Oligopoly

Question 1

What is a monopoly?

Answer 1

This is an industry consisting of a single firm.

Question 2

What is a duopoly?

Answer 2

This is an industry consisting of two firms.

Question 3

What is an oligopoly?

Answer 3

This is an industry consisting of a few firms. Particularly, each firm’s own price our output decisions affect its competitors’ profits.

Question 4

How do we analyse markets in which the supplying industry is duopolistic (simultaneous game)?

Answer 4

Assume the firms compete by choosing output levels.

If firm 1 produces y1 units and firm 2 produces y2 units, then total quantity supplied is y1 + y2.
The market price will be p(y1 + y2).

The firms’ total cost functions are:
c1(y1) and c2(y2)

Suppose firm 1 takes firm 2’s output level choice y2 as given. Then firm 1 sees its profit function as:
π1 (y1, y2) = p(y1 + y2)y1 – c1(y)

Question 5

What is a reaction curve/function (AKA best-reply function)?

Answer 5

This is the actions that a firm may undertake for any given action chosen by a rival firm. In other words, this is how they maximise profits.

Question 6

How do you find the reaction function in a simultaneous game?

Answer 6

e.g. given y2, firm 1’s profit function is
π1 (y1, y2) = (60 – y1 – y2) \y2 – y1⮝2

So, given y2, firm 1’s profit-maximising output level solves
∂π1/∂y1 = 60 – 2yq – y2 – 2y1 = 0

i.e. firm 1’s best response to y2 is
y1 = R1(y2) = 15 – y2/4

Question 7

How do you plot a reaction curve?

Answer 7

Vertical axis = y2
Horizontal axis = y1
Reaction curve = line that intersects with both axis’

Question 8

When does an equilibrium occur between firm’s output?

Answer 8

When each firm’s output level is a best response to the other firm’s output level, for then neither wants to deviate from its output level.

Question 9

When is a pair of output levels a Cournot-Nash equilibrium?

Answer 9

If Y1* = R1(Y2) and Y2 = R2(Y1*)

Question 10

Generally, what is firm 1’s profit function and profit maximising value of y1 given firm 2’s chosen output of y2 (in a simultaneous game)?

Answer 10

F1s profit function: π1 (y1, y2) = p(y1 + y2)y1 – c1(y1)
F1s best response: ∂π1/∂y1 = p(y1 + y2) + y1(∂p(y1 + y2)/∂y1) – c1’(y1) = 0

The solution, y1 = R1(y2), is firm 1’s Cournot-Nash reaction to y2.

Question 11

Generally, what is firm 2’s profit function and profit maximising value of y2 given firm 1’s chosen output of y1 (in a simultaneous game)?

Answer 11

F2s profit function: π2 (y1, y2) = p(y1 + y2)y2 – c2(y2)
F1s best response: ∂π2/∂y2 = p(y1 + y2) + y2(∂p(y1 + y2)/∂y2) – c2’(y2) = 0

The solution, y2 = R2(y1), is firm 2’s Cournot-Nash reaction to y1.

Question 12

What is an iso-profit curve?

Answer 12

This reflects the combinations of price (P) and quantity (Q) that give the same amount of profit.

For firm 1, an iso-profit curve contains all the outputs pairs (y1, y2) giving firm 1 the same profit level (π1).

Question 13

What do iso-profit curves look like?

Answer 13

They look like pointy lower-case n’s.
Vertical axis = y2
Horizontal axis = y1

Increasing profit for firm 1 = pointy n is drawn from left to right
Increasing profit from firm 2 = point n is rotated clockwise 90-degrees (drawn from up to down)

Question 14

What do reaction curves look like?

Answer 14

They are straight lines that go through the tips of the firm’s iso-profit curves.

Question 15

What is a simultaneous game?

Answer 15

This is where the competition between firms involves output levels, as the strategic variables, chosen at the same time.

Question 16

What is a sequential game?

Answer 16

This is when one firm chooses its output level first and then another firm responds. This means 1 firm is a leader and the other is a follower.

Question 17

What is a Stackelberg game?

Answer 17

This is where the leader moves first and then the follower moves sequentially (sequential game).

Question 18

What is the advantage of being the leader in a Stackelberg?

Answer 18

The leader (firm 1) is about to perfectly anticipate the followers (firm 2) reaction to any y1 chosen by themselves. They simply have to consider what firm 2’s best response to their decision would be.

Question 19

What is a stackelberg leaders’ profit function?

Answer 19

π1 (y1) = p(y1 + R2(y2))y1 – c1(y1)

The leader chooses y1 to maximise its profit.

Question 20

Can the leader make a profit at least as large as its Cournot-Nash equilibrium profit?

Answer 20

Yes. The leader could choose its Cournot-Nash output level, knowing that the follower would then also choose its C-N output level. The leader’s profit would then be its C-N profit.

But the leader does not have to do this, so its profit must be at least as large as its C-N profit.

Question 21

Graphically, what does a Cournot-Nash equilibrium look like?

Answer 21

Vertical axis: y2
Horizontal axis: y1

Iso-profit curve for firm 1: n shaped curve
Reaction curve for firm 1: straight line (not vertical) going through middle of firm 1’s iso-profit curve (but almost tangent to it)

Iso-profit curve for firm 2: n shaped curve rotated clockwise 90-degrees
Reaction curve for firm 2: straight line (not horizontal) going through middle of firm 2’s iso-profit curve (but almost tangent to it)

Cournot-Nash equilibrium: intersection between Max of Iso-profit for firm 1 and 2 (y1, y2).

Question 22

When can price and quantity competition be used?

