The next result follows by comparing the situation

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Unformatted text preview: is the pre-alliance solution.9 9 It is straightforward to check that the price of flight through hub H decreases, provided that b > d + e. As for the difference in profits, we have quadratic terms in the denominator and a quadratic term in , and in the numerator. The sign is then given by the sign of the polynomial in part ii) of the proposition. 14 Proposition 4 i) The fare pa is lower than the pre-alliance fare pna + pna . ~2 ~12 ~1 ii) Airline profits with the alliance are higher than before if 18b6 - 48b4 d2 + 16b2 d4 - 8be2 (6b3 + 6b2 d - 5bd2 - 4d3 ) + e4 (23b2 + 40bd + 16d2 ) > 0. profits. It can be observed that the result on fares stated in proposition 1 above remains true in the presence of an airline offering direct non-stop services. The difference 12 /2 - 1 is positive when the above polynomial in b, d and ~a ~ na e is positive. It will be the case for low and equal values of d and e provided that b > d + e. It becomes negative for sufficiently large values of d and e, although they ar...
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