14. 14!
Oligopoly
The Cournot Model
Duopoly
• Two firms competing with each other
• Homogenous good
• The output of the other firm is assumed to be fixed
The Reaction Curve
• A firm’s profit-maximizing output is a decreasing
schedule of the expected output of Firm 2
27!
Firm 1’s Output Decision
28!
MC1
50
MR1(75)
D1(75)
12.5
If Firm 1 thinks Firm 2 will produce
75 units, its demand curve is
shifted to the left by this amount.
Q1
P1
What is the output of Firm 1
if Firm 2 produces 100 units?
D1(0)
MR1(0)
If Firm 1 thinks Firm 2 will
produce nothing, its demand
curve, D1(0), is the market
demand curve.
D1(50)MR1(50)
25
If Firm 1 thinks Firm 2 will produce
50 units, its demand curve is
shifted to the left by this amount.
15. 15!
Reaction Curves and Cournot Equilibrium
29!
Firm 2’s Reaction
Curve Q*2(Q2)
Firm 2’s reaction curve shows how much it
will produce as a function of how much
it thinks Firm 1 will produce.
Q2
Q1
25 50 75 100
25
50
75
100
Firm 1’s Reaction
Curve Q*1(Q2)
x
x
x
x
Firm 1’s reaction curve shows how much it
will produce as a function of how much
it thinks Firm 2 will produce. The x’s
correspond to the previous model.
In Cournot equilibrium, each
firm correctly assumes how
much its competitors will
produce and thereby
maximize its own profits.
Cournot
Equilibrium
Oligopoly
Questions
1) If the firms are not producing at the
Cournot equilibrium, will they adjust
until the Cournot equilibrium is
reached?
2) When is it rational to assume that its
competitor’s output is fixed?
30!
16. 16!
Oligopoly
An Example of the Cournot Equilibrium
Duopoly
• Market demand is P = 30 - Q where Q = Q1 +
Q2
• MC1 = MC2 = 0
31!
The Linear Demand Curve
Oligopoly
An Example of the Cournot Equilibrium
Firm 1’s Reaction Curve
32!
Total Revenue, R1 =PQ1 =(30−Q)Q1
= 30Q1 −(Q1 +Q2)Q1
= 30Q1 −Q1
2
−Q2Q1
The Linear Demand Curve
17. 17!
Oligopoly
An Example of the Cournot Equilibrium
33!
The Linear Demand Curve
Oligopoly
An Example of the Cournot Equilibrium
34!
The Linear Demand Curve
18. 18!
Duopoly Example
35!
Q1
Q2
Firm 2’s
Reaction Curve
30
15
Firm 1’s
Reaction Curve
15
30
10
10
Cournot Equilibrium
The demand curve is P = 30 - Q and
both firms have 0 marginal cost.
Oligopoly
36!
R =PQ=(30−Q)Q= 30Q−Q2
MR =ΔR ΔQ= 30−2Q
MR =0 when Q = 15 and MR =MC
Profit Maximization with Collusion
19. 19!
Oligopoly
Contract Curve
Q1 + Q2 = 15
• Shows all pairs of output Q1 and Q2 that
maximizes total profits
Q1 = Q2 = 7.5
• Less output and higher profits than the Cournot
equilibrium
37!
Profit Maximization with Collusion
Duopoly Example
38!
Firm 1’s
Reaction Curve
Firm 2’s
Reaction Curve
Q1
Q2
30
30
10
10
Cournot Equilibrium15
15
Competitive Equilibrium (P = MC; Profit = 0)
Collusion
Curve
7.5
7.5
Collusive Equilibrium
For the firm, collusion is the best
outcome followed by the Cournot
Equilibrium and then the
competitive equilibrium
20. 20!
First Mover Advantage--The Stackelberg Model
Assumptions
One firm can set output first
MC = 0
Market demand is P = 30 - Q where Q = total
output
Firm 1 sets output first and Firm 2 then makes
an output decision
39!
First Mover Advantage--The Stackelberg Model
Firm 1
Must consider the reaction of Firm 2
Firm 2
Takes Firm 1’s output as fixed and therefore
determines output with the Cournot reaction
curve: Q2 = 15 - 1/2Q1
40!
21. 21!
First Mover Advantage--The Stackelberg Model
Firm 1
Choose Q1 so that:
41!
First Mover Advantage--The Stackelberg Model
Substituting Firm 2’s Reaction Curve for
Q2:
42!
MR1 = ΔR1 ΔQ1 =15−Q1
MR = 0:Q1 =15 and Q2 = 7.5
R1 = 30Q1 −Q1
2
−Q1(15−1 2Q1)
=15Q1 −1 2Q1
2
22. 22!
First Mover Advantage--The Stackelberg Model
Conclusion
Firm 1’s output is twice as large as firm 2’s
Firm 1’s profit is twice as large as firm 2’s
Questions
Why is it more profitable to be the first mover?
Which model (Cournot or Shackelberg) is
more appropriate?
43!
Price Competition
Competition in an oligopolistic industry
may occur with price instead of output.
The Bertrand Model is used to illustrate
price competition in an oligopolistic
industry with homogenous goods.
