s06-answers-mock-final - Economics 302 Intermediate...

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Economics 302 Silve Parviainen Intermediate Microeconomics Spring 2006 Answers to Mock Final 1 Duopoly with Product Diferentiation (a) To fnd the price reaction Function For AA, we start by changing the demand Function to inverse Form: p A = (400 + 1 2 p N ) 1 2 q A . Note that the frst term (in parenthesis) which consists oF a constant and Northwest’s price is beyond the control oF AA, so the company takes that as given. Given the linear inverse demand Function, the marginal revenue Function is MR A = (400 + 1 2 p N ) q A .S ince MR = MC in the equilibrium, we get 400 + 1 2 p N q A =60 = q A = 340 + 1 2 p N , which gives us the price reaction Function p A = (400 + 1 2 p N ) 1 2 ± 340 + 1 2 p N ² = 230 + 1 4 p N (b) To solve For the equilibrium prices, we need the price reaction Functions For both companies. AA’s price reaction Function is given above, and NW’s is Found with the same technique: q N = 750 + p A 3 p N = p N = (250 + 1 3 p A ) 1 3 q N , and MR N = (250 + 1 3 p A ) 2 3 q N =40= MC N = q N = 315 + 1 2 p A . Inserting this into the perceived demand curve gives the NW’s price reaction Function as p N = (250 + 1 3 p A ) 1 3 (315 + 1 2 p A ) = 145 + 1 6 p A . Now, the equilibrium prices can be Found by solving For the two unknowns (prices) in the two price reaction Functions. This gives us p N = 4 , 400 23 $191 and p A = 230 + 1 , 100 23 $278 .
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(c) With the equilibrium prices, the demand for AA tickets is q A = 340 + 2 , 200 23 436 , and for NW tickets q N = 980 12 , 100 23 454 , making the total number of passengers 890.
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This note was uploaded on 09/27/2008 for the course ECON 302 taught by Professor Toossi during the Spring '08 term at University of Illinois at Urbana–Champaign.

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s06-answers-mock-final - Economics 302 Intermediate...

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