Competition Policy & Collusion (collusion focus)

Question 1

2 types of collusion

Answer 1

Overt (firms cooperate)
Tacit (firms don’t cooperate)

Question 2

Why can a collusive outcome be hard to find

Answer 2

There is temptation to deviate

Question 3

How can we find a collusive outcome then (address the temptation to deviate)

Answer 3

Be able to detect and punish deviation

Question 4

Text book example:

Same product, MC=1 Pm=2.

First assume at collusive price both sellers sell all stock

A believes seller B charged 2.
What price does A charge

B) what if at collusive price they can’t sell all their stock

Answer 4

£2 means sell all (since assume sellers can sell all stock)

b) incentive to undercut by 2-epilson to gain more market share to sell all their stock

IRL, collusive prices are more like 2nd case, thus making temptation to deviate from collusion! (this was tacit collusion)

Question 5

Decision to deviate considers what

Answer 5

immediate gain v long term profit loss from punishment

knowns as incentive constraint

(long term profit loss - remember we said is high growth then long term losses are more, thus growth is good for collusion)

Question 6

Structural factors that affect collusion more/less likely (10)

Answer 6

concentration (higher i.e less firms, more likely as easier to agree since less)

entry (low barriers, less likely as other firms can enter)

cross ownership (more likely, if people on multiple firm’s boards, communication easijer)

regular order (more likely)

large buyer (less likely, as potential immediate gain higher so may be willing to accept punishment)

homogenous product (less innovation) (more likely as stable markets make collusion easier - prices are more predictable etc)

elasticity - more inelastic (can set a higher collusive price without losing demand)

Market transparency - when prices/output observable - incentive for info exchange (collusion)

In growing markets collusion more likely (larger profit loss from deviation)

Symmetrical firms - similar costs etc more likely to collude

Question 7

What do firms want

Answer 7

They want as much access as possible to past and current data on rivals price and quantity

Question 8

Assume a scenario where prices and quantities of rivals are unobservable for firm 1

Why is this a problem for firm 1 if they see a drop in their demand?

Answer 8

They won’t be able to tell whether it is the rival undercutting, or an economic shock

Question 9

What is a benefit of observability of prices and quantities?

Answer 9

Rules out price wars which are costly for firms

instead encourages exchange of information

Question 10

How can market authorities actually assist collusion

Answer 10

If they set an explicit upper limit, signals the price to collude at

Question 11

A firm announces price rise effective in 60 days, but reverts to current price if rivals do not follow suit with similar announcements.

This is a way to arrive at a collusive price without price wars. Is this private or public announcement?

Answer 11

private

Question 12

Public announcement example
:Both consumers and rivals have access to price info e.g advertised prices in newspaper

2 opposing effects, which one dominates

Answer 12

Price announcement can still help collusion

price transparency helps find the best deal

Price transparency tends to dominate

Question 13

Incentive constraint model

n firms
πic current profits of firm i
Vic discounted profits from collusion
πid current profits if deviates
Vip discounted profits in punishment phases

So what is the incentive constraint

Answer 13

πic + δVic > πid + δVip

Collude when collusion profits > deviation profits

(or if q asks what discount factor is required to sustain collusion, rearrange to δ)

Question 14

What if pi=pj=p (firm i price=firm j=price i.e a common price

b) if Pi<Pj

c) if Pi>Pj

Answer 14

Demand and profit is split /n

b) firm i gets all demand and profoit

c) firm i gets no demand and no profit

Question 15

Assume the collusive price is Pm (monopoly profits), and if they deviate from it, they face punishment by setting P=c

What is the incentive constraint now

b) how can this be simplified, if q asks what is the discount factor that sustains collusion?

Answer 15

π(pm)/n (1+δ+δ²+…) >= π(pm)

So collude when collusive profits>deviation

profits sharing monopoly price amongst n firms (which is discounted) >= getting the whole monopoly profit ONCE (by deviating)

b) simplified to π(Pm)/n x 1/1-δ >π(Pm)

Cancel out π(Pm) to get 1/n x 1/1-δ > 1
rearrange to get δ>= 1- 1/n

Question 16

So discount factor required to sustain collusion is

δ> 1 -1/n

What happens as n increases

b) what if n=2

Answer 16

Higher discount factor required to sustain collusion.

(makes sense as adding more firms makes agreements harder to come to)

b) standard NONCOOPERATIVE duopoly (emphasis on non-cooperative)

Question 17

So for n=2 we get standard noncooperative duopoly outcome: Now just work this out

Duopoly demand p = 1 - q1-q2, Q = q1+q2
assume no MC

Find quantity price and profit (working pg16)

Answer 17

q1=q2=1/3
p=1/3
π of 1 or 2 = 1/9 each

Question 18

So that was with 2 firms (duopoly)

Now assume we have N firms with identical cost

p= a-bQ and cost TCi = F + cqi²

how do we find q (collusive quantity)

b) once we find q how do we find Q and P

Answer 18

Since now cooperating, want to find max joint sum of profits:

total profit Σπ = p x Σqi - ΣTC

(Price x sum of quantities minus sum of total costs)

Then FOC to get MR and MC, set MR=MC
a - 2bNq = 2cq

Then set MR=MC
Rearrange to find q= a/2(bN+c)

b) Q is just add xN
Q = Na/2(bN+c)

find P by subbing Q into P= a=bQ

Question 19

So given our expressions for q Q and P, what happens when N increases

b) what do we get when N=1
c) key takeaway

Answer 19

Total quantity increase

Collusive quantity of each firm q falls

Price falls

B) monopoly price and output

c) increasing number of firms breaks down collusion

Question 20

We saw when n=2 and non-cooperative, we get standard non-cooperative duopoly i.e cournot

Now what if the duopoly is cooperative

What is our q, Q, P and π of each firm now. Is profit larger when cooperating or non cooperating when n=2?

