Oligopoly

Question 1

Oligopoly

Answer 1

Small amount of large firms.

We will assume 2 firms. (Duopoly)

Question 2

Assumption for oligopoly firms in terms of their decision making

Answer 2

Firms make simultaneous decisions.

Question 3

3 types of oligopoly

Answer 3

Bertrand (price setting)
Cournot (quantity setting)
Stackelberg model (one firm sets output first and other follows)

Question 4

Bertrand duopoly (price-setting)

Main concept

Answer 4

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

Question 5

Result of Bertrand competition

Answer 5

Perfect competition…

We will see how this arises

Question 6

Bertrand duopoly ASSUMPTIONS (4)

Answer 6

No capacity constraints i.e either firm can produce for the whole market demand.

Constant MC

No fixed costs

Homogenous goods

Question 7

Why does a Bertrand duopoly mean perfect competition?

2. If p₂>mc, what is firm 1’s optimal /best response to the price.

Answer 7

If one firm charges less than its rival, all consumers buy from it. (Recall first assumption of no capacity constraints, thus feasible)

If firms set same price, demand is evenly split.

2.
Constant MC
Suppose firm 2 chose price above mc.
For firm 1…
Choosing a price
>p₂ yields no sales/profit
=p₂ , half market sales p₂ - mc D(p₂)/2
<p₂ yield profit (p₁ - c) D(p₁)

So best response to p₂ is the highest price that is below p₂ i.e p₂ - ε where ε is an arbitrarily small real number. (We will take all sales, while keeping price as high as we can e.g if p₂ £12, sell at £11.99 to take all sales)

Question 8

What is firm 1’s best repsonse if p₂<= c and how does this show the Bertrand paradox/equilibrium

Answer 8

C is best response (since we dont want to make a loss. We dont want to undercut or match them)

So Bertrand equilibrium must be {c,c}, both firms set P=MC, so no profit.

This is because undercutting each other means 100% of the sales, and so they continue to undersell until P=MC, since they dont want to make a loss.

Question 9

What is this undercutting dependent on?

Answer 9

Production costs. if both firms are equally efficient they both price at MC of c.

Question 10

So this is not a desireable result. What does this suggest

Answer 10

It suggests price competition is disadvantageous, so firms should consider non-price competition methods.

e.g product differentiation.

Question 11

Cournot duopoly - main concept

Answer 11

Firm simultaneously sets its output, taking the other firms output as given. (Each firm has an idea about how much the other will produce)

Both firms produce a homogenous product, producing outputs y₁ and y₂.

Question 12

Inverse demand curve for cournot

Answer 12

P(y₁+y₂)

Question 13

Starting of with firm 1’s choice.

What do they base their optimal output y₁ on?

Answer 13

They assume firm 2 will produce output ye₂.

So treats as a constant in their profit maximisation problem
Maxp(y₁+ye₂)y₁-c(y₁)

So optimal output for firm 1 depends on how much firm 2 produces: y₁=f₁(ye₂)
This shows output of firm 1 is a function of the expected output of firm 2.

So varying ye₂ shows firm 1’s best response function to different quantities of firm 2.

Question 14

How can we find firm 1’s best respose function.

Answer 14

By varying ye₂ shows firm 1’s best response function to different quantities of firm 2.

Question 15

Then repeat for firm 2. They anticipate firm 1’s output.

What is their best response function

Answer 15

Y₂=f(ye₁)

Question 16

How can we find the nash/cournot equilibrium.

Answer 16

Where outputs are best responses to each other.
Here output maximises profits given output of other ifrm.

y₁ = f₁(y₂) and y₂ = f₂(y₁)

Question 17

Cournot equilibrium and the best response functions graphically (Pg9)

1. Starting with firm 1 - What is the 1st part needed for the diagram?
2. When does firm 1 make most profiot

Answer 17

1.
Isoprofit curves - represent all combinations of y₁ and y₂ that yield same profit for firm 1.

Lower isocurve = higher profit…

2. Most profitable when firm 2 produces nothing. The more firm 2 produces, worse for firm 1 (higher combined output means price falls).

Tricky: Explanation for why upward then downward sloping. (Look at annotations)

Question 18

2nd part needed:

Answer 18

Best response curve

Joins highest points on isoprofit curves, that earn the highest level of profit for firm 1 for different levels of y₂.

Question 19

Now firm 2’s best response curve and isoprofit curves

Answer 19

Same but isoprofits are left facing.

