Week 4 – ECMC02 – Oligopoly
Objectives for this week: (I’ll work you hard but
you can have next week off…)
1. Finish up discussion of price discrimination,
first, second and third degree
2. Cournot model
3. Cartel or joint-monopoly model
4. Compare to (quasi) competitive model
5. Stackelberg leader model
6. Bertrand model
7. Dominant firm/price leadership model
8. Compare and contrast different models of
oligopoly behaviour
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First-degree price discrimination
If consumers each consume one unit and have
different valuations of the good, perfect price
discrimination is achieved by charging a
different price to each individual
If consumers are similar, could charge a take-itor-leave it price equal to the total valuation of
the good (maximum willingness-to-pay) for the
good (= total area under the demand curve up to
the quantity where marginal willingness-to-pay =
MC).
If consumers are similar, could charge a twopart price (two-part tariff) where per-unit cost
equals MC and “entry” fee (or fixed fee) equals
amount of consumer surplus consumer would
normally have received (i.e., fixed fee is
designed to capture all consumer surplus and
turn it into producer surplus).
2
Second-degree price discrimination
Versioning
Imagine a situation where there are two types of
consumers in a market. Type A have relatively
low demand for the good, and want only a small
amount. Type B are the keen consumers who
would be willing to pay more and want to consume
a larger amount. However, you cannot easily
identify the enthusiastic consumers and cannot
separate them from other consumers. How
should you, as the monopolist, produce packages
to extract maximum returns from these two
groups of customers? How can you design
packages (where a package is a particular
quantity of the good sold at a particular price)
which will encourage the customers to selfselect so that the enthusiastic consumers will
pay more?
Examples: Lower price for limited service; higher
price for more complete service.
3
Often packages are low quality at low price and
higher quality at higher price. Then this can be
described as a quality discrimination model (or
price discrimination with quality being used as
instrument of self-selection)
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Willingess
to pay per
unit of
good
Type B
Type A
Quantity of good
(sometimes quality)
5
Take three tries at defining the “best” package
from point of view of monopoly producer
1. Take-it-or-leave-it price equal to maximum
willingness to pay for each type of consumer
Willingess
to pay per
unit of
good
Type B
Type A
Quantity of good
(sometimes quality)
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2. Full price and quantity for Type A; full
quantity but lower price for Type B
Willingess
to pay per
unit of
good
Type B
Type A
Quantity of good
(sometimes quality)
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3. Lower price and lower quantity for Type
A; full quantity but higher price than #2 for
Type B
Willingess
to pay per
unit of
good
Type B
Type A
Quantity of good
(sometimes quality)
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Third-degree price discrimination
Not first degree (perfect)
Not second degree (same menu of prices for all)
But third…segmenting customers into different
groups – dividing the market
Not personalized pricing, not versioning, but
group pricing
Must be able to identify customers with
different purchasing characteristics (essentially
different elasticities of demand)
Must be able to prevent resale between groups
E.g., student discounts on TTC, senior citizen
discounts on TTC and elsewhere, sales into
different markets in the same country or
different countries, men’s and women’s haircuts
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Graphically:
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Rule for profit maximization:
Set MR in each market equal to MC (one
production facility)
MR1 = MR2 = MC
But, since MR1 = MR2,
And because MR = P(1 + 1/ED)
We know that P1(1 + 1/ED1) = P2(1 + 1/ED2)
Or, P1/P2 = (1 + 1/ED2)/(1 + 1/ED1)
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Let’s say elasticity of demand in Market 1 is -4
and elasticity of demand in Market 2 is -2.
What will be the ratio of the prices in these two
markets when the monopolist sells in both?
Since P1/P2 = (1 + 1/ED2)/(1 + 1/ED1)
= (1 – ½)/(1 – ¼)
= (1/2)/(3/4) = 2/3
In other words, the price in Market 1 will be
2/3rds of the price charged in Market 2
12
Imagine a monopoly provider of satellite TV
signals selling into Vancouver and Toronto. You
have to imagine that there are no close
substitutes.
Imagine demand is given by:
QV = 50 – 1/3 PV
QT = 80 – 2/3 PT
Where Q is measured in thousands of
subscriptions per year and P is the subscription
price
Costs are given by TC = 1000 + 30Q
So MC = dTC/dQ = 30
(the cost of servicing one more subscription)
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Turning around the demand functions, we have
PV = 150 – 3QV
PT = 120 – 3/2 QT
Therefore,
MRV = 150 – 6QV
MRT = 120 – 3QT
Therefore, in Vancouver
MRV = 150 – 6QV = 30 or QV* = 20
And substituting into Vancouver’s demand
function
PV* = 150 – 3QV = 150 – 60 = $90
And in Toronto
MRT = 120 – 3QT = 30 or QT* = 30
And substituting into Toronto’s demand function
PT* = 120 – 3/2 QT = 120 – 45 = $75
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How would you calculate demand in the combined
markets if you wanted to calculate the monopoly
solution when markets could not be segmented?
