Managerial economics strategy by m perloff and brander chapter 11 monopolistic competition

Chapter 11
Oligopoly and
Monopolistic
Competition


Table of Contents
•

11.1 Cartels

•

11.2 Cournot Oligopoly

•

11.3 Bertrand Oligopoly

•

11.4 Monopolistic Competition

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Introduction
• Managerial Problem
–

–

Airbus and Boeing are the only two manufacturers of large commercial aircrafts.
If only one receives a government subsidy, how can it gain competitive advantage?
What is the subsidy’s effect on p and q? What happens if both governments subsidize
their firms? Should both firms lobby for government subsidies that result in a subsidy
war?

• Solution Approach
–

We need to focus on two markets. An oligopolistic market has few sellers and barriers
to entry, firms have market power and may or may not collude to form cartels. A
monopolistic competitive market has firms with market power, but there is free entry
in the long run.

• Empirical Methods
–
–
–

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Within a cartel, oligopoly firms collude to raise prices and profits toward monopoly
levels.
Oligopoly firms can independently set quantities (Cournot Model) or prices (Bertrand
Model).
In monopolistic competitive markets, firms charge prices above marginal cost but
make no economic profit in the long run.

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11.1 Cartels
• Cartel Objective: Higher Profits
– Oligopolistic firms have an incentive to form cartels in which they collude
in setting prices or quantities so as to increase their profits.
– The Organization of Petroleum Exporting Countries (OPEC) is a well-known
example of an international cartel.

• Cartel Basic Functioning
– Typically, each member of a cartel agrees to reduce its output from the
level it would produce if it acted independently. As a result, the market
price rises and the firms earn higher profits. If the firms reduce market
output to the monopoly level, they achieve the highest possible collective
profit.
– However, each member has an incentive to cheat.

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11.1 Cartels
• Why Cartels Form
– A cartel forms if members of the cartel believe that they can raise their
profits by coordinating their actions.
– A cartel takes into account how changes in any one firm’s output affect
the profits of all members of the cartel. Therefore, the aggregate profit of
a cartel can exceed the combined profits of the same firms acting

independently.

• Competitive Market versus Cartel
– In Figure 11.1, there are n competitive firms and no further entry is
possible.
– In panel b, at the point of competitive equilibrium, the market output is Qc
= nqc and price is pc . In panel a each firm takes pc and produces qc = Qc /n.
– If the n firms form a cartel and act like a monopoly, the market output
reduces to Qm but the price goes up to pm in panel b. The cartel profit
increases and individual profits go up if firms charge pm and reduce output
to qm in panel a.

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11.1 Cartels
Figure 11.1 Comparing Competition with a
Cartel

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11.1 Cartels
• Why Cartels Fail: External Reasons
– Cartels are generally illegal in developed countries. High fines and jail
terms may prevent collusion.

– Some cartels fail because they do not control enough of the market to
significantly raise the price.

• Why Cartels Fail: Internal Reasons
– Cartel members have incentives to cheat if a member thinks its firm is just
one of many firms so its extra output hardly affects the market price and
the other firms in the cartel can’t tell who is producing more.
– In panel a of Figure 11.1, each firm agreed to qm. However, a price taker
firm maximizes profit selling q*, where pm= MC. It makes extra money by
producing more than qm, as long as MR > MC.
– As more and more firms cheat, pm falls. Eventually, the cartel collapses.

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11.1 Cartels
• Maintaining Cartels: Cheating Detection
– Some cartels may give members the right to inspect each other’s
accounts or divide the market by region or by customers.
– Cartels may turn to industry organizations to collect data on a firm’s
market share.

• Maintaining Cartels: Enforcement
– Most-favored-customer clause: the seller would not offer a lower price to
any other current or future buyer without offering the same price decrease
to the firms that signed these contracts.

