1. Oligopoly
Outline:
•Salient features of oligopolistic market
structures.
•Measures of seller concentration
•Dominant firm oligopoly
•Rivalry among symmetric firms (The Cournot
model)
•The kinked demand curve
2. Oligopoly is a market structure
featuring a small number of sellers that
together account for a large fraction of
market sales.
Oligopoly is derived
from the Greek work
“olig” meaning “few” or
“a small number.”
3. Features of oligopoly
•Fewness of sellers
•Seller interdependence
•Feasibility of coordinated action among
ostensibly independent firms
4. Measures of seller
concentration
The concentration ratio is the
percentage of total market sales
accounted for by an absolute number of
the largest firms in the market.
The four-firm concentration ratio (CR4)
measures the percent of total market sales
accounted for by the top four firms in the
market.
The eight-firm concentration ratio (CR4)
measures the percent of total market sales
accounted for by the top eight firms in the
market.
5. Industry or Product CR4 CR8
Refrigerators 94 98
Motor vehicles 94 98
Soft drinks 94 97
Long distance telephone 92 97
Laundry machines 91 NA
Breakfast foods 88 93
Vaccuum cleaners 80 96
Running shoes 79 97
Beer 77 94
Aircraft engines 72 83
Domestic air flights 68 82
Tires 66 86
Aluminum 64 88
Soap 60 73
Pet food 52 71
Concentration Ratios: Very Concentrated Industries
Source: U.S. Bureau of the Census, Census of Manufacturers
6. Industry or Product CR4 CR8
Fast food 44 57
Personal computers 45 63
Office furniture 45 59
Toys 41 58
Bread 34 47
Lawn equipment 40 57
Machine tools 30 44
Paint 24 36
Newspapers 22 34
Furniture 17 25
Boat building 14 22
Concrete 8 12
Women's dresses 6 10
Concentration Ratios: Less Concentrated Industries
Source: U.S. Bureau of the Census, Census of Manufacturers
7. Seller interdependence
•If Kroger offers deep discounts on soft drinks,
will Wal-Mart follow suit?
•Northwest Airlines “perks” miles do not expire
—how did United, Delta, et al react?
•Verizon carries unused minutes over the to
next month—implications for Cingular, et. al.?
•Some ISP’s now pledge not to sell information
to database companies—will this affect AOL?
•Alcoa’s decision to add production capacity is
conditioned upon the investment plans of rival
aluminum producers.
8. Price-Output Determination in
Oligopolistic Market Structures
We have good models of price-
output determination for the
structural cases of pure
competition and pure monopoly.
Oligopoly is more problematic,
and a wide range of outcomes is
possible.
9. Dominant firm
price leadership
•This is a system of price-output determination we
sometimes see in oligopolistic market structures in
which there is one firm that is clearly dominant.
•General Motors was once the price leader in the
U.S. auto industry.
•Other “dominant” firms include Du Pont in
chemicals, US Steel (now USX), Phillip Morris,
Fedex, Boeing, General Electric, AT&T, and Hewlett
Packard.
10. The model
The dominant firm sets the market price
and remaining firms sell all they wish at
this price.
The demand curve for the price leader
is found by subtracting the market
demand curve from the supply curve of
the remaining sellers in the market.
11. Figure 10.1: Dominant Firm Price Leadership
P'
P*
d L
n
eader's
et demand
Industry demand
Supply curve
for small firms
D
S
d
MC MR
Q* Qs
Dollars per Unit of Output
Output
D
P* is the price
established by
the dominant
firm
Q* + QS
12. Example
Let the market demand curve be given by:
QD = 248 – 2P
The supply curve for 10 small firms in the market is given by:
QS = 48 + 3P
The dominant firm’s “residual” or net demand curve is given by
the market demand curve minus the supply of the 10 other firms,
or:
Q = QD – QS = 248 – 2P – (48 + 3P) = 200 – 5P
The inverse (residual) demand curve facing the dominant firm is
given by:
P = 40 - .2Q
13. Assume the dominant firm has a marginal cost function given
by:
MC = .1Q
The dominant firm would maximize its own profits by setting
MR = MC. To derive the MR, find the revenue (R) function and
take the first derivative with respect to Q:
R = P • Q = (40 - .2Q)Q = 40Q - .2Q2
MR = dR/dQ = 40 - .4Q
Now set MR = MC and solve for Q
40 - .4Q = .1Q
.5Q = 40 ∴ Q = 80 Units
∴ P = 40 – (.2)(80) = $24
At the price established by the dominant firm, the remaining 10
firms collectively supply 120 units (or 12 units each).
14. Cournot Model1
1
Augustin Cournot. Research Into the Mathematical Principles of
the Theory of Wealth, 1838
•Illustrates the principle of mutual interdependence
among sellers in tightly concentrated markets--even
where such interdependence is unrecognized by
sellers.
