Airline Competition A model of airline competition defines f (x, y) as the probability that a customer will buy a ticket from Air-line 1 rather than Airline 2 if the price for a ticket is x from Airline 1 and y from Airline 2. A similar function g(x, y) gives the prob-ability that a customer will buy a ticket from Airline 2 rather than Airline 1 if the price for a ticket is x from Airline 1 and y from Air-line a For simplicity, the model assumes that f(x, = g(y, x). Source: The Journal of the Operational 'Research Society. (a) Explain what the last assumption means, and why it is reasonable. (b) The researchers also assume that

Explain what this assumption means, and why it is reasonable.

(c) One version of the model assumes

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f(x, y) < 0 and f(x, y) > 0. f(x, y) = y(1+x)e x + y Calculate f(x, y) and f(x, y) and verify that the assump- tions of part (b) are satisfied. f(x, y) < 0 and f(x, y) > 0. f(x, y) = y(1+x)e x + y Calculate f(x, y) and f(x, y) and verify that the assump- tions of part (b) are satisfied.

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Since the two functions relates with each other by the relation f x y ... View the full answer