Transcript Oligopoly

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
Oligopoly is derived
from the Greek work
“olig” meaning “few” or
“a small number.”
Oligopoly is a market structure
featuring a small number of sellers that
together account for a large fraction of
market sales.
Features of oligopoly
•Fewness of sellers
•Seller interdependence
•Feasibility of coordinated action among
ostensibly independent firms
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.
Concentration Ratios: Very Concentrated Industries
Industry or Product
Refrigerators
Motor vehicles
Soft drinks
Long distance telephone
Laundry machines
Breakfast foods
Vaccuum cleaners
Running shoes
Beer
Aircraft engines
Domestic air flights
Tires
Aluminum
Soap
Pet food
CR4
CR8
94
94
94
92
91
88
80
79
77
72
68
66
64
60
52
98
98
97
97
NA
93
96
97
94
83
82
86
88
73
71
Source: U.S. Bureau of the Census, Census of Manufacturers
Concentration Ratios: Less Concentrated Industries
Industry or Product
Fast food
Personal computers
Office furniture
Toys
Bread
Lawn equipment
Machine tools
Paint
Newspapers
Furniture
Boat building
Concrete
Women's dresses
CR4
CR8
44
45
45
41
34
40
30
24
22
17
14
8
6
57
63
59
58
47
57
44
36
34
25
22
12
10
Source: U.S. Bureau of the Census, Census of Manufacturers
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.
Price-Output Determination in
Oligopolistic Market Structures
We have good models of priceoutput determination for the
structural cases of pure
competition and pure monopoly.
Oligopoly is more problematic,
and a wide range of outcomes is
possible.
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.
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.
Figure 10.1: Dominant Firm Price Leadership
Dollars per Unit of Output
D Industry demand
S
Supply curve
for small firms
d Leader's
net demand
P'
P*
d
MC
P* is the price
established by
D the dominant
firm
MR
Q* Qs
Q* + QS
Output
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
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).
Cournot
1
Model
•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.
1 Augustin
Cournot. Research Into the Mathematical Principles of
the Theory of Wealth, 1838
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]
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 () functions of sellers 1 and 2 are given by:
1 = (100 – q1 – q2)q1 – 40q1
[5]
2 = (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
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:
 = $900
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 – q12
[8]
Thus:
MR = dR/dq1 = 90 – 2q1
[9]
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
-maximizing output for seller
1 can be obtained from the
following equation:
q1 = 30 - .5q2
[12]
Best reply function
Equation [12] is a best reply function (BRF) for seller 1. It
can be used to compute the -maximizing output for seller
1 for any output selected by seller 2.
60
30 - .5q2
30
10
0
15
25 30
Output of seller 1
In similar fashion, we derive a best reply function for
seller 2. It is given by:
q2 = 30 - .5q1
[13]
q2
30
0
q2 = 30 - .5q1
60
q1
So we have a system with 2 equations and 2 unknowns
(q1 and q2) :
The solutions are:
q1 = 30 – .5q2
q1 = 20 units
q2 = 30 – .5q1
q2 = 20 units
q2
60
Seller 1’s BRF
30
20
0
Equilibrium
20
30
Equilibrium is established
when both sellers are on
their best reply function
Seller 2’s BRF
60
q1
Cournot duopoly solution
QCOURNOT = 40 Units (20 units each)
PCOURNOT = $60
1 = 2 = $400
Note that:
PCOMPETITIVE = $40
QCOMPETITIVE = 60 Units
Therefore
PCOMPETITIVE < PCOURNOT < PMONOPOLY
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
( P  MC ) 1

P
n
[14]
Where  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.
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).
If I cut my price
to $2.49/gallon,
what’s the guy
down the street
going to do?
Price
FD is the “followship” or “constant”
market share” demand curve
NF is the “non-followship” or “changing
market share” demand curve.
NF
FD
0
Quantity
Which demand curve is relevant?
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.
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
Price
Firm faces NF above the
kink and FD below the kink.
FD
K
P0
NF
0
q0
Quantity
Incentive to Price At the Kink
Price
>1
K
P0
0
q0
•Above P0, demand
is elastic—hence by
raising price
revenue will
decrease.
•Below P0, demand
is elastic—hence by
 < 1 decreasing price
revenue will
decrease.
Quantity
Marginal cost can vary in a wide range and the
results do not change
Dollars per Unit of Output
P*
Demand
MC
MC'
MR
Q*
Output