Transcript Managerial Economics - Trent University :: Peterborough

Price and Output
Determination:
Oligopoly
Managerial Economics – Econ 340
Lecture 8
Christopher Michael
Trent University
© 2006 by Nelson, a division of Thomson Canada Limited
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Topics
•
•
•
•
•
Cournot Oligopoly
Collusion versus Competition
Price Leadership
Kinked Demand Curve
Oligopolistic Rivalry and Game Theory
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Overview
• Oligopolistic Market Structures
» Few Firms
• Consequently, each firm must consider the reaction of
rivals to price, production, or product decisions
• These reactions are interrelated
» Heterogeneous or Homogeneous Products
• Example -- athletic shoe market
» Nike has 47% of market
» Reebok has 16%
» Adidas has 7%
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Nokia’s Challenge
in Cell Phones
• The market shares of oligopolists change. In 1998, the market
leader in cell phones was Motorola with 25% market share and
Nokia second with 20%
• In 2002, leadership reversed: Nokia held 37% of the market and
Motorola 17%
• However, technology in phones is changing, bringing wireless
web, photos, and other high-speed G3 technologies
• Entry of other firms and new products, such as Dell, Palm, NEC
and Panasonic pose threats to Nokia’s profit margins
• Nokia must decide whether or not to invest heavily in the 3G
technology for the future.
• Being a leader in a oligopoly does not mean that you remain the
leader for long.
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The Cournot Oligopoly
• Models vary depending on assumptions
of actions of rivals to pricing and
output decisions.
• Augustin Cournot (1838) created a
model that is the basis of Competition
Policy.
Cournot
» Relatively simple assumption: ignore the
interdependency with rivals
» This makes the math easy
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A Numerical Example:
Competition, Monopoly, and Cournot Oligopoly
Let: P = 950 - Q and MC =50
• IN COMPETITION
» P = MC, so 950 - Q = 50
» PC = $50 and QM = 900
$500
PM
Pcournot
• IN MONOPOLY
$350
$50
PC
D
QM QCournot QC
450
600
900
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» MR = MC, so 950 -2Q = 50
» QM = 450 so
» PM = 950 - 450 = $500
• IN DUOPOLY
» Let Q = q1 + q2
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Cournot Solution:
Case of 2 Firms (Duopoly)
• Assume each firm maximizes profit
• Assume each firm believes the other
will NOT change output as they
change output.
» The so-called: Cournot Assumption
• Find where each firm sets MR = MC
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Let Q = q1 + q2
P
= 950 - Q = 950 - q1- q2
and MC = 50
TR1 = Pq1= (950- q1-q2)q1 =950q1 - q12 - q1q2
and
 TR2 = Pq2= (950- q1-q2)q2 =950q2 - q2q1 - q22


Set MR1= MC
&
950 -2q1 - q2 = 50
950 - q1 - 2q2 = 50
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MR2= MC
2 equations &
2 unknowns
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With 2 Equations & 2 Unknowns:
Solve for Output
950 -2q1 - q2 = 950 - q1 - 2q2
So, q2 = q1 Then plug this into the demand
equation we find:
950 - 2q1 - q1 = 950 - 3q1 = 50.
Therefore
q1 = 300
The price is:
600
P = 950 - 600 = $350
Competition
Cournot
Monopoly
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Canada Limited
and Q =
P
Q
50
350
500
900
600
450
Cournot’s
answer is
between the
other two.
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N-Firm Cournot Model
• For 3 firms with linear demand and
cost functions:
QC
»Q = q 1 + q 2+ q 3
» In linear demand and cost
models, the solution is higher
output and lower price
QCournot = { N / (N+1) }QCompetition
THEREFORE, Increasing the
Number of Firms increases
competition. This is the historical
basis for Competition Policy
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N
PC
N
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Example: Cournot as N Increases
N=3
• If N = 3 Triopoly
• P = 950 - Q &
MC=50
• Then, Q = (3/4)(900)
• Q = 675
• P =$275
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N=5
• If N = 5
• P = 950 - Q and MC
= 50
• Then Q = (5/6)(900)
• Q = 750
• P = $200
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Collusion versus Competition?