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Oligopoly
What is it?
Why are there so many models?
Oligopoly is a market in which there are only a
few sellers.
How many? So few that they feel the effects
of each other’s decisions.
Oligopoly markets are ones in which producers
engage in strategic behaviour….
…there is strategic interaction
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What form does competition between these
sellers take?
Could be collusion,
could be a price war,
could be an implicit agreement to share the
market,
could be an advertising war for market share but
no price-cutting
or, perhaps, one producer will have a dominant
position and become a price leader, or a leader in
decisions about output.
Many other possibilities too.
Therefore, many models
All contributing to our understanding….
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Two broad types of models
1.
Good sold is essentially same across
producers (Oligopoly models)
2.
Good sold differs in important ways from
producer to producer (monopolistic
competition or product differentiation)
Other major issue:
What do we assume about entry conditions?
In this whole group of models today, entry is
assumed blocked in some way
In other models, blocking entry is a central
strategic concern
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Cournot Model
Augustin Cournot (1838)
A simple model assuming simple interaction.
Each producer chooses its output assuming other
producers will not react (will keep output same)
In other words, each producer profit maximizes
according to “residual” demand
(However, each producer does, in fact, react)
We are assuming a stable mature market of
producers who do not want to rock the boat
Homogeneous good. Assume duopoly. No entry.
Firms choose output.
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Mineral Water – e.g., Evian and Perrier
Market Demand: P = 100 – Q or Q = 100 - P
Total Costs for each firm TC = 10q
Two firms, so that
q1 + q2 = Q
Firm 1 assumes Firm 2’s output remains constant
(q2), so
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P
100
Market Demand
q2
(100 – q2)
Residual demand curve for Firm 1 is
q1 = (100 – q2) – P
or P = (100 – q2) – q1
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100
Q
Therefore, along the residual demand curve…
MR1 = (100 – q2) – 2q1
Since MC = dTC/dq = 10, profit max occurs where
(100 – q2) – 2q1 = 10
or
q1 = 45 – 0.5q2 [Reaction function for Firm 1]
Often designated as R1 or R1(q2)
22
Firm 2’s reaction function is identical
So
q2 = 45 – 0.5q1 [Reaction function for Firm 2]
Often designated as R2 or R2(q1)
23
On a graph: R1(q2)
q1
90
R2(q1)
45
R1(q2)
45
90
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q2
Only at “equilibrium point” do Firm 1 and Firm 2 not
have incentives to change their output given the
output of the other firm (check this)
So q1 = 45 – 0.5q2
= 45 – 0.5(45 – 0.5q1)
= 22.5 – 0.25 q1
So .75q1 = 22.5
Or
q1 = 30
and
q2 = 30
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This equilibrium concept is called a Nash
equilibrium after John Nash
Sometimes, Cournot-Nash equilibrium
In a Nash equilibrium, neither firm/player has any
incentive to change his strategy (given the
strategy of the other players/firms).
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We know the outputs. What price will be charged?
Each firm produces 30 units of output.
Since market demand is P = 100 – Q, we have P =
100 – 60 = $40
Profit is TR – TC
For each producer, Π = (40 x 30) – (10 x 30) =
$900. Total profit in the industry is $1,800.
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Cartel or Joint Monopoly
Successful cartels - OPEC, bauxite (1970’s),
uranium (1970’s), mercury (1930-1970), iodine
(1878-1940), cement
Unsuccessful cartels – copper, tin, coffee, tea,
cocoa
Try to jointly act like a monopolist. Restrict
output to monopoly level to drive price up.
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Faced with same market demand as above, how
would cartel behave?
P = 100 – Q
TC = 10Q
MR = 100 – 2Q = 10, so Q* = 45
(or q1 = q2 = 22.5, if there are two producers in the
cartel)
P* = 100 – 45 = $55
Π = TR – TC = (55 x 45) – (10 x 45) = $2025
Or Π1 = Π2 = $1012.50
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Quasi-competitive model
(for comparison purposes)
Each firm acts as a price taker, sets P = MC,
ignoring potential market power
If P = 100 – Q and TC = 10Q,
Then 100 – Q = 10 or Q* = 90
Then, P* = 100 – 90 = $10.
