Econ362_Winter2018_Mid2_solv3.pdf

Econ362_Winter2018_Mid2_solv3.pdf - Economics 326 Midterm 2...

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Economics 326 Midterm 2 20 March 2018 Instructor: Heejeong Kim Instructions: You have seventy five minutes to complete this exam. Please number each question, underline your final answers, and present your work clearly. 1. (30 points) True or False. Answer true or false for each of the following statements. If it is false, explain why or give an example to show it is false. (a) A monopolistic movie theater sells tickets to students and non-students. Suppose that the price elasticity of demand for movie ticket is more elastic for students than non-students. Then, the monopolistic movie theater can maximize its profit by charging a lower price to students than a price to non-students. Answer: True Based on the price discrimination rule, a monopolistic firm has to set the price for students ( P s ) and that for non-students ( P n ) such that P s (1 - 1 | ε s | ) = P n (1 - 1 | ε n | ) = MC where | ε s | and | ε n | are the price elasticities of demand for students and non- students. Given that | ε s | > | ε n | , this implies that P s < P n . (b) If f ( x ) is a convex function, then f ( x 0 + x 1 2 ) f ( x 0 )+ f ( x 1 ) 2 holds for any x 0 and x 1 . Answer: False By the definion of convex function, for any θ (0 , 1), θf ( x 0 ) + (1 - θ ) f ( x 1 ) f ( θx 0 + (1 - θ ) x 1 ) (1) for any x 0 and x 1 . Assume that θ = 1 2 . Then, (1) becomes 1 2 f ( x 0 ) + 1 2 f ( x 1 ) f ( 1 2 x 0 + 1 2 x 1 ) Thus, this implies that f ( x o + x 1 2 ) f ( x 0 ) + f ( x 1 ) 2
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(c) A twice continuously differentiable function Q = F ( L, K ) = 1 γ [ L ρ + K ρ ] γ ρ is globally convex.
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