• Sometimes collusion succeeds
• Sometimes forces of competition
win out over collective action
• When will collusion tend to
succeed?
»There are six factors that influence
successful collusion as follows:
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Factors Affecting Likelihood
of Successful Collusion
1. Number and Size Distribution of Sellers.
Collusion is more
successful with few firms or if there exists a dominant firm.
2. Product Heterogeneity. Collusion is more successful with
3.
4.
5.
products that are standardized or homogeneous
Cost Structures. Collusion is more successful when the costs
are similar for all of the firms in the oligopoly.
Size and Frequency of Orders. Collusion is more successful
with small, frequent orders.
Secrecy and Retaliation. Collusion is more successful when
it is difficult to give secret price concessions.
6. Percentage of External Orders. Collusion is more
successful when percentage of orders outside of the cartel is
small.
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Oligopolies & Incentives to Collude
When there are
just a few firms,
profits are
enhanced if all
P
reduce output
But each firm has
incentives to
“cheat” by selling
more
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MC
MC
D
incentive
to cut
price
q
Representative firm
QM
Industry
MR
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Examples of Cartels
• Ocean Shipping
• De Beers -- diamonds
• OPEC - oil cartel, with Saudi Arabia making up
33% of the group’s exports
• Siemens and Thompson-CSF -- airport radar
systems
• Major League Baseball
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PRICE LEADERSHIP
B arom etric P rice L ead er
• Barometric:
D om in an t Firm P rice L ead er
One (or a few firms) sets the price
• One firm is unusually aware of changes in cost or
demand conditions
• The barometer firm senses changes first, or is the first
to ANNOUNCE changes in its price list
• Find barometric price leader when the conditions
unsuitable to collusion & firm has good forecasting
abilities or good management
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Dominant Firm
Price Leadership
• Dominant Firm:
large market share.
• No price or quantity
collusion
• Dominant Firm (L) expects
the other firms (F) to
follow its price and
produce where
MC F = PL
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Net Demand Curve: DL
MC F
DT
DL
leader’s
demand
= DT - MCF
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Graphical Approach to
Dominant Firm Price Leadership
MC F
• Find leader’s
demand curve,
DL = (DT -  MC F)
• Find where
MRL = MCL
DL
MRL
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DT
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Graphical Approach to
Dominant Firm Price Leadership
MC F
PL
DL
MRL
• At QL, find the
MCL leader’s price, PL
• Followers will
supply the
remainder of
Demand:
D (QT - QL) = QF
QL
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Graphical Approach to
Dominant Firm Price Leadership
MC F
MCL
PL
DL
MRL
QL
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QT
D
• Followers will
supply the
remainder of
Demand:
(QT - QL) = QF
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Implications of
Dominant Firm Price Leadership
• Market Share of the Dominant Firm Declines
Over Time
» Entry expands MC F, and Shrinks DL and MRL
• Profitability of the Dominant Firm Declines
Over Time
profits
TIME
• Market Share of the Dominant Firm is
PROCYCLICAL
» rises in booms, declines in recessions
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Numerical Example of
Dominant Firm Price Leadership
Aerotek is the leader, with 6 other firms,
given the following:
1. P = 10,000 – 10 QT is the market
demand
2. QT = QL + QF is the sum of leader &
followers
3. MCL = 100 + 3 QL and
SMCF = 50 + 2 QF
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What is Aerotek’s
Price and Quantity?
• From 2, QL = QT – QF and From 1, QT = 1,000 - 0.1P
• Since followers sell at P=MC, From 3, P = 50 + 2 QF, which
rearranged to be QF = 0.5P - 25
• So, QL = (1,000 - .1P) – (0.5P - 25) = 1,025 -0.6 P, which
can be rearranged to be P = 1,708.3 – 1.67 QL
• MRL = 1,708.3 – 3.34 QL
• And MRL = MCL where: 1,708.3 – 3.34 QL = 100 + 3QL
• The optimal quantity for Aerotek, the leader is QL  254
• P = 1,708.3 – 1.67 QL = 1,708.3 – 1.67(254)  $1,284.
