Chapter 13
Oligopoly
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4. Oligopoly
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A market structure with a small number of firms
(usually big)
Oligopolists “know” each other:
Strategic interaction: actions of one firm will
trigger re-actions of others
Oligopolist must take these possible re-actions
into account before deciding on an action
Therefore
No single, unified model of oligopoly exists
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Stages of evolution
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Market introduction and growth
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New technology, high uncertainty, innovators
profit
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Product is new, no close substitutes
Learning curve is steep
Temporal monopoly in the market possible
But high set-up costs
What market is most receptive of the
product?
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Strategic decisions about market introduction
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Maturity and decline
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No more growth of the market
Product gets more homogeneous
Price (and service) get more important
Price competition (oligopoly)
Overcapacity ==> major ingredient for
price wars
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Cartel: A collusive agreement
made openly and formally
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Cartel
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Cartels act like multiplant monopolies.
Profit of cartel is maximized if marginal costs
among members of cartel are equalized
Would mean that high-cost firms produce less
Instability of cartel: incentive for members to
cheat
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Incentive biggest for small members
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Cartel as a multi-plant monopoly
PRICE
MC1
MC2
D
MC
Supply
D
MR
Q1
FIRM 1
Q2
TOTAL OUTPUT
FIRM 2
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Instability of Cartel:
demand curve gets much flatter (D‘)
We started at Price P0
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Problem 1
The Bergen Company and the Gutenberg Company are the only two firms that
produce and sell a particular kind of machinery. The demand curve for their
product is
P = 580 – 3Q
where P is the price of the products, and Q is the total amount demanded.
The total cost function of the Bergen Company is
TCB = 410 QB.
The total cost function of the Gutenberg Company is
TCG = 460 QG.
a) If these two firms collude, and if they want to maximize their combined profits,
how much will the Bergen Company produce?
b) How much will the Gutenberg Company produce?
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Solution Problem 1
a) Bergen’s marginal cost is always less than Gutenberg’s marginal cost.
Therefore Bergen would produce all the combination’s output. Setting
Bergen’s marginal cost equal to the marginal revenue derived from the
demand function, we get:
410 = 580 – 6Q => QB = 28.33 and QG = 0.
b) If Gutenberg were to produce one unit and Bergen one unit less, it
would reduce their combined profits by the difference in their marginal
costs.
If direct payments of output restrictions between the firms were legal,
Gutenberg would accept a zero output quota. But if competition were to
break out, Gutenberg would make zero profits and Bergen would earn
$2,000. Thus the most Bergen would pay for Gutenberg’s cooperation is
$408.33 and the least Gutenberg would accept to not produce is $0.01.
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Price Leadership by a dominant firm
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One firm sets price and others follow
Industry is composed of a large, dominant firm and many
small firms, big firm has cost-advantage
The demand curve for the dominant firm is derived by
subtracting the amount supplied by the small firms at each
price from the total demanded at that price
Big firm can behave as a monopolist, small firms make no
super-normal profits
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How can a few firms compete
against each other?
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Many different models
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Some simplifying assumptions:
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Identical product
2 firms (can easily be extended to more)
Same (constant) cost functions
Know the (linear) demand function
Firms act simultaneously
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Price Competition (= Bertrand
competition)
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Total costs:
Market demand:
M C
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T C i = 5 0 0 + 4 q i + 0 .5 q i2
P = 100 − q = 100 − qA + qB
= 4 + qi
WTP for first unit = 99, MC = 5
If firm A would set price at 98, firm B would set price to 97 …
If firms compete over prices, they would go down to marginal
costs
P=
Q=
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Example: Collusion (cartel)
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Calculate price, quantity and profit for a
collusion in this example
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Add up marginal costs horizontally
Q = q A + qB = −4 + MC A − 4 + MCB = −8 + 2 MC
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MC = 4 +
Q
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Cournot-Nash Duopoly
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Quantity (capacity) competition
Taking the other‘s output as given,
what output is optimal for firm X?
Series of “What if?” questions necessary
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for each potential output of the rival you
must have a potential answer
Actual decision taken by assuming what
rival will actually do
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Finding the reaction curves
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Reaction curve: given the output of X,
what output of Y is optimal?
Of course, whatever Y does, will
produce further reactions, i.e. X is not
constant in general.
Equilibrium only when both firms „sit“
on their reaction curves: no surprises
and no incentive to alter the behavior
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Problem 2
The International Air Transport Association (IATA) has
been composed of 108 U.S. and European airlines that
fly transatlantic routes. For many years, IATA acted as
a cartel: it fixed and enforced uniform prices.
a) If IATA wanted to maximize the total profit of all
member airlines, what uniform price would it charge?
b) How would the total amount of traffic be allocated
among the member airlines?
c) Would IATA set price equal to marginal cost? Why or
why not?
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Solution Problem 2
a) The IATA would charge the price that clears the
market at the level of output where marginal revenue
equals the horizontally summed marginal cost curves
of each operator in the market.
b) The traffic should be allocated so that the marginal
costs of all the members operating in the market
would be equal and that no member not currently in
the market would have a lower marginal cost.
c) No, the IATA would set a price equal to marginal cost
multiplied by 1/(1+1/e) where e is the elasticity of
demand in the market in question.
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Problem 3
In Britain price competition among bookshops has been suppressed
for over 90 years by the Net Book Agreement (of 1900), which was
aimed at the prevention of price wars. However, in October 1991,
Waterstone and Company began cutting book prices at its 85 British
shops. According to Richard Barker, Waterstone’s operations director,
the decision to reduce the price of about 40 titles by about 25% was
due to price cuts by Dillons, Waterstone’s principal rival.
a) According to the president of Britain’s Publishers Association, the
price-cutting was “an enormous pity” that will “damage many
booksellers who operate on very slim margins. Does this mean that
price-cutting of this sort is contrary to the public interest?
b) Why would Dillons want to cut price? Under what circumstances
would this be a good strategy? Under what circumstances would it be
a mistake?
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Solution Problem 3
a) No. A price war, although always “an enormous pity”
for producers, usually is very good news for
consumers.
b) If demand is elastic at high prices, and if Dillons has
a comparative advantage with respect to its rivals at
high volumes, it may prefer a low competitive price
to a high collusive one. If demand is inelastic, of if
Dillons does not have a comparative advantage over
its rivals at high volumes, it may be a mistake to cut
prices.
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