Duopoly & Games
1.
T
F
In Cournot equilibrium each firm chooses the quantity that maximizes its
own profits assuming that the firm's rival will continue to sell at the same price as before.
2.
T
F
In Bertrand competition between two firms, each firm believes that if it
changes its output, the rival firm will change its output by the same amount.
5.
T
F
In the Cournot model, each firm chooses its actions on the assumption that
its rivals will react by changing their quantities in such a way as to maximize their own
profits.
9.
The demand for y is given by y=256/p
2
. Only two firms produce y. They have
identical costs c(y)=y
2
. If they agree to collude and maximize their joint profits, how
much output will each firm produce?
A.
2
B.
5
C.
10
D.
12
E.
16
Correct Answer
1
F
2
F
5
F
9
A
set MR=MC and solve. See below
no 9. Industry output=Y and each firms output=y. So Y=2y
from Y=256/p
2
we get
R=pY=256/p and solving for p from Y=256/p
2
, p=(256)
1/2
Y
1/2
so R= (256)
1/2
Y
1/2
= 16Y
1/2
, on taking derivatives,
MR= 8 Y
1/2
, remember Y=2y
MC=2y=MR=8(2y)
1/2
,
So (2y)
3/2
=8
8y
3
=64
y
3
=8
y=2
Nash
1.
T
F
A situation where everyone is playing a dominant strategy must be a Nash
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 Spring '08
 TOOSSI
 Game Theory, Nash, Dominant strategy, Dominant strategy equilibrium

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