Chapter 25
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
p
1
= 200
−
q
1
. The inverse demand curve in market 2 is
p
2
= 300
−
q
2
. The firm’s total cost function is
C
(
q
1
+
q
2
) = (
q
1
+
q
2
)
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
−
2
q
1
. In market 2, marginal revenue is 300
−
2
q
2
.
The
firm’s marginal costs are 2(
q
1
+
q
2
). To maximize its profits, the firm sets
marginal revenue in each market equal to marginal cost. This gives us the
two equations 200
−
2
q
1
= 2(
q
1
+
q
2
) and 300
−
2
q
2
= 2(
q
1
+
q
2
). Solving
these two equations in two unknowns for
q
1
and
q
2
, we find
q
1
= 16
.
67
and
q
2
= 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.
25.1 (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
Q
1
= 50
,
000
−
2
,
000
P
1
, where
P
1
is the price in the U.S. measured in U.S. dollars.
The demand for
Sludge’s opus in England is
Q
2
= 10
,
000
−
500
P
2
, where
P
2
is its price
in England measured in U. S. dollars. His publisher has a cost function
C
(
Q
) = $50
,
000 + $2
Q
, where
Q
is the total number of copies of
Orgy
that it produces.
(a)
If McSwill must charge the same price in both countries, how many
copies should it sell?
27,500.
What price should it charge
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
310
MONOPOLY BEHAVIOR
(Ch.
25)
to maximize its profits
$13.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Summer '09
 JOHNG.SESSIONS
 Microeconomics, Monopoly, Supply And Demand

Click to edit the document details