•Illustrates that social welfare can be improved by
the entry of new sellers--even if post-entry structure
is oligopolistic.
15. Assumptions
1. Two sellers
2. MC = $40
3. Homogeneous product
4. Q is the “decision variable”
5. Maximizing behavior
Let the inverse demand function be given by:
P = 100 – Q [1]
The revenue function (R) is given by:
R = P • Q = (100 – Q)Q = 100Q – Q2
[2]
16. Thus the marginal revenue (MR) function is given by:
MR = dR/dQ = 100 – 2Q [3]
Let q1 denote the output of seller 1 and q2 is the output of seller
2. Now rewrite equation [1]
P = 100 – q1 – q2 [4]
The profit (π) functions of sellers 1 and 2 are given by:
π1 = (100 – q1 – q2)q1 – 40q1 [5]
π2 = (100 – q1 – q2)q2 – 40q2 [6]
Mutual interdependence is revealed by the
profit equations. The profits of seller 1 depend
on the output of seller 2—and vice versa
17. Monopoly case
Let q2 = 0 units so that Q = q1—that is, seller 1 is a monopolist.
Seller 1 should set its quantity supplied at the level
corresponding to the equality of MR and MC.
Let MR – MC = 0
100 – 2Q – 40 = 0
2Q = 60 ∴ Q = QM = 30 units
Thus
PM = 100 – QM = $70
Substituting into equation [5], we find that:
π = $900
18. Finding equilibrium
Question: Suppose that seller 1 expects that seller 2
will supply 10 units. How many units should seller 1
supply based on this expectation?
By equation [4], we can say:
P = 100 – q1 – 10 = 90 – q1 [7]
The the revenue function of seller 1 is given by:
R = P • q1 = (90 – q1)q1 = 90q1 – q1
2
[8]
Thus:
MR = dR/dq1 = 90 – 2q1 [9]
19. Subtracting MC from MR
90 – 2q1 – 40 = 0 [10]
2q1 = 50 ∴ q1 = 25 units [11]
Thus the profit maximizing output for seller 1, given that
q2 = 10 units, is 25 units.
We repeat these calculations
for every possible value of q2
and we find that the
π-maximizing output for seller
1 can be obtained from the
following equation:
q1 = 30 - .5q2 [12]
20. Best reply function
Equation [12] is a best reply function (BRF) for seller 1. It
can be used to compute the π-maximizing output for seller 1
for any output selected by seller 2.
Output of seller 1
Outputofseller2
30 - .5q2
60
300
30
10
15 25
21. In similar fashion, we derive a best reply function for
seller 2. It is given by:
q2 = 30 - .5q1 [13]
q1
q2
0
30
60
q2 = 30 - .5q1
22. So we have a system with 2 equations and 2 unknowns
(q1 and q2) :
q1 = 30 – .5q2
q2 = 30 – .5q1
The solutions are:
q1 = 20 units
q2 = 20 units
q2
q1
0
20
20
Equilibrium
Seller 1’s BRF
Seller 2’s BRF
60
30
30 60
Equilibrium is established
when both sellers are on
their best reply function
24. Implications of the model
The Cournot model predicts that,
holding elasticity of demand constant,
price-cost margins are inversely related to
the number of sellers in the market
This principle is expressed by the following
equation
nP
MCP
η
1)(
=
−
[14]
Where η is elasticity of demand and n is the number of
sellers. So as n → ∞, the price-margin approaches zero—
as in the purely competitive case.
25. Theory of 2 demand curves
Sellers in concentrated
market structures must form
expectations about the likely
reaction of rivals before
taking action (for example,
cutting prices).
26. If I cut my price
to $2.49/gallon,
what’s the guy
down the street
going to do?
27. Price
Quantity0
NF
FD
FD is the “followship” or “constant”
market share” demand curve
NF is the “non-followship” or “changing
market share” demand curve.
28. If the firm assumes that rivals will
ignore (that is, fail to match) price
cuts or increases, then NF is
relevant. However, if the firm
assumes that rivals will follow any
price adjustments, then FD
applies.
Which demand curve is relevant?
29. It is reasonable to
assume that rivals will
follow price cuts,but not
price increases. In that
case, the firm faces a
“kinked” demand curve
31. 0
Price
Quantity
K
P0
q0
Incentive to Price At the Kink
η > 1
η < 1
•Above P0, demand
is elastic—hence by
raising price
revenue will
decrease.
•Below P0, demand
is elastic—hence by
decreasing price
revenue will
decrease.
32. Marginal cost can vary in a wide range and the
results do not change
P*
Demand
MC
MC'
MR
Q*
Dollars per Unit of Output
Output
