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Chapter 19
Oligopoly
McGraw-Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All Rights Reserved.
Main Topics
Oligopoly and game theory
The Bertrand model
Cournot quantity competition
Price competition with differentiated products
Collusion
Market entry and monopolistic competition
Antitrust policy
19-2
Oligopoly and Game Theory
Economists use game theory to analyze
oligopoly competition
Game theory looks for price or quantity choices
at which each firm is doing as well as it can
given the prices charged or quantities
produced by its rivals
In a Nash Equilibrium, each firm is making a
profit-maximizing choice given the actions of its
rivals
In game theory, a firm’s most profitable choice
given the actions of its rivals is called its best
response
19-3
Figure 19.1: Oligopoly Pricing Game
19-4
Bertrand Model
 The simplest possible oligopoly market is one with two firms (a
duopoly) that produce identical (homogeneous) goods
 Firms set their prices simultaneously
 Buyers observe prices and decide how much to purchase from each
firm
 Purchase from firm with lower price
 This is the Bertrand model of oligopoly
 After Joseph Bertrand, published in 1883
 Each firm’s most profitable choice depends on what the other
does
 With linear demand curve, a price that is closer to the monopoly price
results in greater profit
 Firms have an incentive to undercut each other’s price in order to win
sales
 Undercutting behavior drive prices down to marginal cost
 Example: two concrete companies, marginal cost = $40 per cubic
yard, monopoly price = $70
19-5
Individual Firm Demand
 To identify the Nash equilibrium in the Bertrand game,
think about each firm’s demand curve
 A firm’s demand curve shows the relationship between
the firm’s price and the quantity it sells given the
behavior of its rivals
 A firm has many demand curves, each one
corresponding to a different choice by its rival
 Notice that if a firm charges a higher price than his
rival, he sells nothing
 If he sets the same price as his rival, his sales equal
half the market demand at that price
 If he charges a lower price than his rival, his sales
equal the market demand at his price
19-6
Figure 19.2: Market Demand and
Firm Demand Curve
19-7
Nash Equilibrium in the
Bertrand Duopoly
 In the concrete company example, if both firms charge $40 it is a
Nash equilibrium
 Recall that $40 is their marginal cost
 $40 is the best each firm can do given that the other is charging $40
 Bertrand result is the same as the perfectly competitive outcome
 Monopoly price would be $70
 To maximize their joint profit each firm would need to charge $70
 Each firm undercuts that price to increase its own profit
 Each firm ignores the negative effect of its behavior on its rival’s profit
 Implies that welfare losses due to market power are limited to
monopoly markets
 Overly optimistic
 Some of the model’s assumptions may be at odds with reality
19-8
Figure 19.3: Nash Equilibrium in
the Bertrand Model
 Joe can’t do better than
charging $40 if his rival is
charging $40
 The parallel argument holds
from his rival’s perspective
 So both firms charging $40 is
a Nash equilibrium
100
Price ($/cubic yard)
 D40 is Joe’s demand curve
when his rival charges $40
 Joe’s profit is zero if he
charges $40, negative if he
charges less than $40, and
zero if he charges more than
$40
D
D40
MC
40
2000
4000
3000
6000
8000
10000
Concrete (Cubic Yards per Year)
19-9
Sample Problem 1 (19.1)
Suppose Joe, Louie, and Rebecca compete
in the Bertrand ready-mix concrete market
described in Section 19.2. Show that in any
Nash equilibrium, all sales must occur at a
price of $40 (equal to marginal cost). Extend
your argument to show that this statement
will be true as long as two or more firms are
competing in the market.
