Oligopoly: Chapter 12
Practice Questions for Mid Term
6. Suppose that two identical firms produce widgets and that they are the only firms in the
market. Their costs are given by C
1
= 60Q
1
and C
2
= 60Q
2
, where Q
1
is the output of Firm 1
and Q
2
the output of Firm 2. Price is determined by the following demand curve:
P = 300 - Q
where Q = Q
1
+ Q
2
.
a.
Find the Cournot-Nash equilibrium. Calculate the profit of each firm at this equilibrium.
To determine the Cournot-Nash equilibrium, we first calculate the reaction function for
each firm, then solve for price, quantity, and profit. Profit for Firm 1,
TR
1
-
TC
1
, is equal to
Therefore,
Setting this equal to zero and solving for
Q
1
in terms of
Q
2
:
Q
1
= 120 - 0.5
Q
2
.
This is Firm 1’s reaction function. Because Firm 2 has the same cost structure, Firm 2’s
reaction function is
Q
2
= 120 - 0.5
Q
1
.
Substituting for
Q
2
in the reaction function for Firm 1, and solving for
Q
1
, we find
Q
1
= 120 - (0.5)(120 - 0.5
Q
1
), or
Q
1
= 80.
By symmetry,
Q
2
= 80. Substituting
Q
1
and
Q
2
into the demand equation to determine the
price at profit maximization:
P
= 300 - 80 - 80 = $140.
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- Spring '11
- gul
- Oligopoly, Reaction function, Everglow
-
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