1 alliance equilibrium between airlines 1 and 2 with

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Unformatted text preview: m between airlines 1 and 2. With an alliance, the airlines 1 and 2 set the fare for flight through hub H cooperatively while competition with flight through hub K remains. Denote by p12 the fare of the interline flight. Demand functions take now the form: Q12 = - bp12 + d(p3 + p4 ) and Q34 = - b(p3 + p4 ) + dp12 . Thus, the profit functions are given by 12 = p12 Q12 , 3 = p3 Q34 , and 4 = p4 Q34 . Solving the system formed by 12 /p12 = 0, 3 /p3 = 0 and 4 /p4 = 0 yields the following equilibrium prices, pa = 12 3b + 2d 2b + d ; pa = pa = 3 4 2 - d2 ) 2(3b 2(3b2 - d2 ) where superscipt a identifies the airline alliance between 1 and 2. The remaining equilibrium variables are, Qa = 12 b (3b + 2d) = bpa ; 12 2 - d2 ) 2(3b 7 Qa = 34 b (2b + d) = bpa 3 2 - d2 ) 2(3b b (3b + 2d)2 b (2b + d)2 a a = b (pa )2 ; 3 = 4 = = b (pa )2 12 3 2 - d2 )2 2 - d2 )2 4 (3b 4 (3b b[(9b2 + d2 )2 + 16bd + 4(b2 + d2 ) 2 ] CS a = 8 (3b2 - d2 )2 The next result follows directly by comparing the situation with an airline a 12 = alliance vis a vis the pre-alliance solution.6 Proposition 1 i) The fare...
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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.

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