Question 1

In the Cournot duopoly model, what is the Nash equilibrium called?

Accepted Answer

Cournot equilibrium

Question 2

Which of the following best describes the Stackelberg duopoly model?

Accepted Answer

Two firms sequentially choose the quantity to produce.

Question 3

Given the market demand $$Q(p) = 1000 - 2p$$ and cost functions $$C_1$$($$q_1) = 200q_1$, C_2$(q_2$) = 200q_2$$, what is the reaction function for Firm 2 in the Stackelberg model?

Accepted Answer

$$q_2$$($$q_1) = 300 - 0.5q_1$

Question 4

In the Stackelberg equilibrium with $$Q(p) = 1000 - 2p$$, $$C_1$$($$q_1) = 200q_1$, C_2$(q_2$) = 200q_2$$, what are the equilibrium quantities produced by Firm 1 and Firm 2?

Accepted Answer

$$(q_1$, q_2$) = (300, 150)$$

Question 5

What is the equilibrium price in the Stackelberg model with $$q_1 = 300$ and q_2$ = 150$$?

Accepted Answer

$$p = 275$$

Question 6

Why does the leader have a first-mover advantage in the Stackelberg game?

Accepted Answer

The leader commits to an action that the follower must take as given and plays a best response to.

Question 7

Suppose the leader’s marginal cost increases to $$250$$ while the follower’s remains at $$200. $$What happens to the Stackelberg equilibrium output levels?

Accepted Answer

Both firms produce the same output.

Question 8

In the Cournot model with reaction functions $$q_1$$($$q_2) = 300 - 0.5q_2$ and q_2$(q_1$) = 300 - 0.5q_1$$, what is the Cournot equilibrium output for each firm?

Accepted Answer

$$(q_1$, q_2$) = (200, 200)$$

Question 9

Refer to the payoff matrix (first image). What is the Cournot equilibrium in this game?

Accepted Answer

(M, M)

Question 10

Refer to the game tree (third image). What is the subgame perfect Nash equilibrium (Stackelberg equilibrium) strategy for Firm 1?

Accepted Answer

Choose M

Question 11

If Firm 1 chooses M in the sequential game (Stackelberg), what is Firm 2’s best response?

Accepted Answer

Choose M

Question 12

In the Stackelberg model, if the leader’s marginal cost rises above $$250$$, what happens to the leader’s output relative to the follower?

Accepted Answer

The leader produces less than the follower.

Question 13

Which of the following is NOT a feature of the Bertrand duopoly model?

Accepted Answer

Firms simultaneously choose quantities.

Question 14

Suppose in a Stackelberg game, the leader’s cost is higher than the follower’s. What is a likely outcome?

Accepted Answer

The leader may earn lower profit than the follower.

Question 15

Given the profit formula for Firm 1 in Stackelberg equilibrium: $$\pi_1$ = p^* q_1$ - C_1$(q_1$)$$, with $$p^* = 275$$, $$q_1 = 300$, C_1$(q_1$) = 200q_1$$, what is Firm 1’s profit?

Accepted Answer

$$\22$$,500$

Question 16

Which of the following best explains why the Stackelberg leader can earn higher profit than in Cournot equilibrium?

Accepted Answer

The leader can commit to a higher output, forcing the follower to reduce output.

Question 17

If the market demand is $$Q(p) = 1000 - 2p$$ and both firms have marginal cost $$200$$, what is the inverse demand function?

Accepted Answer

$$p(q) = 500 - 0.5q$$

Question 18

In the Stackelberg model, what is the marginal revenue for Firm 1 given $$R_1 = 350q_1 - 0.25q$$_$$1^2$$?

Accepted Answer

$$MR_1 = 350 - 0.5q_1$

Oligopoly Models: Cournot, Bertrand, and Stackelberg Duopoly

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