lecture 2 · oligopoly • oligopoly - a small group of firms in a market with substantial barriers...

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OLIGOPOLY

Lecture 2

Chapter 13


Topics

• Market Structures ( A Recap).

• Noncooperative Oligopoly.

• Cournot Model.

• Stackelberg Model.

• Bertrand Model.

• Cartels.

• Comparison of Collusive/cartel, Cournot,

Stackelberg, and Competitive Equilibria.


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


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.


Table 13.1 Properties of Monopoly, Oligopoly,

Monopolistic Competition, and Competition


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.


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.


Noncooperative Oligopoly

• Duopoly - an oligopoly with two firms.

• Three models:

Cournot model

Stackelberg model

Bertrand model


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.


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.


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.


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


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.



(cont.)

• Residual demand curve - the market

demand that is not met by other sellers at

any given price


Approach towards equilibrium


Reaction Functions


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


Figure 13.3 American and United’s

Best-Response Curves


ALGEBRAIC APPROACH

•



(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.



(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



(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



(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.



(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.


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


Table 13.2 Cournot Equilibrium

Varies with the Number of Firms


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


Application: Air Ticket Prices and

Rivalry


Figure 13.4(a) Effect of a Drop in One Firm’s

Marginal Cost on a Duopoly Cournot

Equilibrium


Figure 13.4(b) Effect of a Drop in One Firm’s

Marginal Cost on a Duopoly Cournot

Equilibrium


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.


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.

lecture 2 · oligopoly • oligopoly - a small group of firms in a market with substantial barriers...

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