Download Lecture4.Oligopoly

Week 4 – ECMC02 – Oligopoly
Objectives for this week (and part of next):
1. Finish up discussion of price discrimination,
presenting material on third-degree price
discrimination
2. Introduce theory of oligopoly
3. Cournot model
4. Cartel or joint-monopoly model
5. Quasi-competitive model
6. Stackelberg leader model
7. Bertrand model
8. Bertrand model with differentiated
products
9. Dominant firm/price leadership model
10. Compare and contrast different models of
oligopoly behaviour
1
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
2
Graphically:
3
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)
4
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
5
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)
6
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
7
How would you calculate demand in the combined
markets if you wanted to calculate the monopoly
solution when markets could not be segmented?
8
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
9
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….
10
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
11
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.
12
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
13
P
100
Market Demand
q2
(100 – q2)
Residual demand curve for Firm 1 is
q1 = (100 – q2) – P
or P = (100 – q2) – q1
14
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)
15
Firm 2’s reaction function is identical
So
q2 = 45 – 0.5q1 [Reaction function for Firm 2]
Often designated as R2 or R2(q1)
16
On a graph: R1(q2)
q1
90
R2(q1)
45
R1(q2)
45
90
17
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
18
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).
19
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.
20
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.
21
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
22
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
23
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
24
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
25
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
26
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.
27
Comparison
QuasiCournot Cartel –
competitive Duopoly Joint
Monoopoly
Quantity 90
60
45
Price
$10
$40
$55
Profit
$0
$1,800 $2,025
28
Stackelberg
67.5
$32.50
$1518.75