44!
23. 23!
Price Competition
Assumptions
Homogenous good
Market demand is P = 30 - Q where
Q = Q1 + Q2
MC = $3 for both firms and MC1 = MC2 =
$3
45!
Bertrand Model
Price Competition
Assumptions
The Cournot equilibrium:
•
Assume the firms compete with price, not
quantity.
46!
Bertrand Model
24. 24!
Price Competition
How will consumers respond to a
price differential? (Hint: Consider
homogeneity)
The Nash equilibrium:
• P = MC; P1 = P2 = $3
• Q = 27; Q1 & Q2 = 13.5
•
47!
Bertrand Model
Price Competition
Why not charge a higher price to raise
profits?
How does the Bertrand outcome
compare to the Cournot outcome?
The Bertrand model demonstrates the
importance of the strategic variable
(price versus output).
48!
Bertrand Model
25. 25!
Price Competition
Criticisms
When firms produce a homogenous good,
it is more natural to compete by setting
quantities rather than prices.
Even if the firms do set prices and choose
the same price, what share of total sales
will go to each one?
• It may not be equally divided.
49!
Bertrand Model
Price Competition
Price Competition with Differentiated
Products
Market shares are now determined not just by
prices, but by differences in the design,
performance, and durability of each firm’s
product.
50!
26. 26!
Nash Equilibrium in Prices
51!
Firm 1’s Reaction Curve
P1
P2
Firm 2’s Reaction Curve
$4
$4
Nash Equilibrium
$6
$6
Collusive Equilibrium
Nash Equilibrium in Prices
Does the Stackelberg model prediction for
first mover hold when price is the variable
instead of quantity?
Hint: Would you want to set price first?
52!
27. 27!
The Kinked Demand Curve
53!
$/Q
Quantity
MR
D
If the producer lowers price the
competitors will follow and the
demand will be inelastic.
If the producer raises price the
competitors will not and the
demand will be elastic.
The Kinked Demand Curve
54!
$/Q
D
P*
Q*
MC
MC’
So long as marginal cost is in the
vertical region of the marginal
revenue curve, price and output
will remain constant.
MR
Quantity
28. 28!
Implications of the Prisoners’
Dilemma for Oligopolistic Pricing
Price Signaling
Implicit collusion in which a firm announces
a price increase in the hope that other firms
will follow suit
55!
Price Signaling & Price Leadership
Implications of the Prisoners’
Dilemma for Oligopolistic Pricing
Price Leadership
Pattern of pricing in which one firm
regularly announces price changes that
other firms then match
56!
Price Signaling & Price Leadership
29. 29!
Implications of the Prisoners’
Dilemma for Oligopolistic Pricing
The Dominant Firm Model
In some oligopolistic markets, one large firm
has a major share of total sales, and a group
of smaller firms supplies the remainder of the
market.
The large firm might then act as the dominant
firm, setting a price that maximized its own
profits.
57!
Price Setting by a Dominant Firm
58!
Price
Quantity
D
DD
QD
P*
At this price, fringe firms
sell QF, so that total
sales are QT.
P1
QF QT
P2
MCD
MRD
SF The dominant firm’s demand
curve is the difference between
market demand (D) and the supply
of the fringe firms (SF).
30. 30!
Cartels
Examples of successful
cartels
• OPEC
• International Bauxite
Association
• Mercurio Europeo
Examples of
unsuccessful cartels
• Copper
• Tin
• Coffee
• Tea
• Cocoa
59!
Characteristics:
1) Explicit agreements to set output and price
2) May not include all firms
3) Most often international
Cartels
Characteristics
4) Conditions for success
• Competitive alternative sufficiently deters cheating
• Potential of monopoly power--inelastic demand
Comparing OPEC to CIPEC
Most cartels involve a portion of the market which
then behaves as the dominant firm
60!
31. 31!
The OPEC Oil Cartel
61!
Price
Quantity
MROPEC
DOPEC
TD SC
MCOPEC
TD is the total world demand
curve for oil, and SC is the
competitive supply. OPEC’s
demand is the difference
between the two.
QOPEC
P*
OPEC’s profits maximizing
quantity is found at the
intersection of its MR and
MC curves. At this quantity
OPEC charges price P*.
Cartels
About OPEC
Very low MC
TD is inelastic
Non-OPEC supply is inelastic
DOPEC is relatively inelastic
62!
32. 32!
The OPEC Oil Cartel
63!
Price
Quantity
MROPEC
DOPEC
TD SC
MCOPEC
QOPEC
P*
The price without the cartel:
• Competitive price (PC) where
DOPEC = MCOPEC
QC QT
Pc
The CIPEC Copper Cartel
64!
Price
Quantity
MRCIPEC
TD
DCIPEC
SC
MCCIPEC
QCIPEC
P*
PC
QC QT
• TD and SC are relatively elastic
• DCIPEC is elastic
• CIPEC has little monopoly power
• P* is closer to PC
33. 33!
Cartels
Observations
To be successful:
• Total demand must not be very price elastic
• Either the cartel must control nearly all of the
world’s supply or the supply of noncartel producers
must not be price elastic
65!