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108 Chapter 3 Demand Analysis and Optimal Pricing

Airline Ticket Pricing

Revisited

We are now ready to take a closer look at the pricing policy of the airline in the chapter-

opening example and to suggest how it might succeed at yield management. Consider

again Equation 3.4, which describes current demand:

At its present price, $240, the airline sells 100 coach seats (of the 180 such seats available

per flight). Assuming the airline will continue its single daily departure from each city

(we presume this is not an issue), what is its optimal fare?

The first step in answering this question is to recognize this as a pure selling problem.

With the airline committed to the flight, all associated costs are fixed. The marginal cost of

flying 180 passengers versus 100 passengers (a few extra lunches, a bit more fuel, and so on)

is negligible. Thus, the airline seeks the pricing policy that will generate the most revenue.

The next step is to appeal to marginal revenue to determine the optimal fare. The

price equation is P  290 Q /2. (Check this.) Consequently, MR  290 Q. Note:Even

at a 100 percent load (Q 180), marginal revenue is positive (MR $110). If more seats

were available, the airline would like to ticket them and increase its revenue. Lacking

these extra seats, however, the best the airline can do is set Q 180. From the price equa-

tion, $200 is the price needed to sell this number of seats. The airline should institute a

$40 price cut. By doing so, its revenue will increase from $24,000 to $36,000 per flight.^20

Now let’s extend (and complicate) the airline’s pricing problem by introducing the

possibility of profitable price discrimination. Two distinct market segments purchase

coach tickets—business travelers (B) and pleasure travelers (T)—and these groups dif-

fer with respect to their demands. Suppose the equations that best represent these seg-

ments’ demands are QB 330 PBand QT 250 PT. Note that these demand

equations are consistent with Equation 3.4; that is, if both groups are charged price P,

total demand is Q QBQT(330 P) (250 P)  580 2P, which is exactly

Equation 3.4. The airline’s task is to determine QBand QTto maximize total revenue

from the 180 coach seats.

The key to solving this problem is to appeal to the logic of marginal analysis. With

the number of seats limited, the airline attains maximum revenue by setting MRBMRT.

The marginal revenue from selling the last ticket to a business traveler must equal the mar-

ginal revenue from selling the last ticket to a pleasure traveler. Why must this be so?

Suppose to the contrary that the marginal revenues differ: MRB MRT. The airline can

increase its revenue simply by selling one less seat to pleasure travelers and one more seat

to business travelers. As long as marginal revenues differ across the segments, seats should

be transferred from the low-MR segment to the high-MR segment, increasing revenue all

the while. Revenue is maximized only when MRBMRT.

Q 580 2P.

(^20) The same point can be made by calculating the price elasticity of demand at Q 180 and
P 200. Elasticity can be written as EP(dQ/dP)(P/Q). From the demand equation earlier,
we know that dQ /dP 2. Therefore, we find that EP(2)(200/180) 2.22.
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