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13.2 OLIGOPOLY WITH HOMOGENEOUS PRODUCTS 535

90

Q 2 (LG’ output, units per year) 50 A E FIGURE 13.2

45

Cournot Reaction Functions
30
and Equilibrium
B
R S is Samsung’s reaction function. R LG is LG’s
20
reaction function. Point E, where the two
reaction functions intersect, is the Cournot
R S R LG equilibrium. Points A and B on R S represent
0 the best responses for Samsung if LG produces
0 20 30 35 45 90 20 units and 50 units, respectively; these points
Q (Samsung’s output, units per year) correspond to the profit-maximization solutions
1
shown in Figure 13.1.

Samsung acts as a monopolist relative to its residual demand curve when it chooses
its output. It thus equates MR 50 to its marginal cost MC (which is assumed to be con-
stant at $10 per unit). This occurs at an output of 20 units. An output of 20 units is
thus Samsung’s best response to an output of 50 units from LG. A Cournot firm’s best response A firm’s
best response to a particular level of output by rival firms is the firm’s profit-maximizing profit-maximizing choice of
choice of output given the rival’s output. Figure 13.1(b) shows that when LG’s output output given the level of
is 20 units, Samsung’s best response is to produce 35 units. output by rival firms.
For every possible output that LG might choose, we could determine Samsung’s
profit-maximizing output as we did in Figure 13.1. The curve R in Figure 13.2 sum-
S
marizes Samsung’s profit-maximizing output choices. The curve R is a reaction reaction function A
S
function. It tells us a firm’s best response (i.e., profit-maximizing output choice) to graph that shows a firm’s
the output level of a rival firm. Figure 13.2 also graphs LG’s reaction function R LG . 6 best response (i.e., profit-
Note that both reaction functions are downward sloping. Thus, each firm’s profit- maximizing choice of out-
maximizing output choice becomes smaller as its rival produces more output. put or price) for each possi-
ble action of a rival firm.
Equilibrium in a Cournot Market
Under perfect competition, a key feature of the market equilibrium is that no firm has
an incentive to deviate from its profit-maximizing decision once the market equilib-
rium has been attained. The same is true of an equilibrium in a Cournot market: At a
Cournot equilibrium, each firm’s output is a best response to the other firm’s output Cournot equilibrium
(i.e., in equilibrium, each firm is doing as well as it can given the other firm’s output). An equilibrium in an oli-
Thus, neither firm has any after-the-fact reason to regret its output choice. 7 gopoly market in which
each firm chooses a profit-
maximizing output given
6 If the firms are identical, why do their reaction functions appear different? The reason is that, in
Figure 13.2, the horizontal axis represents Samsung’s output and the vertical axis represents LG’s output. the output chosen by
other firms.
Plotting both curves on the same graph makes one look like the inverse of the other. Algebraically, the
two reaction functions are identical (as is shown in Learning-By-Doing Exercise 13.1).
7 In Chapter 14, you will see that the Cournot equilibrium is a particular example of what is called a Nash
equilibrium. For this reason, some textbooks refer to the Cournot equilibrium as the Cournot-Nash
equilibrium or the Nash equilibrium in quantities.