Question 1

In a sequential-move game where Gooi Cones moves first and Ici Cones moves second, the payoffs in subgame perfect Nash equilibrium are determined by backward induction. If Gooi Cones chooses Yogurt Machines and Ici Cones chooses Gelato Machines, what are the realized payoffs?

Accepted Answer

(400, 150)

Question 2

Consider a sequential-move version of the rock-paper-scissors game. Player 1 moves first, Player 2 moves after observing Player 1’s choice. The winner receives a payoff of 1, the loser -1, and a tie is 0. What is the subgame perfect Nash equilibrium payoff for Player 1?

Accepted Answer

-1

Question 3

In a sequential-move integer game, Marilyn and Noah each choose a positive integer from 1 to 4. The lower number pays $1 to the other player. If both choose the same number, payoffs are zero. What is the subgame perfect Nash equilibrium payoff for Marilyn?

Accepted Answer

0

Question 4

A monopolist faces market demand $$Q(p) = 1500 - 5p$$ and cost function $$C(q) = 120q. $$What is the profit-maximizing quantity for this monopoly?

Accepted Answer

450

Question 5

Given the same monopolist as above, what price does the monopoly set?

Accepted Answer

210

Question 6

For the monopolist above, what is the profit level?

Accepted Answer

40500

Question 7

Suppose the government splits the monopolist into two firms with cost functions $$C_1$$($$q_1) = 120q_1$ and C_2$(q_2$) = 120q_2. If $$the firms compete in Cournot, what is firm 1’s reaction curve?

Accepted Answer

$$q_1$$($$q_2) = 450-0.5q_2$

Question 8

In the Cournot equilibrium for the above duopoly, what is the total output level?

Accepted Answer

600

Question 9

What is the market price in Cournot equilibrium for the duopoly described above?

Accepted Answer

180

Question 10

What is the total profit level of the two firms in Cournot equilibrium?

Accepted Answer

36000

Question 11

Relative to the Cournot equilibrium, the Bertrand equilibrium with homogeneous products ____.

Accepted Answer

results in a larger output at a lower price

Question 12

In a symmetric Bertrand duopoly with marginal cost $$120$$, what is the equilibrium price vector?

Accepted Answer

(120, 120)

Question 13

In the Bertrand equilibrium above, what is the profit of each firm?

Accepted Answer

(0, 0)

Question 14

In the Bertrand equilibrium above, what is the output of each firm?

Accepted Answer

(450, 450)

Question 15

Bertrand equilibrium has the same output, price, and welfare as the competitive equilibrium. What does this imply about efficiency?

Accepted Answer

has the same social welfare (i.e., total surplus) with competitive equilibrium

Question 16

Why is collusion on a high price unlikely in practice under the Bertrand model?

Accepted Answer

Each collusive firm has an incentive to gain market share at the expense of the other firms by cutting prices.

Question 17

In a two-firm Bertrand competition with constant marginal costs of $$2$$ and $$3$$, and market demand $$Q(p) = 10 - p$$, which of the following is a Bertrand equilibrium?

Accepted Answer

($$2.99, 2.99)$$

Question 18

In a Cournot duopoly, suppose Firm 1's reaction curve is $$q_1$$($$q_2) = 50 - 0.5q_2$ and Firm 2's reaction curve is q_2$(q_1$) = 75 - 0.75q_1. $$What is the Cournot equilibrium output for each firm?

Accepted Answer

$$q_1 = 20$$, $$q_2 = 60$$

Question 19

In a Cournot duopoly market with market demand $$Q(p) = 1500 - 5p$$, firm 1 has cost $$C_1$$($$q_1) = 120q_1$ and firm 2 has cost C_2$(q_2$) = 150q_2. $$What are the Cournot equilibrium outputs?

Accepted Answer

(350, 200)

Microeconomics Homework 6: Sequential Games, Monopoly, Cournot & Bertrand Competition

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