• Maintaining Cartels: Government and Barriers to Entry

– Sometimes governments help create and enforce cartels, exempting them
from antitrust and competition laws.
– The fewer the firms in a market, high barriers to entry, the more likely it is
that other firms will know if a given firm cheats and the easier it is to
impose penalties.

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11.2 Cournot Oligopoly
• Cournot Model
– Assumptions: small number of firms and no entry, identical costs and
identical products, firms set their quantities independently and
simultaneously.
– Because the firms set quantities, the price adjusts as needed until the
market clears and profits are interdependent.

• Residual Demand and Best Responses
– Firms use their residual demand curves: market demand that is not met by
other sellers at any given price, Dr(p) = D(p) – So(p).
– A firm maximizes profit with best responses that come from MRr = MC.

• Equilibrium called Nash-Cournot Equilibrium
– A set of quantities chosen by firms such that, holding the quantities of all
other firms constant, no firm can obtain a higher profit by choosing a
different quantity.
– The quantity of equilibrium must be on the best response curve for all
firms.

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11.2 Cournot Oligopoly
• Airlines: Residual Demand
– The strategies for American and United depend on their residual demand
curves and marginal costs.
– If American thinks United flies qU passengers, American’s residual demand
is qA = Q(p) – qU. Alternatively, United’s residual demand is qU = Q(p) – qA

• Airlines: Best Responses
– To maximize profit, American sets MRr=MC and finds its best response
curve for all possible qU. Figure 11.3 shows that if qU = 64, American’s best
response is qA = 64, shuts down if qU = 192, and so on. It also shows
United’s best response curve.

• Airlines: Nash-Cournot Equilibrium
– There is only one pair of outputs where both firms are on their bestresponse curves, qA = qU = 64. At this intersection both firms maximize
profits, are on their best response curves, and don’t want to change their
outputs.

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11.2 Cournot Oligopoly

Figure 11.3 Best-Response Curves for
American and United Airlines

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11.2 Cournot Oligopoly
• Residual Demand, MR and MC
– The market demand function is Q = 339 – p. The residual demand function
for American is qA = (339 – p) – qU or p = 339 – qA – qU.
– American’s marginal revenue function is MRr = 339 – 2qA – qU.
– Both airlines have MC = AC = $147 per passenger per flight.

• MR = MC and Best Responses
– MRr = MC, so 339 – 2qA – qU = 147
– American’s best-response: qA = 96 – 0.5 qU
– Similarly, United’s best response: qU = 96 – 0.5 qA

• Nash-Cournot Equilibrium
– Solving the two best responses by substitution, qA = 96 – 0.5 (96 – 0.5 qA)
– The Nash-Cournot equilibrium values: qA = qU = 64, Q= qA + qU = 128,
p=$211

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11.2 Cournot Oligopoly
• Airlines with Calculus: Inverse Residual Demand, MR and MC
– The market demand function is Q = 339 – p
– The residual demand function for American is qA = (339 – p) – qU
– Inverse residual demand is p = 339 – qA – qU
– American’s revenue function: RA = pqA = (339 – qA – qU)qA= 339qA – q2A –
qUqA
– American’s marginal revenue function: MRr = dRA/dqA= 339 – 2qA – qU
– United’s revenue function: RU = 339qU – q2U – qUqA
– United’s marginal revenue function: MRr = dRU/dqU= 339 – 2qU – qA

• Best Responses and Nash-Cournot Equilibrium
– Same steps and calculations as presented in the algebraic approach.

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11.2 Cournot Oligopoly
• The Number of Firms Matter
– If two Cournot firms set output independently, the price to consumers is
lower than the monopoly price. If there are more than two, the price is
even lower.

• Individual Output and Total Output
– Consider the airlines’ inverse market demand function p = 339 – Q and n
identical firms with MC=AC=$147.
– The best response for any firm is q = 96 – [n – 1]q. So, q= 192/(n+1)
– Total output is Q = qn = 192n/(n+1)

• Number of Firms and Nash-Cournot Equilibrium
– If n = 1, Q = (192 × 1)/2 = 64, p = 243, a monopoly outcome.
– If n = 2, Q = (192 × 2)/3 = 128, p = 211, a duopoly outcome as we found
earlier.
– If n is very large, Q = 192 and p = 147 = MC. The Nash-Cournot
equilibrium approaches the competitive outcome.

