Chapter 26 NAME
Monopoly Behavior
Introduction. Problems in this chapter explore the possibilities of price
discrimination by monopolists. There are also problems related to spatial
markets, where transportation costs are accounted for and we show that
lessons learned about spatial models give us a useful way of thinking about
competition under product differentiation in economics and in politics.
Remember that a price discriminator wants the marginal revenue in
each market to be equal to the marginal cost of production. Since he
produces all of his output in one place, his marginal cost of production
is the same for both markets and depends on his total output. The trick
for solving these problems is to write marginal revenue in each market as
a function of quantity sold in that market and to write marginal cost as
a function of the sum of quantities sold in the two markets. The profit-
maximizing conditions then become two equations that you can solve
for the two unknown quantities sold in the two markets. Of course, if
marginal cost is constant, your job is even easier, since all you have to do
is find the quantities in each market for which marginal revenue equals
the constant marginal cost.
Example: A monopolist sells in two markets. The inverse demand curve
in market 1 is p1= 200 −q1. The inverse demand curve in market 2 is
p2= 300−q2. The firm’s total cost function is C(q1+q2)=(q1+q2)2.The
firm is able to price discriminate between the two markets. Let us find the
prices that it will charge in each market. In market 1, the firm’s marginal
revenue is 200 −2q1. In market 2, marginal revenue is 300 −2q2.The
firm’s marginal costs are 2(q1+q2). To maximize its profits, the firm sets
marginal revenue in each market equal to marginal cost. This gives us the
two equations 200 −2q1=2(q1+q2) and 300 −2q2=2(q1+q2). Solving
these two equations in two unknowns for q1and q2, we find q1=16.67
and q2=66.67. We can find the price charged in each market by plugging
these quantities into the demand functions. The price charged in market
1 will be 183.33. The price charged in market 2 will be 233.33.
26.1 (0) Ferdinand Sludge has just written a disgusting new book, Orgy
in the Piggery. His publisher, Graw McSwill, estimates that the demand
for this book in the United States is Q1=50,000 −2,000P1,where
P1is the price in the U.S. measured in U.S. dollars. The demand for
Sludge’s opus in England is Q2=10,000 −500P2,whereP2is its price
in England measured in U. S. dollars. His publisher has a cost function
C(Q) = $50,000 + $2Q,whereQis the total number of copies of Orgy
that it produces.
(a) If McSwill must charge the same price in both countries, how many
318 MONOPOLY BEHAVIOR (Ch. 26)
(b) If McSwill can charge a different price in each country and wants to
maximize profits, how many copies should it sell in the United States?
23,000. What price should it charge in the United States?
$13.50. How many copies should it sell in England? 4,500.
26.2 (0) A monopoly faces an inverse demand curve, p(y) = 100 −2y,
and has constant marginal costs of 20.
(e) What is the deadweight loss due to the monopolistic behavior of this
(f) Suppose this monopolist could operate as a perfectly discriminating
monopolist and sell each unit of output at the highest price it would fetch.
Calculus 26.3 (1) Banana Computer Company sells Banana computers in both
the domestic and foreign markets. Because of differences in the power
supplies, a Banana purchased in one market cannot be used in the other
market. The demand and marginal revenue curves associated with the
two markets are as follows:
Banana’s production process exhibits constant returns to scale and it
takes $1,000,000 to produce 100 computers.
NAME 319
(Hint: If there are constant returns to scale, does long-run average cost
change as output changes?) Draw the average and marginal cost curves
on the graph.
(b) Draw the demand curve for the domestic market in black ink and
the marginal revenue curve for the domestic market in pencil. Draw the
0 100 200 300 400 500 600 700 800
10
20
30
40
50
60
Dollars (1,000s)
Red line
Blue line
Black line
Pencil line
LRAC
LRMC
Banana Computers
(c) If Banana is maximizing its profits, it will sell 250 computers in
320 MONOPOLY BEHAVIOR (Ch. 26)
(d) At the profit-maximizing price and quantity, what is the price elas-
ticity of demand in the domestic market? −3.What is the price
(e) Suppose that somebody figures out a wiring trick that allows a Banana
computer built for either market to be costlessly converted to work in the
other. (Ignore transportation costs.) On the graph below, draw the new
inverse demand curve (with blue ink) and marginal revenue curve (with
black ink) facing Banana.
