20- 10 x, if < x ≤ 1 1 I thank Anne Guan for pointing out my error. All remaining errors are mine. 1 (b) If the monopolist cannot discriminate, the rm solves max x R ( x )- C ( x ) The rst order condition is 1 3 (55- 20 x ) = 5 , if 1 ≤ x ≤ 5 . 5 20- 10 x = 5 , if...
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