A model of airline competition defines (x, y) as the probability that a customer will buy a

A model of airline competition defines ƒ(x, y) as the probability that a customer will buy a ticket from Airline 1 rather than Airline 2 if the ticket price is x from Airline 1 and y from Airline 2. A similar function g(x, y) gives the probability 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 Airline 2. For simplicity, the model assumes that ƒ(x, y) = g(x, y).

One version of the model assumes

Calculate ƒ_x(x, y) and ƒ_y(x, y) and verify that the assumptions of part (b) are satisfied.

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f(x, y) = y(1 + x)e x + y -X