Week 9 - Oligopoly and Duopoly

Question 1

What is an oligopoly?

Answer 1

An oligopoly is a market with more than one firm, but where the number of firms is relatively small, leading to strategic competition among firms.

Question 2

Why is game theory used to analyze oligopolies?

Answer 2

Because firms in an oligopoly compete strategically, considering how rivals will respond to their actions and how they should respond to rivals, making game theory a useful tool for analysis.

Question 3

What is a duopoly?

Answer 3

A duopoly is a special case of an oligopoly with exactly two firms.

Question 4

What is the Bertrand model?

Answer 4

The Bertrand model is a simultaneous decision-making model in an oligopoly where firms set prices.

Question 5

What assumption does Bertrand competition make?

Answer 5

Each firm simultaneously sets its price, taking the other firm’s price as given.

Question 6

What is the Bertrand paradox?

Answer 6

The Bertrand paradox is the result where even with only two firms, Bertrand competition can lead to a situation equivalent to perfect competition, resulting in zero profits for both firms.

Question 7

In Bertrand competition, what happens if one firm charges less than its rival?

Answer 7

All consumers buy from the firm that charges less.

Question 8

What is the result if both firms set the same price in Bertrand competition?

Answer 8

Demand is evenly split between the firms.

Question 9

What are the conditions assumed for simplicity in the Bertrand model?

Answer 9

Constant marginal costs and no fixed costs, with firms selling identical (homogeneous) products.

Question 10

How do consumers behave in Bertrand competition?

Answer 10

Consumers will not buy from a firm that charges more than its rival, similar to behavior in a competitive market.

Question 11

What is the best response for a firm if the rival’s price p2>c?

Answer 11

The best response is to choose a price just below
p2 , i.e., 𝑝2 − 𝜖, where
𝜖 is an arbitrarily small real number.

Question 12

What happens if a firm’s price
p1 is above, equal to, or below
p2 in Bertrand competition?

Question 13

What is the Bertrand equilibrium when both firms have the same marginal cost
𝑐?

Answer 13

The Bertrand equilibrium is
{c,c}.

Question 14

Why do firms in Bertrand competition price at marginal cost if they are equally efficient?

Answer 14

Because any other price would be undercut by the rival firm, leading both to price at marginal cost to avoid losing all customers.

Question 15

What is a possible way to relax the Bertrand result?

Answer 15

Introducing product differentiation, which is likely in markets with a small number of firms, can relax the Bertrand result.

Question 16

What is the Cournot model?

Answer 16

The Cournot model is a simultaneous decision-making model in an oligopoly where firms set quantities (output levels).

Question 17

What is the key assumption of Cournot competition?

Answer 17

Each firm simultaneously sets its output, taking the other firm’s output as given.

Question 18

How many firms are involved in Cournot duopoly and what do they produce?

Answer 18

Two firms, 1 and 2, produce a homogeneous product.

Question 19

How is the inverse demand curve represented in Cournot duopoly?

Answer 19

p (y1+y2)

Question 20

What does each firm consider when choosing its output?

Answer 20

Each firm takes the other firm’s output as given.

Question 21

What is Firm 1’s belief about Firm 2’s output denoted as?

Question 22

What is Firm 1’s profit maximisation problem?

Question 23

What does solving Firm 1’s profit maximisation problem provide?

Question 24

What does varying y2e allow Firm 1 to find?

Answer 24

Firm 1’s optimal output for different levels of output for Firm 2, defining Firm 1’s best response function.

Question 25

What is Firm 2’s best response function denoted as?

Question 26

What defines the Nash Equilibrium in Cournot competition?

Answer 26

The two firms simultaneously setting outputs which are best responses to each other.

Question 27

What conditions must the Cournot equilibrium output choices (y1,y2) satisfy?

Question 28

What does each firm do at Cournot equilibrium?

Answer 28

Each firm is simultaneously choosing the output that maximises its profits, given the output of the other firm.

Question 29

How are best response functions and Cournot equilibrium shown in a diagram?

Answer 29

Best response functions slope down, indicating that if Firm 1 expects Firm 2 to set a higher output, Firm 1 will reduce its own output.

Question 30

Draw the isoprofit graphs for cournot duopoly

Question 31

What do isoprofit curves show?

Answer 31

Combinations of the two firms’ outputs that give a common level of profit for one of the firms.

Question 32

What is shown in the diagram of Firm 1’s best response curve and isoprofit curves?

Answer 32

Firm 1’s best response curve and combinations of outputs that yield the same profit level for Firm 1.

Question 33

What does each isoprofit curve represent for Firm 1?

Answer 33

All combinations of
𝑦
1
y
1
​
and
𝑦
2
y
2
​
that lead to a single level of profit for Firm 1.

Question 34

How does a lower isoprofit curve relate to Firm 1’s profit?

Answer 34

A lower isoprofit curve corresponds to a higher level of profit for Firm 1.

Question 35

What is the most profitable scenario for Firm 1 for any given
𝑦
1
y
1
​
?

Answer 35

It is most profitable for Firm 1 if Firm 2 produces nothing.

Question 36

How does Firm 2’s output affect Firm 1’s profit?

Answer 36

The more Firm 2 produces, the worse it is for Firm 1, as higher combined output causes the price to fall.

Question 37

What does the best response curve for Firm 1 represent?

Answer 37

It joins the levels of
𝑦1 that maximise Firm 1’s profits for different levels of 𝑦2.

​

Question 38

What must be true for Firm 1 to be on the best response curve?

Answer 38

Firm 1 must be earning the highest level of profit possible for a given 𝑦2, and thus must be on the lowest possible isoprofit curve.

Question 39

How do the isoprofit curves behave when they cross Firm 1’s best response curve (BR1)?

Answer 39

The isoprofit curves must be horizontal when they cross BR1.

Question 40

How do Firm 2’s best response curve and isoprofit curves behave?

Answer 40

Firm 2’s best response curve joins the highest points on each isoprofit curve, and the isoprofit curves must be vertical when they cross Firm 2’s best response curve.

Question 41

What is the Stackelberg model?

Answer 41

The Stackelberg model is a model of quantity leadership in an oligopoly, where one firm sets its output first and the other follows.