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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 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.”
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.
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
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
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 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.
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
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
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 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.
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 (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
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
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]
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]
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
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
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
Cournot duopoly solution
QCOURNOT = 40 Units (20 units each)
PCOURNOT = $60
π1 = π2 = $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
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.
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
Quantity0
NF
FD
FD is the “followship” or “constant”
market share” demand curve
NF is the “non-followship” or “changing
market share” demand curve.
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?
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
0
Price
Quantity
FD
NF
K
P0
q0
Firm faces NF above the
kink and FD below the kink.
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.
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

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Oligopoly

  • 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
  • 23. Cournot duopoly solution QCOURNOT = 40 Units (20 units each) PCOURNOT = $60 π1 = π2 = $400 Note that: PCOMPETITIVE = $40 QCOMPETITIVE = 60 Units Therefore PCOMPETITIVE < PCOURNOT < PMONOPOLY
  • 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
  • 30. 0 Price Quantity FD NF K P0 q0 Firm faces NF above the kink and FD below the kink.
  • 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