Question

Delta has market power on the routes connecting smaller cities around Atlanta. Tickets for these routes are priced at $300 round trip. The expected volume per airplane trip at this price is 330. All aircraft capacities are 420 and the marginal cost of a round trip passenger is $20.

1. What information do you need to identify whether or not $300 is the profit maximizing price?
2. If demand is Q = 480 - .5P, what is the profit at the $300 price point? What is the profit maximizing price and quantity?

Answer 1

a) In order to identify whether $300 is the profit maximizing price, we need to have information on the total revenue function that may be obtained using the demand function for airline trips, and the total cost of the airline trip.

b) At P = $300,

Total revenue = PQ = P( 480 - 0.5 P) =( 960 - 2Q) Q

Total cost = marginal cost × Q = MC × Q = 20 Q

Profit = P Q - 20 Q = (960 - 2Q) Q - 20Q

Maximizing with respect to Q, we get,

960 - 20 - 4Q = 0

940 = 4Q

Q = 235

P = 480 - 0.5× 235 = $362.5

The profit maximizing quantity is 235 and the price is $362.5.