Transcript Contestable Market Model

Lecture 9
Oligopoly
An oligopoly is a market structure with a small number of firms together
controlling the market.
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Lecture 9
Oligopoly
There is no single model of oligopolistic behavior. In general there is a
spectrum bounded by:
A Contestable Market Model
A Collusive Model
We shall discuss these two general models and various forms within
them
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Lecture 9
Contestable Market Model
In it’s extreme, this is a market structure where the firms in an oligopoly
compete against one-another as if there was no oligopoly; that is they
compete freely in the market.
In general however there are degrees of this market structure. Oligopolies
engaged in a contestable market model usually compete on the basis of
price or market share but they use specific characteristics emerging from
the fact that they are oligopolies to their benefit.
We will examine some of these.
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Lecture 9
Contesting the Market Based on Price
This is the situation of price competition where firms in an oligopoly
compete against one-another based on price.
Consider the simple situation – without loss of generality – of a
duopoly (a market with only two operators in it).
Further assume that there is a simultaneous game established
between them. That is, they make business decisions – set prices and
quantities – independently of each other. (Remember this is a limiting
case)
Furthermore the two firms produce identical products and have
identical cost functions
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Let us assume that the cost function for either firms is:
TC  500  4QX  0.5QX2
The market demand seen by both firms:
P  100  Q  100  QA  QB
The marginal cost for a firm would be:
MCX  dTCX / dQX  4  QX
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In a pure competitive environment, both firms will be willing – would
eventually have to – bring down their prices to the marginal cost (but not
lower than it)
For both firm A and B:
P  100  QA  QB  4  QA  MCA
P  100  QA  QB  4  QB  MCB
QA  48  0.5QB
QB  48  0.5QA
Solving for one of the Q’s
QB  48  0.5( 48  0.5QB )
QB  32
And therefore
similarly
Q  QB  QA  64
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QA  32
Lecture 9
Substituting in the demand equation:
P  100  Q  100  64  $36
Total revenue:
And a total cost of:
Leaving a profit of:
$36  32  $1152
500  4( 32 )  0.5( 32 2 )  $1140
$1152  $1140  $12
We will contrast this case with that of collusive behavior later in the lecture
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Lecture 9
Price Leadership
In some oligopolies, one firm sets the price and others follow. The firm that sets
the price is called a:
Price Leader
How should the price leader set the price and output levels?
Under this model, the price leader sets the price but allows all other smaller
operators to sell at that price. Whatever amount the small firms DONOT
supply at the price provided, will be picked up by the price leader.
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It is important to note:
1. The price leader controls the market. If a price follower tries
to sell below the set price, the price leader will move in and
take up that market share
2. The price follower cannot of course sell at a price higher
than the one set by the market leader as there will be no
incentive for the consumer to by at a higher price
As such, prices stabilize at the price set by the price leader
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Setting a price – as a price leader:
1. As each small firm will take the price as given, they would
produce output at the quantity such that their price equals
their marginal cost.
2. As such a supply curve for each and therefore for all (as a
horizontal sum of all their marginal costs) small suppliers may
be obtained.
3. The demand curve of the dominant firm can be derived by
subtracting the amount supplied by the small firms from the
total amount demanded (note that demand varies with price.
That is demand varies if different prices are set by the
dominant firm and followed by the small firms).
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4. Thus the demand curve for the dominant firm D can be
obtained as the horizontal difference at each price
between the market demand curve and the supply curve
of the dominated firms.
5. The dominant curve knows its marginal cost (MC). By
determining the demand curve as above, it can set the
price and quantity at a point where MC intersects its
demand curve and as such maximize profits.
6. Of course, this would not necessarily be a point of
maximum profit (usually it is not) for the smaller operators
collectively or individually.
