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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)

First, lets re-write the demand equations, to be P=f(Q).

First class:
Pa = 4200 - 2Qa
MRa = 4200 - 4Qa

Excursion:
Pb = 2200 - .25*Qb
MRb = 2200 - .5*Qb

a) set MC = MR in each equation, then solve for Qa and Qb. I get Qa=1000, Qb=4000. Ergo, Pa=2200, Pb=1200.

b) Undoubtedly, the airline will make more profit by charging two prices instead of one. The two prices I calculated are the profit-maximizing prices in each market; so the firm cant do any better than that.

(Do you need to calculate the profit-maximizing price if the firm was forced to charge a single price??. It's a little tricky operation, but very do-able.)