Answer 22

In a monopoly setting, price or quantity competition make no difference. In an oligopoly setting, price and quantity competition lead to different outcomes.
- Price competition is much more aggressive than quantity competition

Question 23

What are Bertrand games?

Answer 23

Games in which firms use only price strategies and play simultaneously are Bertrand games.

Each firm’s marginal production cost is constant at c. All firms set their prices simultaneously.

Question 24

Do Bertrand games have a nash equilibrium?

Answer 24

Yes, exactly one. Where all firms set their prices equal to the marginal cost (C).

This is because if one firm sets prices higher than another firm’s price, then the higher-priced firm will have no customers. Hence at equilibrium, all firms must set the same price (C), as this prevents undercutting.

Question 25

What assumptions are there in Betrand games?

Answer 25

• Few firms that sell to many customers
• Firms produce identical products at a constant marginal cost (c)
• Each firm independently sets its price in order to maximise profits
• Barriers to entry
• Consumers enjoy: (i) perfect information; (ii) zero transaction costs

Question 26

What is the inverse, direct and derived demand in betrend games?

Answer 26

Derived demand is the demand conditional upon the price charged by the other firm. We need the derived demand for each firm.

Inverse demand: p = a – bQ
Direct demand: Q = a/b – P/b

Take firm 2. Assume that firm 1 has set a price of p1. If firm 2:

• Sets a price greater than p1, she will sell nothing
• Sets a price less than p1, she gets the whole market
• Sets a price of exactly p1, consumers are indifferent between the two firms (the market is shared, presumable 50:50)

Derived demand for firm 2:
Q1 = 0 if p2 > p1
Q2 = a/b – p2/b if p2 < p1
Q2 = (a/b – p2/b)/2 if p2 = p1

Derived demand for firm 1:
Vice versa

Question 27

What is the logic of undercutting?

Answer 27

The logic of it is trying to gain as much market share as possible, as this leads to more profit. Each firm will keep undercutting each other until they get to p = c, where neither can go any lower. Cutting prices below costs would result in negative profits for both firms.

Question 28

What is a Bertrand equilibrium?

Answer 28

A Bertrand equilibrium (or Nash-Bertrand equilibrium) is a set of prices such that no firm can obtain a higher profit by choosing a different price if the other firms continue to charge these prices.

What is firm 2’s Best Response function in a Bertrand game?
Firm 2’s BR to any price set by Firm 1:
P*2 = (a + c)/2		if p1 > (a + c)/2
P*2 = p1 – E		if c < p1 (a + c)/2
P*2 = c			if p1  c

Firm 1 has a symmetric BR
Note: E = something small

Question 29

What is the Bertrand paradox?

Answer 29

The Bertrand equilibrium with homogenous products and identical constant MCs (c) is pi = c for all I = 1, 2, …, n.

Therefore, it coincides with the competitive equilibrium.
This is paradoxical and unrealistic.

Question 30

How can you solve the Bertrand paradox?

Answer 30

One way to solve the paradox is to consider product differentiation.
- Firms prefer to differentiate their products:
o To generate consumer loyalty
o Not to loose all he demand when they price above their rivals
Another way to solve the paradox is to consider repeated interactions.
- In an infinitely repeated Bertrand game, sufficiently patient firms can sustain a collusive agreement consisting in setting the monopoly price pm > c.

Question 31

What is the difference between Cournot, Stackelberg and Bertrand games?

Answer 31

Stackelberg: strategic game in which the leader moves first and then the follower firms move sequentially.

• The firms sell homogenous products,
• Competition is based on output and
• Firms choose their output sequentially and not simultaneously
• Note: sequential price games are not stackelberg, they are just called sequential price games

Cournot:

• The firms produce homogenous goods,
• They compete simultaneously on output and market share, and
• They expect their rivals will not change their output in response to any change that they make.

Bertrand: there are two versions of this model, depending on whether the products are homogenous or differentiated.
- Homogenous
o The firms produce standardised products at the same MC
o It is in the best interest of each firm to undercut
o The price war leads to P = MC
- Differentiated
o Price competition doesn’t necessarily lead to a competitive outcome
o This is because each firms demand wont become zero when it raises its price (as they will still have loyal customers.

Things to note:

• The aggregate Stackelberg is greater than the aggregate Cournot output, but less than the aggregate Bertrand output.
• The Stackelberg price is lower than the Cournot price, but greater than the Bertrand price.
• The aggregate Stackelberg output is greater than pure monopoly or cartel, but less than the perfectly competitive market.
• The Stackelberg price is lower than the pure monopoly or cartel price, but greater than the perfectly competitive price.

Question 32

What is collusion?

Answer 32

This is an attempt to enforce market discipline and reduce competition between a group of supplier.

• A group of firms that collude is called a cartel.
• Collusion is studied by means of repeated games.

Question 33

How do cartel members agree to prevent excessive competition?

Answer 33

By coordinating their actions:

• Prices
• Market shares
• Exclusive territories.

Question 34

How can cartels be sustained?

Answer 34

Collusion is sustainable if the present value of staying in the cartel exceeds the present value of cheating on the cartel.

Question 35

What are the two types of repeated games?

Answer 35

Finitely repeated: the game is played for a finite and known number of rounds, for example, 2 rounds/repetitions.
- These are very rare
Infinitely or indefinitely repeated: the game has no predetermined length; players act as though it will be played indefinitely, or it ends only with some probability.
- These are very common

Question 36

How may players discount payoffs received in the future?

Answer 36

By using a constant discount factor:

δ = 1/(1 + r), where 0 < δ < 1.