Oligopoly
U.S. Wireless Telecommunications
Industry: does the Sprint/NEXTEL merger
increase or decrease competition?
•
62.0 million subscribers
•
60.7 million subscribers
•
53.6 million subscribers
(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Oligopoly
Oligopoly is a market with a small number of
sellers whose actions are interdependent
 A duopoly is a market with two sellers

(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Outline
pricing
 capacity
 price/capacity leadership
 restraining competition
 antitrust (competition) policy

(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Pricing: Monopoly
(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Homogenous Product
Bertrand model: sellers who produce at constant marginal cost
without capacity constraint compete on price
 Suppose one of the two firms charges price p, above marginal
cost
 The other firm has three choices:
price > p: lose all customers
price = p: split the market in half
price < p: gain the whole market, even marginally below p
 Pricing just below p is most profitable. The same logic would
apply to the other firm. So, the Nash equilibrium is for both
firms to charge price = p.

(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Differentiated Products

Sellers compete partially on price, partially on
product design/placement
(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Pricing:
Differentiated Products
the Hotelling model of duopoly
(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Suppose Ajax’s price is p1, Bacchus’s
price is p2, what is the market share
for each of them?




Suppose the transportation cost per unit of distance
is t.
Ajax and Bacchus share the market. Intuitively, if a
consumer is located closer to Ajax, then he or she is
more likely to buy from Alex, given the prices.
In the equilibrium, there must be consumer who is
located on the border between Ajax’s market share
and Bacchus’s market share. Suppose the border is x
distance from Ajax.
This consumer should be indifferent between buying
from Ajax and buying from Bacchus.
(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Suppose the marginal benefit of the consumer is 10,
then the net benefit after subtracting price and
transportation cost is
-- if buying from Ajax, 10-p1-x*t
-- if buying from Bacchus, 10-p2-(1-x)*t

Because in equilibrium, the buyer on the border is
indifferent to buying from either Ajax or Bacchus
We have 10-p1-x*t=10-p2-(1-x)*t
Namely, x=(p2-p1+t)/2t
(c) 2000-2007, I.P.L. Png & D.E. Lehman
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What is Ajax’s optimal pricing rule,
given Bacchus setting price at p2?
We know that in equilibrium, the market
share of Ajax is x=(p2-p1-t)/2t.
 What is the best p1 for Ajax in order to
maximize profits?
 Suppose the marginal production cost for
Ajax is c.

(c) 2000-2007, I.P.L. Png & D.E. Lehman
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




Total profits of Ajax is
p1*x=(p1-c)*(p2-p1+t)/2t
Taking first order derivative with respect to p1,
We get the optimal pricing of Ajax is
p1=(p2+c+t)/2, given p2—best response function of
Ajax
In a similar way, we can get the optimal pricing of
Bacchus is
p2=(p1+c+t)/2, given p1– best response function of
Bacchus
(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Pricing:
Strategic Complements
Actions are strategic complements if an
adjustment by one party leads other parties
to adjust in the same direction
 Example: if Ajax lowers price and Bacchus
responds by lowering price, then prices are
strategic complements

(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Pricing:
Differentiated Products
Differentiated sellers: best response price functions
(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Question, if transportation cost
varies, what will happen?

If t=0, p1=p2=c, Bertrand result.

If t is higher, then both p1 and p2 are higher.
(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Pricing:
Product Design
Desire for market share leads firms to locate
“close” to their customers
 Desire to avoid direct competition leads firms
to locate away from their competitor (less
differentiation leads to more direct price
competition)
 Optimal solution is a complex tradeoff

(c) 2000-2007, I.P.L. Png & D.E. Lehman
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The impact of introducing Euro on
Online shopping: lower search cost
leads to higher price?
There are two kinds of consumers: shoppers
and non-shoppers
 If retailers focus more on the second group of
consumers, and try differentiate their
products, then price may go higher.

(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Outline
pricing
 capacity
 price/capacity leadership
 restraining competition
 antitrust (competition) policy

(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Capacity Competition
Cournot model: sellers produce at constant
marginal cost and compete on production
capacity (homogeneous product)
 Residual demand curve: market demand less
the quantities supplied by other sellers
 Best response functions show the best
capacity choice for each seller as a function of
the other seller’s capacity choices

(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Example
Mars Cellular and Pluto Wireless compete on
capacity
 Market demand = 300 – 3p
 Marginal cost = $30/subscriber/month

(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Mars’ best response function given Pluto’s capacity is
 TR1=Q1*p
 p=100-(Q1+Q2)/3
 So TR1=Q1*(100-(Q1+Q2)/3)
 MR1=100-(2Q1/3)-(Q2/3)
 To maximizing profits, we have MR1=MC=30
 So the optimal capacity of Mars is
 Q1=150-(3MC/2)-Q2/2.
 This is Mar’s best response function given Pluto’s Q2.

