Chapter 27
NAME
Oligopoly
Introduction.
In this chapter you will solve problems for firm and indus
try outcomes when the firms engage in Cournot competition, Stackelberg
competition, and other sorts of oligopoly behavior. In Cournot competi
tion, each firm chooses its own output to maximize its profits given the
output that it expects the other firm to produce. The industry price de
pends on the industry output, say,
q
A
+
q
B
, where A and B are the firms.
To maximize profits, firm A sets its marginal revenue (which depends on
the output of firm A and the expected output of firm B since the expected
industry price depends on the sum of these outputs) equal to its marginal
cost. Solving this equation for firm A’s output as a function of firm B’s
expected output gives you one reaction function; analogous steps give you
firm B’s reaction function. Solve these two equations simultaneously to
get the Cournot equilibrium outputs of the two firms.
Example:
In Heifer’s Breath, Wisconsin, there are two bakers, Anderson
and Carlson.
Anderson’s bread tastes just like Carlson’s—nobody can
tell the di
ff
erence. Anderson has constant marginal costs of $1 per loaf of
bread. Carlson has constant marginal costs of $2 per loaf. Fixed costs are
zero for both of them. The inverse demand function for bread in Heifer’s
Breath is
p
(
q
) = 6

.
01
q
, where
q
is the total number of loaves sold per
day.
Let us find Anderson’s Cournot reaction function. If Carlson bakes
q
C
loaves, then if Anderson bakes
q
A
loaves, total output will be
q
A
+
q
C
and price will be 6

.
01(
q
A
+
q
C
).
For Anderson, the total cost of
producing
q
A
units of bread is just
q
A
, so his profits are
pq
A

q
A
= (6

.
01
q
A

.
01
q
C
)
q
A

q
A
= 6
q
A

.
01
q
2
A

.
01
q
C
q
A

q
A
.
Therefore if Carlson is going to bake
q
C
units, then Anderson will choose
q
A
to maximize 6
q
A

.
01
q
2
A

.
01
q
C
q
A

q
A
. This expression is maximized
when 6

.
02
q
A

.
01
q
C
= 1.
(You can find this out either by setting
A’s marginal revenue equal to his marginal cost or directly by setting
the derivative of profits with respect to
q
A
equal to zero.)
Anderson’s
reaction function,
R
A
(
q
C
) tells us Anderson’s best output if he knows
that Carlson is going to bake
q
C
. We solve from the previous equation to
find
R
A
(
q
C
) = (5

.
01
q
C
)
/.
02 = 250

.
5
q
C
.
We can find Carlson’s reaction function in the same way. If Carlson
knows that Anderson is going to produce
q
A
units, then Carlson’s profits
will be
p
(
q
A
+
q
C
)

2
q
C
= (6

.
01
q
A

.
01
q
C
)
q
C

2
q
C
= 6
q
C

.
01
q
A
q
C

.
01
q
2
C

2
q
C
.
Carlson’s profits will be maximized if he chooses
q
C
to satisfy
the equation 6

.
01
q
A

.
02
q
C
= 2. Therefore Carlson’s reaction function
is
R
C
(
q
A
) = (4

.
01
q
A
)
/.
02 = 200

.
5
q
A
.
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334
OLIGOPOLY
(Ch.
27)
Let us denote the Cournot equilibrium quantities by ¯
q
A
and ¯
q
C
. The
Cournot equilibrium conditions are that ¯
q
A
=
R
A
(¯
q
C
) and ¯
q
C
=
R
C
(¯
q
A
).
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 Oligopoly, Supply And Demand, Ben

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