Airline pricing is a good example of price discrimination. Airlines set different prices for first-class and excursion. Suppose the economics division of a major airline company estimates the demand and marginal revenue functions for first-class and excursion fares from Los Angeles to Beijing as:
First Class
Qa = 2100 - 0.5 Pa
MRa = 4200 - 4 Qa
Excursion
Qb = 8800 - 4 Pb
MRb =2200 - 0.5 Qb
where Q = number of passengers and P = ticket price
a. If the marginal cost of production is $200 per passenger, what fare and what number of passengers will maximize profit?
b. Would the airline make more profit by charging a single price? (If a single price is to be set, the demand equations from each market segment have to be combined)
Can someone please help with this question?
To find the fare and number of passengers that will maximize profit, we need to consider the profit-maximizing condition, which states that profit is maximized when marginal revenue equals marginal cost.
a. For First Class:
Marginal Cost (MCa) = $200 per passenger
MRa = 4200 - 4 Qa
Setting MRa equal to MCa, we have 4200 - 4 Qa = 200.
Simplifying, we get 4 Qa = 4000, and Qa = 1000.
To find the fare (Pa), we substitute the value of Qa into the demand function, Qa = 2100 - 0.5 Pa.
1000 = 2100 - 0.5 Pa
0.5 Pa = 1100
Pa = $2200
For First Class, the fare that maximizes profit is $2200 and the number of passengers is 1000.
For Excursion:
Marginal Cost (MCb) = $200 per passenger
MRb = 2200 - 0.5 Qb
Setting MRb equal to MCb, we have 2200 - 0.5 Qb = 200.
Simplifying, we get 0.5 Qb = 2000, and Qb = 4000.
To find the fare (Pb), we substitute the value of Qb into the demand function, Qb = 8800 - 4 Pb.
4000 = 8800 - 4 Pb
4 Pb = 4800
Pb = $1200
For Excursion, the fare that maximizes profit is $1200 and the number of passengers is 4000.
b. To determine if the airline would make more profit by charging a single price, we need to calculate the profit for each market segment separately and compare it to the total profit when combining the demand equations.
For First Class:
Profit (πa) = (Pa - MCa) * Qa
Profit (πa) = ($2200 - $200) * 1000
Profit (πa) = $2,000,000
For Excursion:
Profit (πb) = (Pb - MCb) * Qb
Profit (πb) = ($1200 - $200) * 4000
Profit (πb) = $4,000,000
Total Profit:
Profit (π) = Profit (πa) + Profit (πb)
Profit (π) = $2,000,000 + $4,000,000
Profit (π) = $6,000,000
Therefore, the airline would make more profit by charging a single price, as the total profit from combining the demand equations is $6,000,000, which is higher than the individual profits from each market segment.