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PS 6 Solutions
Econ 367
Kaushik Basu
1.
Let us consider Firm 1.
Since they are symmetric firms, the analysis will be the
same for firm 2.
P=100Q
Q= q
1
+ q
2
Profit firm 1 = P*q
1
Firm 1 maximizes (100( q
1
+ q
2
)) q
1
=100q
1
q
1
2
q
1
q
2
Differentiate w/ respect to q1 and set equal to zero to maximize
1002q1q2=0
q
1
=50q
2
/2
By symmetry q
2
=50q
1
/2
Solving the system of these two best response functions, the NE is (100/3,100/3)
The firms could make more money by producing the monopoly amount and sharing
profits.
We know that monopoly profits is greater than the Cournot firm’s profits
because the monopolist could have picked q
1
*+q
2
* but did not.
In an unlimited capacity state, firm 2 produces more than 20.
When limited to 20, firm 1
will plug this amount into its best response function and produce 40.
NE (40,20)
2.
In a symmetric Bertrand game, the firms always cut their prices down to cost in
an attempt to gain more profit.
Here cost=0.
For any price firm 1 chooses above
zero, the other firm will price one cent below and gain the entire market.
Then
Firm 1 will undercut this new price in order to gain a profit greater than 0.
This
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 Spring '08
 BASU

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