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11.2 Cournot Oligopoly
• Non Identical Firms: Unequal Costs Case
– In the Cournot model, a firm’s best-response function comes from MR =
MC. If MC rises or falls, then the firm’s best-response function shifts.
– Consider the Airline example, products are not differentiated, so American
and United charge the same price. United’s MC drops from $147 to $99.

• Best Responses
– There is no change for American’s best-response.
– United’s MRr curve is unaffected, but its best-response function shifts to
the right in panel b of Figure 11.4. United wants to produce more than
before for any given level of American’s output.

• Nash-Cournot Equilibrium
– In panel b of Figure 11.4, the Nash-Cournot equilibrium shifts from e1 (both
firms sold 64) to e2, at which United sells 96 and American sells 48.
– United’s profit increases from $4.1 million to $9.2 million, while

American’s profit falls to $2.3 million. Consumers also win because p falls
from $211 to $195.

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11.2 Cournot Oligopoly
Figure 11.4 Effect of a Drop in One Firm’s
Marginal Cost on a Nash-Cournot Equilibrium

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11.2 Cournot Oligopoly
• Non Identical Firms: Differentiated Products Case
– By differentiating its product from those of a rival, an oligopolistic firm can
shift its demand curve to the right and make it less elastic.
– The less elastic the demand curve, the more the firm can charge because
consumers are willing to pay more for a product that ‘seems’ superior.

• Higher Prices and Choices
– Although differentiation leads to higher prices, which harm consumers,
differentiation is desirable in its own right. Consumers value having a
choice, and some may greatly prefer a new brand to existing ones.

• Nash-Cournot Equilibrium

– If consumers think products differ, the Cournot quantities and prices may
differ across firms. Each firm faces a different inverse demand function
and hence charges a different price.

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11.2 Cournot Oligopoly
• Mergers
– Mergers could be vertical or horizontal and both want to increase profit.
– Vertical mergers may lower cost with a more efficient supply chain
organization. Horizontal mergers may increase market power and reduce
competition.

• More Market Power May Not Be Enough
– Cournot with 3 firms: Using Q=192n/(n+1), each firm flies 48k passengers,
p=$195 and earns $2.3 million.
– Two firms merge, Cournot duopoly: Now, each of the remaining two firms flies
64k passengers and earns $4.1 million. Bad for the merged firms ($2.05 <
$2.3).

• Cost Advantage Pays Off
– If the merger results in even a modest cost advantage, the merger may be
worthwhile. In our example, if MC of the merged firms drops from $147 to
$138, profit becomes $4.9 million. Great for the merged firms ($2.45 > $2.3).
– In general, the reduction in the number of firms may raise price insufficiently
to make a merger profitable unless there is cost reduction.

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11.3 Bertrand Oligopoly
• Setting Prices
-

Oligopoly firms set prices and then consumers decide how many units to
buy.
The Bertrand equilibrium differs from the Cournot equilibrium; it depends
on whether firms produce identical or differentiated products.

• Best Responses
– In a duopoly setting, Firm 1’s best response curve comes from answering
“What is Firm 1’s best response—what price should it set—if Firm 2 sets a
price of p2 = x?” for all possible values of x.
– Similarly, Firm 2’s best response curve: “What is Firm 2’s best response
(p2) if Firm 1 sets a price of p1 = y?” for all possible values of y.

• Nash-Bertrand Equilibrium
– Nash-Bertrand equilibrium: a set of prices such that no firm can obtain a
higher profit by choosing a different price if the other firms continue to
charge these prices.