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Kinked Oligopoly Demand Curve
• Belief in price rigidity
founded on experience of
the great depression
• Price cuts lead to
everyone following
P
» highly inelastic
• Price increases, no one
follows
» highly elastic
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no one follows
a price increase
everyone
follows
price cuts
a kink at the price
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A Kink Leads to Breaks
in the MR Curve
P
D
• Although MC rises, the
optimal price remains
constant
MC2
• Expect to find price
MC1 rigidity in markets with
kinked demand
• QUESTION:
D
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MR
» Where would we more
likely find KINKS and
where NOT?
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Oligopolistic Rivalry
& Game Theory
• John von Neuman & Oskar Morgenstern—
» Game Theory used to describe situations where individuals
or organizations have conflicting objectives
» Examples: pricing of a few firms, strategic arms race,
advertising plans for a few firms, output decisions of an
oligopoly
• Strategy—is a course of action
» The PAYOFF is the outcome of the strategy.
» Listing of PAYOFFS appear in a payoff matrix.
• A Strategy Game – involves decisions with
consciously interdependent behaviour of two or more
participants.
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Two Person Game
ASSUMPTIONS
•
•
•
•
•
•
•
•
•
Each player knows the alternatives of all players
Preferences of all players are known
Single period game
Each player can invade the territory of the other (Maraude) or
Guard own territory
Kahn’s payoff is given first, Randle’s payoff is second.
Randle ranks Guard above Maraude.
Randle has a Dominant Strategy: a decision that maximizes
welfare independent of the other player’s strategy choice
Knowing what Randle will do, Kahn decides to Guard as well.
An Equilibrium—none of the participants can improve their
payoff
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Two Person Game
Randle
Guard
Maraude
st Worst, 4th
Better,
1
Guard
Kahn
Maraude Worse, 2nd Best, 3rd
We will get to {Guard, Guard}
which is an Equilibrium
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Six or Seven Territories?
6 territories
Sharp
6 territories 7 territories
$40
$70
$35
$55
$30
$60
$45
$45
7 territories
Xerox
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• Sharp and Xerox
compete in copiers.
Payoffs for Xerox are in
the lower triangle
• The payoffs depend on
the number of territories
in which they compete
• Sharp has a dominant
strategy of 6 territories.
• What should Xerox do?
• We see we get to {6, 6}
as the iterated dominant
strategy.
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Other Strategic Games
• These are viewed as single period, but businesses
tend to be on-going, or multiple-period games
• These are two-person games, but oligopolies often
represent N-person games, where N is greater than 2
• Some games are zero-sum games in that what one
player wins, the other player loses, like poker
• Other games are non-zero sum games where the
whole payoffs depend on strategy choices by all
players.
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The Prisoner’s Dilemma
• Often the payoffs vary
depending on the
strategy choices
• The Prisoner’s
Dilemma
• Noncooperative Solution
» both confess: {C, C}
• Cooperative Solution
» both do not confess {NC,NC}
• Off-diagonal represents a
» Two suspects are
Double Cross
caught and held
suspect 2
separately
NC
C
• Their strategies are
1 yr
0 yrs
either to Confess (C) or
NC
1 yr
15 yrs
Not Confess (NC)
6 yrs
» a one-period game suspect 1 15 yrs
0 yrs
6 yrs
C
» Suspect 1 in lower
triangle (Bold Red)
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Paradox?
• The Prisoner’s Dilemma highlights the
situation where both parties would be best off
if they cooperated
• But the logic of their situation ends up with a
non-cooperative solution
• The solution to cooperation appears to be
transforming a one-period game into a
multiple-period game.
• The actions you take now will then have
consequences in future periods.
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