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WOLFRAM|DEMONSTRATIONS PROJECT

Cournot Competition with Two Firms

​
inverse demand function p(Q)b-aQ, Q
q
1
+
q
2
a ∈ [1, 5]
1.
b ∈ [1, 5]
5.
profit function for firm i∈{1,2}:
π
i
(
q
1
,
q
2
)=(p(Q)-
c
i
)
q
i
c
i
represents the marginal cost of firm i
c
1
∈[0,3]
1.
c
2
∈[0,3]
1.
plot 45° line
model
p(Q) = 5.-1.Q
π
1
(
q
1
,
q
2
) = (p(Q) - 1.)
q
1
π
2
(
q
1
,
q
2
) = (p(Q) - 1.)
q
2
Cournot equilibrium
*
(
q
1
)
b-2
c
1
+
c
2
3a
= 1.33333
*
(
q
2
)
=
b+
c
1
-2
c
2
3a
= 1.33333
equilibrium price: 2.33333
red line: best response of firm 1 for
q
2
green line: best response of firm 2 for
q
1
point: Cournot equilibrium
This Demonstration illustrates a simple Cournot competition in which there are only two firms, and the inverse function is
p(
q
1
,
q
2
)=b-a(
q
1
+
q
2
)
. The horizontal axis represents
q
1
and the vertical one represents
q
2
. A red line and a green line represent the best response of firms 1 and 2 for the production of another firm, respectively. Cournot equilibrium corresponds to the purple point at which two best response lines intersect.
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