Question 20

Then we can show the 2 best responses together and find the cournot equilibrium. How?

2. Evaluation of this point…

Answer 20

Draw 2 best response curves. Where they intersect, we can see optimal output, given other firms output. (cournot equilibrium)

2.
However doesnt mean joint profits are maximised. There is an area below C that generates higher profits for both. (Only achievable by collusion)

Question 21

Linear demand case: assume constant MC of c and no fixed cost.

Steps…

Answer 21

Market demand p(y₁

Question 22

Stackelberg duopoly (sequential quantity setting)

Answer 22

Firm 1 sets output, then firm 2 observes and sets its own output.

Question 23

So firm 2’s maximisation problem is different

Answer 23

Rather than expectations like cournot, it KNOWS what firm 1 has produced, so sets it’s PM output given this output level.

Question 24

But what does firm 1 base its output choice on?

2. How does it do this?

Answer 24

Bases its output on how it expects firm 2 to respond. They know that firm 2 will maximise their profits by using their best response, essentially making this a constraint faced by firm 1.

2. By choosing its preferred point on firm 2’s best response function.

Question 25

How does this look like on a diagram (pg13)

Answer 25

IT DOESNT TOUCH/MEET TANGENT AT THE HIGHEST POINT ON ISPROFIT CURVE!!!

Question 26

Linear demand case for Stackelberg duopoly

Answer 26

Solve backwards to look at firm 2’s PM problem
Firm 2 faces a known output of y₁

Question 27

Vdveve

Question 28

Dwd

Question 29

Comparing cournot and stackelberg equilibriums (pg15), draw both. 1st one for linear case, 2nd with isoprofit curves in the general case

Who is better off in each type?

Answer 29

In Stackelberg firm 1 benefits from being leader, firm 2 loses from being follower, compared to the cournot case.

As isoprofit is lower

Question 30

Collusion - recall Cournot diagram, where at the equilbrium, they are at optimal points of output given the others choice.

However joint profit could be higher.

They could collude and access it. How (2)

Answer 30

Both set the monopoly price

or agree to share monopoly output between them

Question 31

Diagram for collusion of 2 firms acting like a monopolist

Green line represents output combinations that equal a monopoly output. Why?

Answer 31

Look at end of BR1. Here we see firm ones best response when firm 2 produces nothing i.e only firm in the market i.e monopoly output.

Same for end of BR2 on the y axis.

Question 32

We will look at the latter, where firms share the monopoly level output.

Where do they produce

Answer 32

Point A and B represnet where firms 1 and 2 share monopoly output and both earn higher profits.

So produce on line segment AB.

Question 33

2 problems with colluding

Answer 33

Illegal (so can’t bind each other to comply to their agreement)

Neither firm is on best response curve when colluding, so although profits maximised, there is incentive to cheat and change outputs.

Question 34

Diagram including collusion

Question 35

How firms can successfully coordinate / collude

Answer 35

If there is repeated interaction, we can create a punishment for firms that do not stick to the collusive outcome.

Trigger strategy.

Question 36

Trigger strategy

We will show for Bertrand, rather than cournot as simpler

Answer 36

Firm 1 strategy
First period, set price to monopoly price Pm.

In future periods, if firm 2 has history of always setting Pm, set price of Pm.

If firm 2 has ever deviated from Pm, set a price of c in every future period

Intuitton: deviation is punished, no profits can be earnt in future.

Question 37

Profits if firms always collude vs if one deviates

Answer 37

Always collude - earn πm/2 in this period and every period.
(Monopoly profit/2)

Deviate - it will earn πm (monopoly profit) in this period, but rival will punish them so they never earn a profit again.

Question 38

although firms discount future profits, unless impatient, they will prefer half monopoly profits (πm/2) every period rather than the one-off full monopoly profit. E.g only if cashflow problems we might want more.

We can see this with a discount factor of δ<1… what does this mean

Answer 38

This means firms would be equally happy to have £δ now, or £1 in next period. Higher δ means firm is more patient.

Payoff for firm that colludes at monopoly price
Vc= 1/1-δ x πm/2

Payoff for firm that deviates
Vd= πm. (Since earns no more)

When we compare 2 expressions, we can see collusion is better than deviating once. So unless firm is very impatient, collusion should be sustained.

Question 39

Evaluation of trigger strategy

Answer 39

A lack of credibility when a firm threatens a trigger strategy, as punishing the firm that deviates is also punishing the firm playing the srategy; neither will earn a profit again.