Chapter 19 Oligopoly McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All Rights Reserved.

Chapter 19

Oligopoly

McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All Rights Reserved.

Main Topics

Oligopoly and game theoryThe Bertrand modelCournot quantity competitionPrice competition with differentiated productsCollusionMarket entry and monopolistic competitionAntitrust 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 theBertrand 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

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 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

Pri

ce

($

/cu

bic

ya

rd)

2000 4000 6000 8000 10000

40

100

MC

D40

3000

Concrete (Cubic Yards per Year)

D

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 aCournot 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

Figure 19.8: Nash Equilibrium in the Cournot Model

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

1000 2000 3000 4000 5000 6000

1000

2000

3000

4000

5000

6000

Jo

e’s

Ou

tpu

t (C

ub

ic y

ard

s p

er

ye

ar)

Rebecca’s Output (Cubic yds per year)

Nash equilibrium

BRJoe

BRRebecca

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:

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

dENP

MCP 1

19-21

Price Competition with Differentiated Products

Often, the products that firms in an oligopoly market sell are not homogeneousCoke 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 andNash 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 differentiatedConsumers 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 possibilityFirms engage in explicit collusion when they

communicate to reach an agreement about pricesIllegal in many countries, including the U.S.

Tacit collusion is anotherCollusion without communication, sustaining a price

above the noncooperative priceGenerally not illegal, but less likely to be successful

19-31

Market Entry andMonopolistic 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

marketAs the fixed cost shrinks and the number of firms grows,

the possible profits of an active firm approach zeroSize of the marketIntensity 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 surplusIf entry by the first firm would be unprofitableGovernment may want to subsidize entry by first firm

to increase aggregate surplusOnce one firm has entered the market, excessive

entry may result and lower aggregate surplusBusiness 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?