1 © 2006 by Nelson, a division of Thomson Canada Limited Christopher Michael Trent University...

1© 2006 by Nelson, a division of Thomson Canada Limited

Christopher MichaelTrent University

Managerial Economics – Econ 340Lecture 8

Price and Output Determination:

Oligopoly


Topics

• Cournot Oligopoly

• Collusion versus Competition

• Price Leadership

• Kinked Demand Curve

• Oligopolistic Rivalry and Game Theory


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%


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.


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.» Relatively simple assumption: ignore the

interdependency with rivals» This makes the math easy

Cournot


A Numerical Example:Competition, Monopoly, and Cournot Oligopoly

• IN COMPETITION» P = MC, so 950 - Q = 50

» PC = $50 and QM = 900

• IN MONOPOLY» MR = MC, so 950 -2Q = 50

» QM = 450 so

» PM = 950 - 450 = $500

• IN DUOPOLY

» Let Q = q1 + q2

D

PM

Pcournot

PC

QM QCournot QC

450 600 900

$500

$350

$50

Let: P = 950 - Q and MC =50


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


Let Q 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 - q2

2

Set MR1= MC & MR2= MC

950 -2q1 - q2 = 50

950 - q1 - 2q2 = 50

2 equations &2 unknowns


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 and Q = 600

The price is: P = 950 - 600 = $350P Q

Competition 50 900Cournot 350 600Monopoly 500 450

Cournot’sanswer is

between theother two.


N-Firm Cournot Model• For 3 firms with linear demand and

cost functions:

» 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

QC

N

N

PC

THEREFORE, Increasing the Number of Firms increases competition. This is the historical basis for Competition Policy


Example: Cournot as N Increases

• If N = 3 Triopoly

• P = 950 - Q & MC=50

• Then, Q = (3/4)(900)• Q = 675• P =$275

• If N = 5• P = 950 - Q and MC

= 50• Then Q = (5/6)(900)• Q = 750• P = $200

N = 3 N = 5


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:


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 products that are standardized or homogeneous

3. Cost Structures. Collusion is more successful when the costs are similar for all of the firms in the oligopoly.

4. Size and Frequency of Orders. Collusion is more successful with small, frequent orders.

5. 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.

Factors Affecting Likelihood of Successful Collusion


Oligopolies & Incentives to Collude

When there are just a few firms, profits are enhanced if all reduce output

But each firm has incentives to “cheat” by selling more

MC MC

P

q

D

QM

incentiveto cut price

MR

Representative firm Industry


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


PRICE LEADERSHIP

• Barometric: 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

B arom etric P rice L ead er D om in an t F irm P rice L ead er


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

DT

MC F

DL

Net Demand Curve: DL = DT - MCF

leader’sdemand


• Find leader’s demand curve, DL = (DT - MC F)

• Find where MRL = MCL

DT

MC F

DL

MRL

Graphical Approach to Dominant Firm Price Leadership


• At QL, find the leader’s price, PL

• Followers will supply the remainder of Demand: (QT - QL) = QF

D

MC F

DL

MRL

MCL

PL

QL



• Followers will supply the remainder of Demand: (QT - QL) = QF

D

MC F

DL

MRL

MCL

PL

QL QT



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

• Market Share of the Dominant Firm is PROCYCLICAL» rises in booms, declines in recessions

TIMEprofits


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


• 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.

What is Aerotek’s Price and Quantity?


Kinked Oligopoly Demand Curve

• Belief in price rigidity founded on experience of the great depression

• Price cuts lead to everyone following» highly inelastic

• Price increases, no one follows» highly elastic

everyonefollowsprice cuts

no one follows a price increase

a kink at the price

P


A Kink Leads to Breaks in the MR Curve

• Although MC rises, the optimal price remains constant

• Expect to find price rigidity in markets with kinked demand

• QUESTION:» Where would we more

likely find KINKS and where NOT?

P

D

D

MR

MC2

MC1


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.


Two Person Game

• 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

ASSUMPTIONS


Randle

Kahn

Guard

Maraude

Guard Maraude

Better, 1st Worst, 4th

Worse, 2nd Best, 3rd

We will get to {Guard, Guard}which is an Equilibrium

Two Person Game


Six or Seven Territories?

• 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.

Sharp

Xerox

6 territories 7 territories6 territories 7 territories

$40 $70 $35 $55

$30 $60 $45 $45


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.


The Prisoner’s Dilemma• Often the payoffs vary

depending on the strategy choices

• The Prisoner’s Dilemma» Two suspects are

caught and held separately

• Their strategies are either to Confess (C) or Not Confess (NC)

» a one-period game» Suspect 1 in lower triangle

(Bold Red)

• Noncooperative Solution» both confess: {C, C}

• Cooperative Solution» both do not confess {NC,NC}

• Off-diagonal represents a Double Cross

suspect 2

suspect 1

NC

C

NC C1 yr 0 yrs

15 yrs 6 yrs

1 yr 15 yrs

0 yrs 6 yrs


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.

1 © 2006 by Nelson, a division of Thomson Canada Limited Christopher Michael Trent University...

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Transcript of 1 © 2006 by Nelson, a division of Thomson Canada Limited Christopher Michael Trent University...