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# 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 Differentiation (a) To find 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 first 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 . Since 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 = 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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