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Example: Home Depot
A simplified demand curve for home improvement supplies in a given town
is:
Q  100  5P
The demand curve for the Mom and Pop home improvement store(s) in
the same region is:
QM &P  10  P
Home depot’s marginal cost is:
MC  2QHD
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To derive the demand for Home Depot’s products:
QHD  Q  QM &P  ( 100  5P )  ( 10  P )  90  6 P
The price is therefore:
QHD  90  6 P
P   61 QHD  906  15  61 QHD
Home Depot’s total revenue is of course:
TR  PQHD  ( 15  QHD )QHD  15QHD  Q
1
6
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1
6
2
HD
Lecture 9
Marginal Revenue is:
MRHD
dTRHD
QHD

 15 
dQHD
3
Setting this equal to marginal cost:
MRHD
QHD
 15 
 2QHD  MCHD
3
QHD  6 73
P  13.93
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Lecture 9
Collusion and Cartels
Conditions in oligopolistic industries often favor collusion amongst the
organizations forming the oligopoly:
Numbers are small, and
Firms are aware of their interdependence
Collusion has its advantages:
Increased profit
Decreased uncertainty
Better opportunity to prevent entry of new players
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But collusion also brings forth some issues and problems:
Unilateral breaking of collusion by one or a few firms
may lead to substantial losses for those who have not
broken collusion
They are often forbidden by law or by cultural norms
Even when no intent is there to break collusion, it is
expensive to maintain a collusive agreement
Products have to be homogeneous
If collusion is in the open, it is often called a cartel and the action is called
price or supply regulation
Most national laws prohibit formation of cartels but they do exist as
international entities. Examples include OPEC and IATA (International Air
Transport Association)
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Breakdown of Collusion
It is not surprising that collusive arrangements tend to break down.
What happens however is that they usually break down, the market reorganizes, new collusions are formed only to break down again……
MC
PC is price set by cartel
PC
ATC
PR
PR is price set by rouge seller
BC is the base cost @cartel
BR is base cost rouge seller
BC
BR
Demand
MR
QC
QR
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Given that demand in oligopolies is often extremely elastic with respect to
price, it can be seen that if a seller cheats or even has a secret “sidearrangement” at a lower price, it can increase profits significantly.
From game theory we know that if we engage in a one-shot or a limited
horizon game, it pays to cheat if the consequences of cheating are bearable
For a cartel participant, if the intent is to stay in the cartel, then cheating is not
an option. However, the cartel participants know that the other participants are
likely to break the cartel if opportunity arises and therefore the cartel will break
anyway, so why not let it be them who breaks it and at least reaps the benefit?
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On the other hand, they know that the cartel’s survival is to their collective
advantage and if there is no cheating, then it is best to stay in the cartel.
They also know that if caught cheating, they may be punished.
In final analysis, they would break cartel if they are confident that their
cheating will not be discovered too early (see the mathematics of cheating in
lecture 6) or that if discovered, the punishment will not be sufficiently harsh.
The largest and most powerful players in the cartel would want the cartel to
survive, why?
They will do whatever it takes to keep it together…..
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They (and other cartel members) would expend effort to make it impossible to
cheat. This is done two ways:
• Regulation and watchdogs
• Threat of severe punishment
Regulation and use of watchdogs are instituted to make it systemically
impossible to cheat
Threat of punishment is there to make it psychologically and economically
unprofitable to cheat
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When regulations and watchdogs are inadequate (often) or are corrupted,
the first method fails
Use of punishment is an interesting case:
If punishment is harsh enough – it will work and will keep the cartel
together (e.g. Colombian drug cartels) but only for a limited period. Often
the “enforcer” becomes too powerful and triggers a rebellion that causes
the cartel to collapse
If they are not harsh enough– the cartel will fall apart
Reality is though that as most “legal” cartels are international entities,
punishment must be administered internationally and unless the
commodity in question is of extraordinary value (e.g. oil) national
governments will not unite to form an international “punishment” force. As
such punishment often does not work over international cartels.
