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13 - 1 Copyright © 2012 Pearson Education. All rights reserved.
OLIGOPOLY
Lecture 2
Chapter 13
13 - 3 Copyright © 2012 Pearson Education. All rights reserved.
Topics
• Market Structures ( A Recap).
• Noncooperative Oligopoly.
• Cournot Model.
• Stackelberg Model.
• Bertrand Model.
• Cartels.
• Comparison of Collusive/cartel, Cournot,
Stackelberg, and Competitive Equilibria.
13 - 4 Copyright © 2012 Pearson Education. All rights reserved.
Oligopoly
• Oligopoly - a small group of firms in a market with substantial barriers to entry.
• Cartel - a group of firms that explicitly agree to coordinate their activities.
• Monopolistic competition - a market structure in which firms have market power but no additional firm can enter and earn positive profits
13 - 5 Copyright © 2012 Pearson Education. All rights reserved.
Market Structures
• Markets differ according to:
the number of firms in the market,
the ease with which firms may enter and
leave the market, and
the ability of firms in a market to differentiate
their products from those of their rivals.
13 - 6 Copyright © 2012 Pearson Education. All rights reserved.
Table 13.1 Properties of Monopoly, Oligopoly,
Monopolistic Competition, and Competition
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What is Oligopoly
• derived from the Greek words
‘Oligoi’ meaning few and
‘Poleo’ meaning to sell
• a market structure characterized by
small or few number of firms and
where there exist a great deal of
interdependence among them.
13 - 8 Copyright © 2012 Pearson Education. All rights reserved.
Types of Oligopoly
• There are two types of oligopoly namely
• Perfect Oligopoly: this is where a few firms
produce or sell homogeneous products. E.g.
banking industry in Ghana.
• Imperfect Oligopoly: where a few firms sell
differentiated products. E.g. Motor car retail
outlets, cigarettes, etc.
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Noncooperative Oligopoly
• Duopoly - an oligopoly with two firms.
• Three models:
Cournot model
Stackelberg model
Bertrand model
13 - 10 Copyright © 2012 Pearson Education. All rights reserved.
Noncooperative Oligopoly (cont.)
• Three restrictive assumptions:
All firms are identical in the sense that they
have the same cost functions and produce
identical, undifferentiated products.
We initially illustrate each of these oligopoly
models for a duopoly
The market lasts for only one period.
13 - 11 Copyright © 2012 Pearson Education. All rights reserved.
Noncooperative Oligopoly (cont.)
• Duopoly equilibrium:
A set of actions taken by the firms is a Nash
equilibrium if, holding the actions of all
other firms constant, no firm can obtain a
higher profit by choosing a different
action.
13 - 12 Copyright © 2012 Pearson Education. All rights reserved.
Cournot Model
• Developed by French mathematician-
Augustin Cournot (1807-1877)
• Four assumptions:
(1) there are two firms and no other firms can
enter the market, i.e. duopoly model
(2) the firms have identical costs, (=0)
(3) they sell identical products, and
(4) the firms set their quantities simultaneously.
13 - 13 Copyright © 2012 Pearson Education. All rights reserved.
Cournot Model of an Airlines Market
• Example: American Airlines and United Airlines compete for customers on flights between Chicago and Los Angeles.
• Cournot equilibrium (Nash-Cournot equilibrium) - a set of quantities sold by firms such that, holding the quantities of all other firms constant, no firm can obtain a higher profit by choosing a different quantity
13 - 14 Copyright © 2012 Pearson Education. All rights reserved.
The crucial behavioural assumption
• each duopolist in selecting his/her own rate
of output assumes that the other duopolist
output will remain constant.
• This assumption by Cournot implies a self-
delusory behaviour on the part of each
duopolist.
• Each duopolist behaves as if he/she can act
without provoking an output reaction from
the other duopolist. i.e. no learning-by-doing
model.
13 - 15 Copyright © 2012 Pearson Education. All rights reserved.
Cournot Model of an Airlines Market
(cont.)
• Residual demand curve - the market
demand that is not met by other sellers at
any given price
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Approach towards equilibrium
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Reaction Functions
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Figure 13.2 American Airlines’ Profit-
Maximizing Output p
, $ p
er
passe
nge
r
MC
MR D
(a) Monopoly
q A , Thousand American Airlines
passengers per quarter
339
147
243
0 339 169.5 96
MR r D r D p
, $ p
er
passe
nge
r
MC
(b) Duopoly
q A , Thousand American Airlines
passengers per quarter
q U = 64
339
147
275
211
0 339 275 137.5 64 128
13 - 19 Copyright © 2012 Pearson Education. All rights reserved.
