Midterm 1 Answers - Industrial Organization EC460 Spring...

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Unformatted text preview: Industrial Organization: EC460 Spring 2009 Instructor: Thomas D. Jeitschko First Midterm, Wednesday, March 4 Instructions This is a closed-notes, closed-book exam, however, you may use a calculator. There are four questions and you are required to answer all four questions for 25 points each. You have 75 minutes to complete the exam. 1 Imperfect Competition Consider a market with demand given by P = 180 & 4 Q . The cost to produce the good is given by C = Q 2 . Calculate (a) market output, (b) market price, (c), consumer surplus, and (d) total surplus (consumer surplus plus market pro&t) for the following three scenarios: 1. Monopoly Answer A &rm maximizes pro&t by producing at the level that marginal revenue is equal to marginal cost. For the monopoly, revenue is : MR = d dQ [ PQ ] = d dQ [(180 & 4 Q ) Q ] = 180 & 8 Q MC = dC dQ = d dQ & Q 2 ¡ = 2 Q MR = MC 180 & 8 Q = 2 Q Q m = 18 P m = 180 & 4 Q m = 108 1 Pro&t ( & ) = Revenue & C = P m Q m & ( Q m ) 2 = (108) (18) & (18) 2 = 1 ; 620 CS = 1 2 (18) (180 & 108) = 648 TS = & + CS = 2 ; 268 2. Cournot duopoly (2 &rms competing in output) Answer MC 1 = 2 Q 1 MR 1 = d dQ & 180 Q 1 & 4 Q 2 1 & 4 Q 1 Q 2 ¡ = 180 & 8 Q 1 & 4 Q 2 MR 1 = MC 1 180 & 8 Q 1 & 4 Q 2 = 2 Q 1 180 = 10 Q 1 + 4 Q 2 By symmetry, 180 = 14 Q 1 Q d 1 = 90 7 ¡ 12 : 86 P d = 180 & 4( Q d 1 + Q d 2 ) = 540 7 ¡ 77 : 14 & 1 = P d Q d 1 & ¢ Q d 1 £ 2 = ( 540 7 )( 90 7 ) & ¢ 90 7 £ 2 = 40 ; 500 49 ¡ 826 : 53 CS = 1 2 ¢ Q d 1 + Q d 2 £ ¢ 180 & P d £ = 64 ; 800 49 ¡ 2 ; 975 : 51 TS = & + CS = 40 ; 500 49 + 40 ; 500 49 + 64 ; 800 49 = 145 ; 800 49 ¡ 2 ; 975 : 51 3. Five perfectly competitive &rms. Answer Firm 1 calculates output level by setting marginal cost equal to MR , which is equal to P . MR = P = MC P = 2 Q 1 2 To solve the market equilibrium, we use the fact that Q (market quantity) = 5 Q 1 : P = 2 Q 1 = 2 Q 5 2 Q 5 = P = 180 & 4 Q Q & = (180)5 22 Q & 1 = Q & 5 = 90 11 ¡ 8 : 18 P & = 2 Q & 5 = 180 11 ¡ 16 : 36 & 1 = P & Q & 1 & ( Q & 1 )...
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This note was uploaded on 03/29/2009 for the course ECON 460 taught by Professor Boyer during the Spring '08 term at Michigan State University.

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Midterm 1 Answers - Industrial Organization EC460 Spring...

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