In that example: P = 100 – 0.01Q
Cournot Quantity Competition
 In many settings a firm can sell only a limited quantity
at a time
 Bertrand model may overstate firms’ ability to steal business
from one another
 In some situations quantities rather than prices drive
market outcomes
 In the Cournot model of oligopoly:
 Firms choose quantities simultaneously
 Price clears the market given the total quantity produced
 Named after French mathematician Augustin Cournot,
introduced in 1838
 Assume homogeneous goods
 Provides insights when firms make capacity decisions
that determine sales capabilities
19-11
Figure 19.4: Price Determination
in the Cournot Model
 Given the output of the
two firms:
 The price clears the
market
 Amount demanded equals
amount supplied
 Here, total output is
4,000
 Price = $60/cubic yard
19-12
Nash Equilibrium in a
Cournot Market
 Important difference from equilibrium in Bertrand market:
equilibrium price is always above marginal cost
 P=MC will yield profit of zero
 Firm could do better by reducing output
 This would raise market-clearing price above marginal cost
 Profit would be positive
 In a Nash equilibrium each firm’s output choice maximizes its
profit given its rival’s output choice
 Need to find each firm’s best response for each possible output level
for its rival
 First step is to derive one firm’s demand curve for each possible
output level for its competitor
 For the cement example, the firm’s demand curve is shifted
leftward from the market demand curve by an amount equal to its
rival’s output at every price
19-13
Best Responses
 A firm’s best response is the quantity that equates his
marginal revenue with his marginal cost
 The marginal revenue curve is derived from the firm’s
demand curve
 By graphing the firm’s best response at each of its
competitor’s possible output levels we obtain its best
response curve:
 Shows its best choice in response to each possible action by
its rival
 Nash equilibrium occurs where the two firms’ best
response curves cross
19-14
Figure 19.6: Best Responses in
the Cournot Model
19-15
Figure 19.7: Best Response
Curves in the Cournot Model
19-16
 The Nash equilibrium is
the point where the best
response curves cross
 Each firm produces 2,000
cubic yards
 Can also find these
equilibrium output
choices using algebra
Joe’s Output (Cubic yards per year)
Figure 19.8: Nash Equilibrium in
the Cournot Model
6000
5000
4000
3000
BRRebecca
Nash equilibrium
2000
BRJoe
1000
1000 2000 3000
4000 5000 6000
Rebecca’s Output (Cubic yds per year)
19-17
Figure 19.9: Deadweight Loss
from Duopoly vs. Monopoly
 Deadweight loss with
oligopoly:
 Equals area of the light
red triangle
 $20,000 per year
 Deadweight loss of
monopoly
 Equals total of dark and
light red areas
 $45,000 per year
 Larger than oligopoly
because monopoly price
is further above marginal
cost
19-18
Sample Problem 2 (19.3)
Repeat worked out problem 19.1 (page
712), but assume instead that Joe and
Rebecca both have a marginal cost of
$55 per cubic yard. What is the
deadweight loss in this market?
In this problem: Qd = 10,000 – 100P
Oligopoly and Perfect Competition
 When the number of competitors in a market grows
very large, expect firms to begin acting like price takers
 In a Cournot market, as the number of firms grows
larger, the market outcome approaches competitive
equilibrium
 Expand the cement example to include additional firms
 Joes doesn’t care who is producing the rest of the output in the
market, the effect on the price he receives is the same
 Only their total output matters in determining his best response
 His best response function will take the same form as before
but consider the total output of his rivals rather than just
Rebecca’s output
 As the number of firms increases the price falls and the
quantity produced increases
19-20
Markups in a Cournot Model
 In Cournot oligopoly, size of the markup is related to the elasticity
of market demand:
P  MC  1 

d 
P
 NE 
 Here, N denotes the number of identical Cournot competitors
 For a given number of firms, the less elastic the demand the
greater the markup
 The less elastic the demand, the greater the increase in price that
results from a given reduction in a firm’s output
 The more attractive the idea of restricting output
 For a given demand elasticity, the larger the number of firms, the
lower the markup
 Confirms that as N grows larger, the markup falls to zero, so the
market price approaches the marginal cost
19-21
Price Competition with
Differentiated Products
Often, the products that firms in an oligopoly
market sell are not homogeneous
Coke and Pepsi, for example
When consumer do not view similar products
as perfect substitutes, those products are
differentiated
The Bertrand model result of competition
driving prices down to marginal cost does not
hold with differentiated products
Firms can make a positive profit by raising their
price above marginal cost
19-22
Differentiated Products: Coke and
Pepsi Example
 Assume there are no other relevant products
 Marginal cost to produce a can of either brand is 30
cents
 If Pepsi’s price is 30 cents and Coke charges slightly
more, it will lose some customers but not all of them
 Coke can make a positive profit by raising its price above
marginal cost
 Coke’s demand curve decreases gradually as its price
rises
 Coke’s marginal revenue curve is derived from its demand
curve
 A lower Pepsi price shifts Coke’s demand curve to the
left since they are substitutes
19-23
Figure 19.12: Coke’s Demand Curves
19-24
Best Responses and
Nash Equilibrium
 Obtain Coke’s best response curve by graphing the
firm’s best response at each possible price that Pepsi
might charge
 Coke’s profit-maximizing sales quantity occurs at the
intersection of the marginal revenue and marginal cost curves
 The corresponding price is found on the firm’s demand curve
 Coke’s best response curve is upward sloping
 The more Pepsi charges, the more Coke should charge
 Follow the same steps to find Pepsi’s best response curve
 Graph the two curves with Coke’s price on one axis
and Pepsi’s on the other
 Nash equilibrium is where the two curves cross
 Each firm chooses the price that maximizes its profit given its
rival’s price
19-25
Figure 19.14: Nash Equilibrium
with Differentiated Products
19-26
Incentives to Differentiate
Competition becomes more intense as
products become less differentiated
Consumers are more willing to switch in response to
price differences
A firm has an incentive to differentiate its
products from those of rivals
Product differentiation is an important strategy
firms use to ensure a profit
19-27
Sample Problem 3 (19.8)
Suppose a single monopolist controls the market
for Coke and Pepsi in worked out problem 19.2
(page 722). If the monopolist sets the same price
for Coke and Pepsi, what price would maximize
its profit? How does that price compare to the
equilibrium prices in worked-out problem 19.2?
