Page 551 - Microeconomics, Fourth Edition

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PROBLEMS 525
the elasticities are constant; that is, they do not vary with 12.21. A pipeline transports gasoline from a refinery at
price. Since both are coach fares, you may also assume point A to destinations at R and T. The marginal cost of
that the marginal cost of service is about the same for transporting gasoline to each destination is MC 2. The
business and vacation travelers. Suppose an airline facing pipeline has a fixed cost of 160. The demand curve for the
these demand elasticities wants to set P R (the price of a transportation of gasoline from A to R is Q R 100 10P R ,
round-trip ticket to regular business travelers) and P V where Q R is the number of units transported when P R is the
(the price of a round-trip ticket to vacation travelers) to transport price per unit. The demand for pipeline move-
maximize profit. What prices should the firm charge if ments from A to T will be 20 units as long as P T 12.
the marginal cost of a round trip is 200? If P T 7 12, the customers at T will purchase gasoline
from another source, buying no gasoline shipped through
12.20. La Durazno is the only resort hotel on a small the pipeline. These demand curves are shown below.
desert island off the coast of South America. It faces two a) If this firm were unable to engage in price discrimina-
market segments: bargain travelers and high-end travel- tion (so that it can only choose a single P for the two mar-
ers. The demand curve for bargain travelers is given by kets), what would the profit-maximizing tariff be? What
Q 1 400 2P 1 . The demand curve for high-end travel- level of profit would the firm realize?
ers is given by Q 2 500 P 2 . In each equation, Q de-
notes the number of travelers of each type who stay at the b) If this firm were able to implement third-degree price
hotel each day, and P denotes the price of one room per discrimination to maximize profits, what would the
day. The marginal cost of serving an additional traveler profit-maximizing prices be? What level of profits would
of either type is $20 per traveler per day. the firm realize?

12
10 Demand for Demand for
transportation transportation
P P
R T
from A to R from A to T

Y Y
100 R 20 T

a) Under the assumption that there is a positive demand 12.22. A seller produces output with a constant marginal
from each type of traveler, what is the equation of the cost MC 2. Suppose there is one group of consumers
overall market demand curve facing the resort? with the demand curve P 1 16 Q 1 , and another with the
b) What is the profit-maximizing price under the demand curve P 2 10 (1/2)Q 2 .
assumption that the resort must set a uniform price for all a) If the seller can discriminate between the two markets,
travelers? For the purpose of this problem, you may what prices would she charge to each group of con-
assume that at the profit-maximizing price, both types sumers? (You may want to exploit the monopoly mid-
of travelers are served. Under the uniform price, what point rule from Learning-By-Doing Exercise 11.5.)
fraction of customers are bargain travelers, and what b) If the seller cannot discriminate, but instead must
fraction are high end? charge the same price P 1 P 2 P to each consumer
c) Suppose that the resort can engage in third-degree group, what will be her profit-maximizing price?
price discrimination based on whether a traveler is a c) Which, if any, consumer group benefits from price dis-
high-end traveler or a bargain traveler. What is the crimination?
profit-maximizing price in each segment? Under price d) If instead P 1 10 Q 1 , does either group benefit
discrimination, what fraction of customers are bargain from price discrimination?
travelers and what fraction are high end?
d) The management of La Durazno is probably unable to 12.23. A cruise line has space for 500 passengers on
determine, just from looking at a customer, whether he each voyage. There are two market segments: elderly
or she is a high-end or bargain traveler. How might La passengers and younger passengers. The demand curve
Durazno screen its customers so that it can charge the for the elderly market segment is Q 1 750 4P 1 . The
profit-maximizing discriminatory prices you derived in demand curve for the younger market segment is Q 2
part (c)? 850 2P 2 . In each equation, Q denotes the number of