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Lecture 9
Collusive Pricing
Let us review the case of contesting the market based on price:
We had:
TC  500  4QX  0.5QX2
MCX  dTCX / dQX  4  QX
Total revenue:
And a total cost of:
Leaving a profit of:
$36  32  $1152
500  4( 32 )  0.5( 32 2 )  $1140
$1152  $1140  $12
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Now let us examine the case of a duopoly where there is collusion:
The cartel’s marginal cost will be the horizontal sum of the two marginal cost
curves, in our case:
QA  4  MCB
QB  4  MCA
Q  8  2MC
The cartel will set its marginal revenue equal to its marginal cost (as it will wish
to act monopolistically)
TR  PQ  ( 100  Q )Q  100Q  Q 2
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The marginal revenue will be:
dTR
MR 
 100  2Q
dQ
Setting marginal cost and marginal revenue equal:
MR  100  2Q  4  0.5Q  MC
Q  38.4
Substituting in the cartel demand curve, we get a price of $100-$38.4= $61.6
The cartel’s total revenue is $61.6 x 38.4 = $2,365.44
As each firm produces the same amount (38.4 / 2 = 19.2), they both have the
same marginal cost (4+19.2 = $23.2)
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Also the firms likewise will split the total revenue:
TR  PQ  $2365.44 / 2  $1,182.72
Each firm has a total cost of:
TC  500  4( 19.2 )  0.5( 19.2 )2  $761.12
Each firm therefore makes a profit of:
TR TC  $1,182.72  $761.12  $421.60
This is more than 35 times the profit of $12 if they were to compete !!!
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Lecture 9
Capacity (Quantity) Competition
Given the difficulty of maintaining a collusive arrangement and the general
social and legal undesirability of cartel arrangements, how can firms avoid the
lose-lose situation of direct competition and approach the win-win of a cartel
arrangement without collusion?
The answer is to try to reach Nash Equilibrium.
This can be done by competing on quantity (production capacity)
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Reaching a Nash Equilibrium – Cournot Solution
Let us first make certain assumptions:
1. The firms move simultaneously
2. They have the same view of the market (e.g. they see the
same demand curve)
3. Know each other’s cost functions
4. They optimize their quantity decision assuming the other
firm’s quantity decision is given
These are all reasonable assumptions.
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Using the details from the previous example, we now solve for maximizing
profit when the competitor’s profit is maximized (Nash Equilibrium)
Let us be firm A:
We maximize profit when our total revenue PQA exceed our total cost
maximally.
TR  PQA  ( 100  QA  QB )QA  100QA  QA2  QAQB
Our marginal revenue is:
TRA
MRA 
 100  2QA  QB
QA
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To maximize profit, we set MC=MR
MRA  100  2QA  QB  4  QA
QA  32  31 QB
This is called the reaction function of firm A (us). It tells us the profit
maximizing amount to produce, given the output of our competitor.
Because firm B has the same cost function, and both firms face the
same market demand curve, firm B’s reaction function is similarly:
MRB  100  2QB  QA  4  QB
QB  32  31 QA
Note that this does not need to necessarily be the case and reaction
functions may differ. The analysis will however remain the same
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Solving the two equations for the two unknown quantities QA and QB will give
the respective production quantities for each firm.
It turns out that QA=QB=24 and as such Q=QA+QB=48
As P=100-Q, then price is P=100-48=$52
So each firm makes a total revenue of $1248 (52x24) and each firm’s
total cost is $884 and each firm makes a profit of $364
Whilst this is not quite the profit that a collusive arrangement would yield, it
is still over 30 times better than the pure competition price
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Lecture 9
First Mover Advantage
Does the early bird get the worm?
Now, let us consider the situation where one firm gets to move (set quantity
and price) before the other firm.
This can be done right (when the price set is such that it maximizes the
other party’s profit having now had to go second) or wrong (when the price
set is not optimal for the adversary).
If set right, our firm can rest assured that the adversary will not come into the
market with a different price.
Using the information from our running example:
Let us say that we (firm A) move first.
P  ( 100  QA  QB )  100QA  ( 32  31 QA )  68  23 QA
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Our firm’s total revenue will be:
TR  PQA  68QA  23 QA2
Our marginal revenue is:
MRA 
TRA
 68  43 QA
QA
So we will set our marginal revenue equal to our marginal cost:
MRA  68  43 QA  4  QA  MCA
QA  27.43
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Substituting into firm B’s reaction function yields
QB  32  31 27.43  22.86
Therefore Q=22.86+27.43=50.29
Substituting into the demand curve function gives the price $49.71.
Our revenue is $1,363.59 and firm B’s revenue is $1,136.33
Respective profits are (you calculate the costs): $377.71 and $283.67
It pays to be first – Early bird gets the worm
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