So Π = 0
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Comparison
QuasiCournot
competitive Duopoly
Quantity
Price
Profit
90
$10
$0
60
$40
$1,800
Cartel –
Joint
Monoopoly
45
$55
$2,025
Cournot Model gives result between competitive
and monopoly
Firms do not acquire and use knowledge about
other firms
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Stackelberg Model
Heinrich von Stackelberg (1930’s)
Amendment to Cournot model. Two firms. One
firm knows the reaction function of the other firm
and maximizes profit subject to the behaviour of
the other firm (as described by the reaction
function).
This firm is the Stackelberg leader
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Assume Firm 1 is the Stackelberg leader
Firm 1 knows Firm 2’s reaction function
R2(q1) = 45 – 0.5q1
Therefore, q1 = (100 – q2) – P
Or
q1 = (100 – [45 - 0.5q1]) – P
or
P = 55 - 0.5q1
Therefore, MR1 = 55 - q1 = 10
So, q1* = 45
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Since Firm 2 follows its reaction function
q2 = R2(q1) = 45 – 0.5q1 or 45 – 22.5 = 22.5
Therefore, Q* = 45 + 22.5 = 67.5
P* = 100 – Q = $32.50
Π1 = (32.50 x 45) – (10 x 45) = $1012.50
Π2 = (32.50 x 22.5) – (10 x 22.5) = $506.25
Total Π = $1518.75.
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Comparison
QuasiCournot Cartel –
competitive Duopoly Joint
Monoopoly
Quantity 90
60
45
Price
$10
$40
$55
Profit
$0
$1,800 $2,025
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Stackelberg
67.5
$32.50
$1518.75
Bertrand Model
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Price Leadership or Dominant Firm Model
I think this model is easiest to learn diagrammatically,
and then mathematically.
Price
MCCF - Sum of marginal
costs of competitive
fringe
Total
Demand
P*
DDF
MCDF - Marginal
Cost of
Dominant Firm
Q*CF Q*DF
MRDF
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Quantity
Notice first the total market demand curve for the
industry as a whole. Then notice the marginal cost curve
for the competitive fringe of firms. This is a model in
which there is one firm which is dominant and then a
fringe of small firms who are so small that they behave
like perfectly competitive firms – they take the price
that is give by the dominant firm (and then set P = MC to
profit maximize).
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The basic story in this model is that the dominant firm
leaves room for the competitive fringe (and therefore
profit maximizes according to the “residual” demand
curve. Since the fringe of firms behaves like perfect
competitors, the sum of their marginal cost curves is
essentially their supply curve. It represents the amount
that these firms together will want to supply at any
possible price.
Therefore, the residual demand curve is total demand
minus this supply by the competitive fringe. This is
exactly what the curve labeled DDF represents.
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Our story is that the dominant firm profit maximizes
using this residual demand curve. That means setting MR
= MC for this demand curve. This is exactly where Q*DF
comes from (it is the quantity at which MR is just equal
to MC for the dominant firm. The dominant firm will
charge the profit-maximizing price, which is P*.
Once P* is established by the dominant firm, the
competitive fringe (who are price takers) will just take
this price and set P* = MC. This gives us the profitmaximizing quantity Q*CF for the competitive fringe.
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We can take an algebraic example. Assume that the
overall industry demand curve is P = 100 – Q and that the
sum of the marginal costs of the competitive fringe is P =
10 + 4Q. The marginal cost of the dominant firm is
constant at MC = 18.
The price at which the total demand and the competitive
fringe marginal cost curve intersect will give us the
vertical intercept of the residual demand curve.
Therefore:
100 – Q = 10 + 4Q or 5Q = 90 or Q = 18 and P = $82.
Therefore, the vertical intercept is $82.
The residual demand curve will join with the industry
demand curve exactly at the price at which the quantity
supplied by the competitive fringe = 0. Since the
equation of the competitive fringe’s MC curve is P = 10 +
4Q, the competitive fringe will supply nothing when P =
$10. The quantity demanded according to the industry
demand curve is 10 = 100 – Q or Q = 90 at a price of $10.
We now have two points on the dominant firm’s residual
demand curve. It starts at P = $82 and Q = 0 and it joins
the industry demand curve at P = $10 and Q = 90. Since
the demand curve is linear between these two points, we
can calculate the slope to be (82 – 10)/(90 – 0) = 72/90 =
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4/5 or 0.8. Therefore, the equation of the (top part of
the) dominant firm demand curve is P = 82 – 0.8Q
Therefore, the dominant firm’s MR curve is MR = 82 –
1.6Q. Since the MC curve of the dominant firm is MC =
18, we have 82 – 1.6Q = 18 or Q*DF = 40. Substitute this
into the equation for the dominant firm demand curve to
get the price the dominant firm will charge: P* = 82 –
0.8(40) = $50.
At a price of $50, the competitive fringe will supply 50 =
10 + 4Q, or Q*CF = 10.
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