0 100 200 300 400 500 600 700 800
10
20
30
40
Dollars (1,000s)
Blue line
LRAC
LRMC
Banana Computers
Black line
(f) Given that costs haven’t changed, how many Banana computers
should Banana sell? 400. What price will it charge? $15,714.
How will Banana’s profits change now that it can no longer practice price
26.4 (0) A monopolist has a cost function given by c(y)=y2and faces
a demand curve given by P(y) = 120 −y.
(a) What is its profit-maximizing level of output? 30. What price
will the monopolist charge? $90.
NAME 321
(b) If you put a lump sum tax of $100 on this monopolist, what would its
output be? 30.
(c) If you wanted to choose a price ceiling for this monopolist so as to
maximize consumer plus producer surplus, what price ceiling should you
choose? $80.
(d) How much output will the monopolist produce at this price ceiling?
40.
(e) Suppose that you put a specific tax on the monopolist of $20 per unit
output. What would its profit-maximizing level of output be? 25.
26.5 (1) The Grand Theater is a movie house in a medium-sized college
town. This theater shows unusual films and treats early-arriving movie
goers to live organ music and Bugs Bunny cartoons. If the theater is
open, the owners have to pay a fixed nightly amount of $500 for films,
ushers, and so on, regardless of how many people come to the movie.
For simplicity, assume that if the theater is closed, its costs are zero. The
nightly demand for Grand Theater movies by students is QS= 220−40PS,
where QSis the number of movie tickets demanded by students at price
PS. The nightly demand for nonstudent moviegoers is QN= 140 −20PN.
(a) If the Grand Theater charges a single price, PT, to everybody, then
at prices between 0 and $5.50, the aggregate demand function for movie
(b) What is the profit-maximizing number of tickets for the Grand The-
ater to sell if it charges one price to everybody? 180. At what price
would this number of tickets be sold? $3. How much profits would
(c) Suppose that the cashier can accurately separate the students from
the nonstudents at the door by making students show their school ID
cards. Students cannot resell their tickets and nonstudents do not have
access to student ID cards. Then the Grand can increase its profits by
charging students and nonstudents different prices. What price will be
322 MONOPOLY BEHAVIOR (Ch. 26)
110. What price will be charged to nonstudents? $3.50. How
many nonstudent tickets will be sold? 70. How much profit will the
(d) If you know calculus, see if you can do this part. Suppose that
the Grand Theater can hold only 150 people and that the manager
wants to maximize profits by charging separate prices to students and
to nonstudents. If the capacity of the theater is 150 seats and QS
tickets are sold to students, what is the maximum number of tickets
an expression for the price of nonstudent tickets as a function of the
number of student tickets sold. (Hint: First find the inverse nonstu-
an expression for Grand Theater profits as a function of the number
QSonly. (Hint: Make substitutions using your previous answers.)
tickets should the Grand sell to maximize profits? 90. What price
is charged to students? $3.25. How many nonstudent tickets are
26.6 (2) The Mall Street Journal is considering offering a new service
which will send news articles to readers by email. Their market research
indicates that there are two types of potential users, impecunious stu-
dents and high-level executives. Let xbe the number of articles that
a user requests per year. The executives have an inverse demand func-
tion PE(x) = 100 −xand the students have an inverse demand function
PU(x)=80−x. (Prices are measured in cents.) The Journal has a zero
marginal cost of sending articles via email. Draw these demand functions
in the graph below and label them.
NAME 323
20 40 60 80 100 120
20
40
60
80
100
120
Quantity
Price
0
P (X) = 100 – X
E
P (X) = 80 – X
U
(a) Suppose that the Journal can identify which users are students and
which are executives. It offers each type of user a different all or nothing
deal. A student can either buy access to 80 articles per year or to none
at all. What is the maximum price a student will be willing to pay for
the lesson on consumer’s surplus and the area under the demand curve.)
An executive can either buy access to 100 articles per year or to none at
all. What is the maximum price an executive would be willing to pay for
(b) Suppose that the Journal can’t tell which users are executives and
which are undergraduates. Thus it can’t be sure that executives wouldn’t
buy the student package if they found it to be a better deal for them.
In this case, the Journal can still offer two packages, but it will have to
let the users self-select the one that is optimal for them. Suppose that it
offers two packages: one that allows up to 80 articles per year the other
that allows up to 100 articles per year. What’s the highest price that the
undergraduates will pay for the 80-article subscription? $32.
(c) What is the total value to the executives of reading 80 articles per
the right of a vertical line at 80 articles.)