Transcript Nash Equilibrium - McGraw Hill Higher Education

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
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
19-10
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
19-11
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
19-12
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
19-13
Figure 19.6: Best Responses in
the Cournot Model
19-14
Figure 19.7: Best Response
Curves in the Cournot Model
19-15
 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)
19-16
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
19-17
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
19-18
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
19-19
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
19-20
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
19-21
Figure 19.12: Coke’s Demand Curves
19-22
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
19-23
Figure 19.14: Nash Equilibrium
with Differentiated Products
19-24
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
19-25
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
19-26
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
19-27
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
19-28
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
19-29
Figure 19.17: Factors Affecting
the Number of Firms
19-30
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
19-31
Figure 19.19: Entry and Welfare
19-32
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
19-33
Figure 19.20: Monopolistic
Competition
19-34
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
19-35
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
19-36
Figure 19.23: Welfare Effects of
Horizontal Mergers
19-37
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
19-38