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Unformatted text preview: variables from those in the previous section. The pre-alliance equilibrium is characterized by the following prices, travel volumes and profits: ~1 pna = ~2 pna 1 - b( + ) + e + 2 = 2 3b + 2d 3b - 2bd - 2e2 ! 1 - b( + ) + e + = 2 3b + 2d 3b2 - 2bd - 2e2 13 ! ~3 ~4 pna = pna ~5 pna = 2e( + ) + (3b - 2d) 2(3b2 - 2bd - 2e2 ) ~ 12 p1 Qna = b~na ; ~ 34 Qna = b~na ; p3 ~5 Qna = b~na p5 ~ na ~ na ~ na ~ na 1 = 2 = b (~na )2 ; 3 = 4 = b (~na )2 ; p1 p3 ~ na 5 = b (~na )2 p5 We next compute the equilibrium when airlines 1 and 2 form an alliance. Demands now take the form Q12 = - bp12 + d(p3 + p4 ) + ep5 , Q34 = - b(p3 + p4 ) + dp12 + ep5 and Q5 = - bp5 + e(p12 + p3 + p4 ). Maximization of 12 = p12 Q12 , 3 = p3 Q34 , 4 = p4 Q34 and 5 = p5 Q5 with respect to prices yields, ~12 pa = ~3 pa ~5 pa (6b2 - 2e2 ) + (4bd + 2e2 ) + e(3b + 2d) 12b3 - 4bd2 - 7be2 - 4de2 (2bd + e2 ) + (4b2 - e2 ) + e(2b + d) a = p4 = ~ 12b3 - 4bd2 - 7be2 - 4de2 e(3b + 2d) + e(4b + 2d) + 2(3b2 - d2 ) = 12b3 - 4bd2 - 7be2 - 4de2 Travel volumes and profits are obtained as above. The next result follows by comparing the situation with alliance 1 and 2 vis a v...
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This note was uploaded on 05/12/2010 for the course MAN 6721 taught by Professor Kraft during the Spring '10 term at University of Florida.
- Spring '10