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Exams Take Test: Midterm 2H
Take Test: Midterm 2
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QUESTION 1
Consider the following Stackelberg environment. There are three firms in the
market. All firms produce a homogenous good. Firm 1 chooses how much to
supply first. Firm 2 chooses how much to supply after observing the quantity
supplied by firm 1. Finally, firm 3 observes the quantity supplied by firm 1 and
firm 2 and chooses how much to supply. The market demand is .
For firm , the total cost function is . Firm 2 solves:
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Dominick Sperando 9
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Consider the following Stackelberg environment. There are three firms in the
market. All firms produce a homogenous good. Firm 1 chooses how much to
supply first. Firm 2 chooses how much to supply after observing the quantity
supplied by firm 1. Finally, firm 3 observes the quantity supplied by firm 1 and
firm 2 and chooses how much to supply. The market demand is .
For firm , the total cost function is . What is the quantity
produced by firm 1?
QUESTION 3
Consider the following Stackelberg environment. There are three firms in the
market. All firms produce a homogenous good. Firm 1 chooses how much to
supply first. Firm 2 chooses how much to supply after observing the quantity
supplied by firm 1. Finally, firm 3 observes the quantity supplied by firm 1 and
firm 2 and chooses how much to supply. The market demand is . Fo
firm , the total cost function is . Profit of firm is In this
environment,
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QUESTION 4
Consider the following Stackelberg environment. There are three firms in the
market. All firms produce a homogenous good. Firm 1 chooses how much to
supply first. Firm 2 chooses how much to supply after observing the quantity
supplied by firm 1. Finally, firm 3 observes the quantity supplied by firm 1 and
firm 2 and chooses how much to supply. The market demand is .
For firm , the total cost function is . What is the quantity
produced by firm 2?
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QUESTION 5
Consider the following Stackelberg environment. There are three firms in the
market. All firms produce a homogenous good. Firm 1 chooses how much to
supply first. Firm 2 chooses how much to supply after observing the quantity
supplied by firm 1. Finally, firm 3 observes the quantity supplied by firm 1 and
firm 2 and chooses how much to supply. The market demand is .
For firm , the total cost function is . What is the quantity
produced by firm 3?
25
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25
12.5
50
18.75
QUESTION 6
Consider the following Stackelberg duopoly. Both firms produce a
homogenous good. Firm 1 chooses how much to supply first. Firm 2 chooses
how much to supply after observing the quantity supplied by firm 1. The market
demand is . For firm , the total cost of production is
. What is the optimization problem that firm 1 solves?
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QUESTION 7
Consider the following Stackelberg duopoly. Both firms produce differentiated
goods. For form 1, the demand is . For form 1, the
demand is . Firm 1 chooses the price first. Firm 2
chooses the price after observing the choice of firm 1. For firm , the total cost
function is . What is the price set by firm 2?
107/12
71/3
147/12
35/3
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QUESTION 8
Consider the following Stackelberg duopoly. Both firms produce differentiated
goods. For form , the demand is . Firm 1 chooses the price
first. Firm 2 chooses the price after observing the choice of firm 1. For firm , the
total cost function is . What is ?
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85
72.5
60
48.5
QUESTION 9
Consider a standard Stackelberg environment. Two firms produce
heterogenous goods. The demand function for good is ,
where is the price. Firm faces the following cost function:
. Firm 1 chooses the price first. Firm 2 chooses the price
after observing . In this environment,
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QUESTION 10
Consider the following Stackelberg duopoly. Both firms produce differentiated
goods. For form , the demand is . Firm 1 chooses the price
first. Firm 2 chooses the price after observing the choice of firm 1. For firm , the
total cost function is . What is ?
85
72.5
60
48.5
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QUESTION 11
Consider the following Stackelberg duopoly. Both firms produce a
homogenous good. Firm 1 chooses how much to supply first. Firm 2 chooses
how much to supply after observing the quantity supplied by firm 1. The market
demand is . For firm , the total cost of production is
. What is the quantity produced by firm 1?
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QUESTION 12
Consider the following Stackelberg duopoly. Both firms produce differentiated
goods. For form 1, the demand is . For form 1, the
demand is . Firm 1 chooses the price first. Firm 2
chooses the price after observing the choice of firm 1. For firm , the total cost
function is . What is the price set by firm 1?
63/9
71/9
140/3
35/3
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QUESTION 13
Consider the following Stackelberg duopoly. Both firms produce a
homogenous good. Firm 1 chooses how much to supply first. Firm 2 chooses
how much to supply after observing the quantity supplied by firm 1. The market
demand is . For firm 1, the marginal cost of production is . Fo
firm 2, the marginal cost of production is . What function describes the
eaction of firm 2 to the observed quantity produced by firm 1?
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QUESTION 14
Consider the following Stackelberg duopoly. Both firms produce a
homogenous good. Firm 1 chooses how much to supply first. Firm 2 chooses
how much to supply after observing the quantity supplied by firm 1. The market
demand is . For firm 1, the marginal cost of production is . Fo
firm 2, the marginal cost of production is . What is the quantity produced by
firm 1?
105
48
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120
12
QUESTION 15
Consider the following Stackelberg duopoly. Both firms produce a
homogenous good. Firm 1 chooses how much to supply first. Firm 2 chooses
how much to supply after observing the quantity supplied by firm 1. The market
demand is . For firm 1, the marginal cost of production is . Fo
firm 2, the marginal cost of production is . What is the market clearing price?
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QUESTION 16
Consider the following Extended Form Game:
What is the payoff that player 2 derives from the strategy {A, (B',A')}?
1
3
4
7
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True
False
Consider the following Extended Form Game:
Player 2 threatens she will play B' no matter what. Is this threat credible?
QUESTION 18
Consider the following Extended Form Game:
Player 1 always plays B. Player 2 chooses the strategy (B', B'). What is the
payoff of player 1?
3
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9
1
5
QUESTION 19
Consider the following Extended Form Game:
What payoff does player 1 derives if player 1 chooses the strategy (B,A) and
player 2 chooses the strategy (A', B')?
9
5
8
1
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True
False
Consider the following Extended Form Game:
Player 2 threatens to play (A',B') no matter what. Is this threat credible?
QUESTION 21
Consider the following Extended Form Game:
What is the Subgame Perfect Nash Equili
ia?
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(B,(B', B'))
{ (B,(B',A')), (B,(B', B'))}
{(B, B')}
{ (B,(A', B')), (B,(B', B'))}
QUESTION 22
Consider the following Extended Form Game:
What is the Subgame Perfect