Problem 3. British airways has regular flights between Arizonia and Oregon. It can treat travers A and B as separate markets. Suppose that it notes a demand function of Q=16-P for A travelers and a demand function Q=10-P for B travelers and that it has a cost function for all travelers of C(Q)=10+Q2. How much should it charge in each market to maximize its profit? Verify that your answer represents a profit-maximizing point rather than a profit-minimizing point for the airline.
Problem 3. British airways has regular flights between Arizonia and Oregon. It can treat travers A and B as separate markets. Suppose that it notes a demand function of Q=16-P for A travelers and a demand function Q=10-P for B travelers and that it has a cost function for all travelers of C(Q)=10+Q2. How much should it charge in each market to maximize its profit?
Verify that your answer represents a profit-maximizing point rather than a profit-minimizing point for the airline.
Answer -
Need to find-
How much should it charge in each market to maximize its profit
Given in the question-
British airways has regular flights between Arizonia and Oregon. It can treat travers A and B as separate markets. Suppose that it notes a demand function of Q=16-P for A travelers and a demand function Q=10-P for B travelers and that it has a cost function for all travelers of C(Q)=10+Q2
For Market "A"
Q = 16 -P
P = 16 - Q..........(1)
C(Q) = 10 + Q2
Profit = Rveneue - Total cost
Revenue = Price*Qunatity
Revenue = (16-Q)*Q
Reveneue = 16Q - Q2
Marginal revenue = 16 - 2Q
Marginal cost = 2Q
Profit = 16Q - Q2 - 10 - Q2
Profit = 16Q - 2Q2 - 10
Profit max. for market "A"
Marginal revenue = margina cost
16 - 2Q = 2Q
16 = 4Q
Q = 4
P =$12
Verifying the price is profit max.
Second derivative of profit function should be less than zero at Q = 4
First derivative of Profit function = 16 - 4Q
Secod derivative of profit function will be = -4 (negative value)
So, Q =4 is profit max. point
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