(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Similarly, pluto’s best response function given
Mars’ Q1 is
 Q2=150-(3MC/2)-Q1/2

(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Capacity
Best Response Capacity Functions
(c) 2000-2007, I.P.L. Png & D.E. Lehman
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
If Pluto’s Mc decreases to $20 then its best
response function will shift upward, and this
will result in a larger market share for Pluto.
(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Capacity:
Cost Differences
A decrease in marginal cost for one firm will
lead to an increased market share for that
firm and a decreased market share for the
other firm
 This is seen by shifting outward the best
response function of the firm with the lower
marginal cost
 Changes in fixed costs do not shift the best
response functions

(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Capacity:
Multiple Sellers
With multiple sellers with
differing marginal cost, the
incremental margin
percentage in the industry
can be represented by
( p  c ) HHI

p

where HHI is the Herfindahl –
Hirschman Index, c is the
industry weighted average
cost, and  is the elasticity
of demand.
(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Capacity:
Strategic Substitutes
Actions by various parties are strategic
substitutes if an adjustment by one party
leads other parties to adjust in the opposite
direction
 Capacity levels in the Cournot model are
strategic substitutes

(c) 2000-2007, I.P.L. Png & D.E. Lehman
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
HHI is equal tot the sum of the squares of each
firm’s market share.

Suppose there three firms in an industry, each has a
market share of 0.1, 0.2., 0.7.

Then, in fractions, HHI=0.01+0.04+0.49=0.54. (for
our previous fomular, we need to use fractions to
calculate HHI.)

Or in percentage points, HHI=100+400+4900=5400.
(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Outline
pricing
 capacity
 price/capacity leadership
 restraining competition
 antitrust (competition) policy

(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Price Leadership
Consider an industry with fixed costs and a
market leader
 The leader can use a first mover advantage
by choosing output and price to create a
residual demand curve for a potential entrant
that leaves no room for profit
 This is known as “limit pricing”

(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Price/Capacity Leadership:
Price
(c) 2000-2007, I.P.L. Png & D.E. Lehman
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For this to work, two conditions must be
statisfied:
 1. leader’s first move is viewed as a
commitment.
 2. entry would incur a fixed cost

(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Price/Capacity Leadership:
Capacity

The Stackelberg Model: the leader commits to
capacity before the follower

The leader takes into account the follower’s
subsequent choice of capacity

The result is an industry production capacity greater
than in Cournot competition (with a lower price)

The leader has a larger market share than the
follower (first mover advantage, even though the
follower gets to observe the leader’s capacity before
choosing its capacity)
(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Outline
pricing
 capacity
 price/capacity leadership
 restraining competition
 antitrust (competition) policy

(c) 2000-2007, I.P.L. Png & D.E. Lehman
34
Restraining Competition:
Cartels
Cartels are agreements among sellers (or
buyers) to raise the price above (below, for a
buyers’ cartel) the competitive level
 Cartels are generally illegal

(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Restraining Competition:
Horizontal Integration
Horizontal integration is the combination of
two entities in the same, or similar,
businesses under a common ownership.
 Vertical integration is the combination of the
assets for two (or more) successive stages of
production under a common ownership.
 Horizontal integration has the potential to
increase market power.

(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Outline
pricing
 capacity
 price/capacity leadership
 restraining competition
 antitrust (competition) policy

(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Antitrust (Competition) Policy:
Competition Laws
Prohibit collusion on price or other means
 Prohibit monopolies or monopsonies from
abusing market power
 Prohibit mergers or acquisitions that would
substantially lessen competition in the
market.

(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Antitrust (Competition) Policy:
Merger Guidelines
Post-merger
HHI
Increase in HHI
0 - 50
50 - 100
> 100
> 1,800
safe
suspect
suspect
1,000 –
1,800
safe
safe
suspect
0 – 1,000
safe
safe
safe
(c) 2000-2007, I.P.L. Png & D.E. Lehman
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Summary
Prices are strategic complements
 Production capacities are strategic substitutes
 Sellers who can commit to capacity before their
competitors may have a first mover advantage,
potentially to the point of excluding all potential
entrants
 Restraining competition – either through agreement
or horizontal integration – can increase profits for
sellers
 Anti-trust (competition) authorities monitor industry
behavior. The Herfindahl-Hirschman Index is a
commonly used gauge for screening mergers

(c) 2000-2007, I.P.L. Png & D.E. Lehman
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