1
Winter 2005
Prof. Cai
Econ 106G:
Midterm Exam
10:2011:50 Friday, February 11, 2005
The midterm exam consists of THREE questions, with total points of 100. Q1 and
Q2 account for 30 points each, and Q3 accounts for 40 points. You have one and
half hour to work on them. Optimally use your time. Read each question very
carefully, clearly write down each step, and mark your answers.
Good luck!
1.(30 points)
In a market there are three firms. The total market demand is given
by
100
p
Q
=−
, where
123
Qqq q
=++
. All three firms have a constant marginal cost of
10. Firm 1 chooses its quantity
1
q
first. After observing
1
q
, firms 2 and 3 make their
quantity choices simultaneously.
(a)
Derive the best responses for firms 2 and 3. For any given
1
q
,
derive the Cournot
equilibrium for the subgame where firms 2 and 3 make their quantity choices
simultaneously. (15 points)
(b)
Derive firm 1’s optimal quantity. How much will firm 2 and firm 3 produce in
equilibrium? What are the profits of the three firms in equilibrium? (15 points).
2. (30 points) Suppose there are 4 people in a committee whose policy positions are
represented as from the far left to the far right, 1, 2, 3, and 4. Accordingly we call them
committee member/player 1, 2, 3, or 4. There is an election for the position of committee
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 Winter '04
 cai
 Game Theory, Chairman, mixed strategy equilibrium

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