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11.3 Bertrand Oligopoly
• Identical Products
– Two firms with identical costs and
identical products, MC = AC = $5.
– In Figure 11.5, Firm 1’s bestresponse curve starts at $5 and
then lies slightly above the 45°
line. That is, Firm 1 undercuts its
rival’s price as long as its price
remains above $5.
– Firm 2’s best response curve also
starts at $5 and undercuts its
rival’s price if p2 > 5.
– Nash-Bertrand Equilibrium at
intersection point e, p2 = p1 = $5
= MC. Same as perfect
competition equilibrium.

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Figure 11.5 Nash-Bertrand
Equilibrium with Identical
Products


11.3 Bertrand Oligopoly
• Bertrand versus Cournot with Identical Products

- The Nash-Bertrand equilibrium differs substantially from the Nash-Cournot
equilibrium. Zero profits (p = MC) versus positive profits (p > MC).
- The Cournot model seems more realistic than the Bertrand model in two
ways.

• Bertrand’s “Competitive” Equilibrium is Implausible
– In a market with few firms, why would the firms compete so vigorously
that they would make no profit?
– Oligopolies typically charge a higher price than competitive firms. So, the
Nash-Cournot equilibrium is more plausible.

• Bertrand’s Equilibrium Price Depends on Cost Only
– The Nash-Cournot equilibrium price is sensitive to demand conditions and
the number of firms as well as on cost. So, it is better to study
homogeneous goods markets.

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11.3 Bertrand Oligopoly
Figure 11.6 Nash-Bertrand
• Differentiated Products
Equilibrium with Differentiated
– Two firms, identical costs MC = AC = Products
$5 and differentiated products
– In Figure 11.6, neither firm’s bestresponse curve lies along a 45° line
through the origin because Coke
and Pepsi are similar but some

consumers prefer one to the other
independently of the price. So
neither firm has to exactly match a
price cut by its rival.
– Nash-Bertrand Equilibrium at
intersection point e, p2 = p1 = $13 >
MC
– Plausible: Firms set p > MC, and
prices are sensitive to demand
conditions and number of firms

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11.4 Monopolistic Competition
• Monopoly/Oligopoly + Competitive Behavior
-

Monopolistic competition: market structure that has the price setting
characteristics of monopoly or oligopoly and the free entry of perfect
competition.
These firms have oligopoly market power (face downward sloping demand
curves), but earn zero profit due to free entry, as do perfectly competitive
firms.

• 1st Reason for Downward Sloping Demand
– Market demand may be limited so there is room for only few firms. So, the
residual demand curve facing a single firm is downward sloping.

– For example in a small town, the market may be large enough to support only
a few plumbing firms, each of which provides a similar service.

• 2nd Reason for Downward Sloping Demand
– Firms differentiate their products. So each firm can retain those customers who
particularly like that firm’s product even if its price is higher than those of
rivals.
– For example, gourmet food trucks serve differentiated food in monopolistically
competitive markets.

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11.4 Monopolistic Competition
• Equilibrium
– Firms have identical cost
Figure 11.7 Monopolistic
functions and produce
Competition
identical products.
– In Figure 11.7, a
monopolistically competitive
firm, facing the firm-specific
demand curve D, sets its
output where MR = MC.
– At that quantity, the firm’s
average cost curve, AC, is
tangent to its demand

curve, p = AC
– At the equilibrium the
monopolistically competitive
firm makes zero profit. The
entry and exit responses of
firms ensure this.
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11.4 Monopolistic Competition
• Profitability: If Identical Costs & Products, Zero Profit
– If all firms in a monopolistically competitive market produce identical
products and have identical costs: each firm earns zero economic profit in
the long run.
– Thus, all firms in the industry are on the margin of exiting the market
because even a slight decline in profitability would generate losses.

• Profitability: If Differentiated Costs & Products, Positive Profit
– If those firms have different cost functions or produce differentiated
products: most likely firms differ from each other in their profitability.
– If so, low-cost firms or firms with superior products may earn positive
economic profits in the long run.

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