Answer 20

They maximise joint profits MR=MC

Working pg 17
q=1/4
Q =1/2
p=1/2
π1,2 = 1/8

as we can see compare to non-cooperative
Q=2/3 p=1/3 q=1/3 π=1/9. profit larger when cooperating

Question 21

How can we show incentive to deviate from these collusive outcomes. Now assume firm 1 plays collusive outcome i.e q1=1/4

What does firm 2 do? is there incentive to deviate (solve)

Answer 21

Choose their quantity q2 to maximise profit given q1=1/4

sub q1=1/4 into firm 2’s profit max expression
maxπ2 = (1-1/4-q2)q2
FOC to get q2 = 3/8
then find profit by finding price first
P=1-1/4-3/8=3/8

So profit is π=3/8 x 3/8 = 9/64!
Deviation proft > collusive profit 1/8!

Question 22

So there is incentive for both to deviate from collusive levels, given the other doesn’t also deviate

a) what is profit for each if both deviate

b)So what is the nash equilibrium

Answer 22

Deviation quantity is q=3/8
So P= 1-3/8 - 3/8 = 1/4 (both now set q1 and q2=3/8)=
1/4 x 3/8 = 3/32
So this is profit if they both deviate

b)
For both to deviate! because….

BOTH are better off colluding and earn 1/8 profit each.
However there is incentive to deviate to earn 9/64 profit (given the other doesn’t also deviate).

So with no commitment mechanism both end up deviation and get 3/32 each. (worse off)

Question 23

What is the trigger strategy

b) when is this be upheld? and find the discount factor for this to hold! (first state present value of collusion profits vs deviation profits present value) (working pg19)

Answer 23

Players play collusion quantity (q=1/4 in our example) , unless someone deviates, then play cournot quantity (q=1/3)

b) this will be the strategy as long collusion profits>deviation profits,

PV of collusive profits = πc x 1/1-δ
PV of deviation profits πd + (πcournot x δ/1-δ)
i.e one-off deviation profit + discounted punishment profits onward

When rearrange this inequality we get discount factor>9/17

Question 24

However it may not be realistic to punish (cournot) forever, so now punish for T amount of rounds, then revert to collusion

Green Port model does this

Question 25

In this model we assume Probability a of no demand so no profits, and probability (1-a) demand is positive so we do get profits. We do not know cause of their demand, whether been undercut by other firm, or low demand (economic shock) What is expected discounted profit from collusion (v)?

Answer 25

V = π/n (1/1-δ) which simplifies to V = π/n + δ(v) i.e shared profit from collusion

Question 26

Now incorporate probabilities (a) and (1-a) what is our expected discounted profit (v) now when we incorporate probabilities. Explain the intuition

Answer 26

V = (1-a)[π/n + δ(v)] + a(δT+¹)(V) So probability of good times (1-a) x collusive outcome + probability of bad outcome (t=0 earns nothing as punishment, so from t+1 start earning collusive outcome V again.

Question 27

We can rearrange to get V on one side it makes it easier to find out what happens to expected discounted profit probability of bad outcome a increases punishment period T increases

Answer 27

V = 1/ [1-δ(1-a+aδT)] x π/n if probability of bad outcome increases, expected discounted profit falls if punuishment period increases, expected discounted profit falls

Question 28

So for green porter model what is the IC for sustainable collusion b) if we rearrange to make δ subject

Answer 28

(1-a)(π/n + δV) ≥ (1-a)π + (1-a)δT+¹V b) δ(1-δT)V ≥ π - π/n

Question 29

RS1986 model do?

Answer 29

looks how demand changes can affect collusion

Question 30

So if demand grows overtime. Does this make collusion easier or harder to sustain

Answer 30

easier, as deviating compares immediate gain vs long term losses. So thus long term loss would be larger if demand growth is high

Question 31

Assume growth factor g, in a duoply so for t=0 D(p) = g⁰D(p) but for t=5 g⁵D(p) Derive the IC, (rmb its duopoly) b) what if we rearrange to δ c) what can we see for impact of growth

Answer 31

π/2 + δ(g)π/2 + … + δt(g) to the t π/2 ≥ π + δ(g)0 shared duopoly profits + discounted shared duopoly profits also accounting for growth rate >= deviation profit b) δ>= 1/2g c) g>1 facilitates collusion (since required discount factor for collusion becomes lower) g<1 hinders collusion so growth is good for collusion.

Question 32

What is IC for meeting every period vs every 2 periods B) which is harder to sustain collusion

Answer 32

Every period δ >= 1 - 1/n (Rearranged from π(pm)/n x 1/1-δ >= π(pm) pg 16 working) Every 2 period δ² >= 1 - 1/n B) Harder to sustain collusion when firms meet every 2 periods; require more patience when interactions are less frequent!