Page 205 - DECO101_MICRO_ECONOMICS_ENGLISH

Micro Economics

Notes
X 2

190

100 A's reaction function

50
Cournot's equilibrium
e B's reaction function
30
0 X 1
80 96 200
or

X = 80
1
and
X = 50–0.25X = 50–(0.25)(80) = 30
1
2
Thus total output in the market is
X = X +X =110
1
2
and the market price
P = 100 – 0.5 (110)= 45
∂ R ∂ (PX ) ∂ P
MR = 1 = 1 = P X
+
1
∂ X 1 ∂ X 1 1 ∂ X
MR = 45+80(–0.5)
1
MR = 5
1
while MR = 45+30(–0.5)
2
MR = 30
2

That is the firm with the larger output has the smaller marginal revenue. The profi ts of the
duopolists are
π = PX – C 1
1
1
π = (45)(80)–5(80) = 3200
1
and
π = PX –C 2
2
2
π = (45)(30) – 0.25 (30) = 900
2
2
The second-order condition is satisfied for both duopolists

∂Π 1 = 95 X − 0.5X ∂Π 2 = 100 2X − 0.5X ⎫
−
−
∂ X 1 1 2 ∂ X 2 2 1 ⎪ ⎪
∂Π 1 =− < ∂Π 2 =− 2 < ⎬ ⎪
2
2
∂ X 2 1 1 0 ∂ X 2 2 0 ⎪ ⎭

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