Figure 13.3 American and United’s
Best-Response Curves
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ALGEBRAIC APPROACH
•
13 - 21 Copyright © 2012 Pearson Education. All rights reserved.
ALGEBRAIC APPROACH
•
13 - 22 Copyright © 2012 Pearson Education. All rights reserved.
ALGEBRAIC APPROACH
•
13 - 23 Copyright © 2012 Pearson Education. All rights reserved.
ALGEBRAIC APPROACH
•
13 - 24 Copyright © 2012 Pearson Education. All rights reserved.
Cournot Model of an Airlines Market
(cont.)
• Market demand function is
Q = 339 − p
p - dollar cost of a one-way flight
Q total quantity of the two airlines (thousands of
passengers flying one way per quarter).
• Each airline has a constant marginal cost, MC,
and average cost, AC, of $147 per passenger
per flight.
13 - 25 Copyright © 2012 Pearson Education. All rights reserved.
Cournot Model of an Airlines Market
(cont.)
• Residual demand American faces is:
qA = Q(p) − qU = (339 − p) − qU.
rewriting
p = 339 − qA − qU
• The marginal revenue function is:
MRr = 339 − 2qA − qU
13 - 26 Copyright © 2012 Pearson Education. All rights reserved.
Cournot Model of an Airlines Market
(cont.)
• American Airlines’ best response is the
output that equates its marginal
revenue, and its marginal cost:
MRr = 339 − 2qA − qU = 147 = MC
and rearranging
qA = 96−1/2 qU
13 - 27 Copyright © 2012 Pearson Education. All rights reserved.
Cournot Model of an Airlines Market
(cont.)
• United’s best-response function is
qU = 96−1/2 qA
This statement is equivalent to saying that
the Cournot equilibrium is a point at which
the bestresponse curves cross.
13 - 28 Copyright © 2012 Pearson Education. All rights reserved.
Cournot Model of an Airlines Market
(cont.)
• To solve the model:
qA = 96−1/2 (96−1/2 qA)
and solve for qA.
• Doing so, we find that
qA = 64; qU = 64
Q = qA + qU = 128.
Cournot equilibrium price is $211.
13 - 29 Copyright © 2012 Pearson Education. All rights reserved.
The Cournot Equilibrium and the Number
of Firms
• We can write a typical Cournot firm’s profit-maximizing
condition as:
If n = 1, the Cournot firm is a monopoly,
• The more firms there are, the larger the residual demand elasticity,
nε, a single firm faces.
As n grows very large, the residual demand elasticity approaches
negative infinity , and the equation above becomes
p = MC,
• which is the profit-maximizing condition of a price-taking competitive
firm.
MCn
pMR
11
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Table 13.2 Cournot Equilibrium
Varies with the Number of Firms
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The Cournot Equilibrium and the Number
of Firms
• Cournot firm’s Lerner Index depends on the
elasticity the firm faces
Thus, a Cournot firm’s Lerner Index equals the
monopoly level, −1/ε, if there is only one firm
1p MC
p n
13 - 32 Copyright © 2012 Pearson Education. All rights reserved.
Application: Air Ticket Prices and
Rivalry
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Figure 13.4(a) Effect of a Drop in One Firm’s
Marginal Cost on a Duopoly Cournot
Equilibrium
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Figure 13.4(b) Effect of a Drop in One Firm’s
Marginal Cost on a Duopoly Cournot
Equilibrium
13 - 35 Copyright © 2012 Pearson Education. All rights reserved.
Solved Problem 13.1
• Derive United Airlines’ best-response
function if its marginal cost falls to $99 per
unit.
• Answer
Determine United’s marginal revenue
function corresponding to its residual demand
curve.
Equate United’s marginal revenue function
and its marginal cost to determine its best-
response function.
13 - 36 Copyright © 2012 Pearson Education. All rights reserved.
Solved Problem 13.2
• Intel and Advanced Micro Devices (AMD) are the only two firms
that produce central processing units (CPUs), which are the brains
of personal computers. Both because the products differ physically
and because Intel’s advertising “Intel Inside” campaign has
convinced some consumers’ of its superiority, consumers view the
CPUs as imperfect substitutes. Consequently, the two firms’
inverse demand functions differ:
pA = 197 − 15.1qA − 0.3qI,
pI = 490 − 10qI − 6qA,
• where price is dollars per CPU, quantity is in millions of CPUs, the
subscript I indicates Intel, and the subscript A represents AMD.
Each firm faces a constant marginal cost of m = $40 per unit. (For
simplicity, we will assume there are no fixed costs.) Solve for the
Cournot equilibrium quantities and prices.
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