In that problem: QC = 45 – 50PC + 200(PP-PC),
QP = 45 – 50PP + 200(PC-PP) and MC=0.30
Collusion
 In the real world firms compete against each other over
and over
 Repetition can make a big difference in the outcome of
oligopolistic competition
 In the infinitely repeated Bertrand model, firms play
the Bertrand pricing game over and over with no
definite end
 The noncooperative outcome is the repetition of the
Nash equilibrium that would arise if the firms were to
compete just one time
 There may be other equilibrium outcomes
 Sometimes possible for firms to sustain the monopoly price
 E.g., by adopting a grim strategy
19-29
Collusion, continued
 Collusion relies on the credible threat of a future price
war to keep firms from undercutting each other’s prices
 If future profits are important enough firms will not want
to risk a price war
 This will be the case if the interest rate is not to high
 So future losses are significant from today’s perspective
 Factors that inhibit collusion:
 With more firms, there is more to gain today and less to lose in
the future from undercutting
 Differing marginal costs
 Observing rivals’ costs imperfectly
19-30
Tacit vs. Explicit Collusion
What determines which equilibrium prevails
when firms compete repeatedly?
Explicit collusion is one possibility
Firms engage in explicit collusion when they
communicate to reach an agreement about prices
Illegal in many countries, including the U.S.
Tacit collusion is another
Collusion without communication, sustaining a price
above the noncooperative price
Generally not illegal, but less likely to be successful
19-31
Market Entry and
Monopolistic Competition
Firms enter an oligopolistic market in response
to profit opportunities
Several factors affect the number of firms that
enter:
Fixed cost associated with becoming active in the
market
As the fixed cost shrinks and the number of firms grows,
the possible profits of an active firm approach zero
Size of the market
Intensity of competition
Because profits are lower in a market with more intense
competition, fewer firms will enter
19-32
Figure 19.17: Factors Affecting
the Number of Firms
19-33
Market Entry and Social Welfare
Firms’ individual entry decisions in oligopoly
markets may not maximize aggregate surplus
Entry may not occur even if it would increase
aggregate surplus
If entry by the first firm would be unprofitable
Government may want to subsidize entry by first firm
to increase aggregate surplus
Once one firm has entered the market, excessive
entry may result and lower aggregate surplus
Business stealing arises when some of a new
entrant’s sales come at the expense of existing
firms
19-34
Figure 19.19: Entry and Welfare
19-35
Product Differentiation and
Monopolistic Competition
 In markets with product differentiation firms must
decide what kind of good to produce
 Monopolistic competition is a market with:
 A large number of firms
 Each produces a unique product
 Prices above marginal cost
 Close to zero profit, net of fixed costs
 Firm’s demand curve is downward sloping due to
differentiation
 At the firm’s profit-maximizing price and quantity, P=AC
so the firm breaks even
 Entry in monopolistically competitive markets may be
excessive or insufficient relative to the level that
maximizes aggregate surplus
19-36
Figure 19.20: Monopolistic
Competition
19-37
Antitrust Policy
 Antitrust legislation focuses on maintaining rules of
competition that enable markets to produce good
outcomes
 Limit welfare losses from market power
 Investigation and intervention occur only when the rules may
have been violated
 Thee U.S. laws provide the foundation of antitrust policy:
 Sherman Act (1980), Clayton Act (1914), and Federal Trade
Commission Act (1914)
 Enforced by the DOJ, FTC, and through private suits
 Two categories of antitrust laws:
 Collaboration among competitors
 Exclusion from the market
 Firms engage in price fixing when they agree on the
prices they will charge or the quantities they will produce
19-38
Horizontal Mergers
 In a horizontal merger, two or more competing firms
combine their operations
 A main form of collaboration
 In the US, large firms who wish to merge must notify the DOJ and
FTC in advance
 Concern with horizontal mergers is that they may raise
market prices by reducing competition
 Can also have beneficial effects:
 Cost reductions from reorganized production processes
 Increase aggregate surplus
 Reduce market prices
 Antitrust agencies must weigh these factors when
deciding whether to approve a merger
 Typical test applied for merger approval in the U.S.
requires that prices not rise
19-39
Figure 19.23: Welfare Effects of
Horizontal Mergers
19-40
Exclusionary Behavior
 Focuses on the ways a dominant firm can reduce
competition by excluding rivals from the market
 Either fully or by impairing their competitiveness
 Recent Microsoft case involved exclusionary behavior
 Exclusionary behaviors may include:
 Predatory pricing
 Exclusive contracts
 Bundling
 Difficult to restrain dominant firms without limiting their
surplus-enhancing actions
 Balancing these two concerns is a challenge
19-41
Sample Problem 4 (19.18)
An economist has found that patients
who suffer from diseases that are more
prevalent than other diseases are more
likely to take the medicine their doctors
prescribe. Why might this be so?