Download OLIGOPOLY-II ea session 14, 2007

OLIGOPOLY-II
Overview
• Comparison of Duopoly with Collusion &
Competition in a reaction curve framework
• Price competition – Bertrand Model
• Competition vs. collusion in a game
theoretic framework
• Kinked demand curve model
• Price signaling & price leadership
• Dominant firm model
• Cartels
Duopoly Example from
Text Revisited
Q1
30
Firm 2’s
Reaction Curve
For the firm, collusion is the best
Outcome, followed by the Cournot
Equilibrium and then the
competitive equilibrium
Competitive Equilibrium (P = MC; Profit = 0)
15
Cournot Equilibrium
Collusive Equilibrium
10
7.5
Firm 1’s
Reaction Curve
Collusion
Curve
7.5 10
15
30
Q2
Price Competition (homogenous
good) – The Bertrand Model
• If two duopolists producing a homogenous good
compete by simultaneously choosing price, the
good being homogenous, consumers will buy from
the lowest price seller
– The lower priced firm will supply the entire market and
the higher priced firm will sell nothing
• Competitive price cutting by the firms will
lead to the perfectly competitive outcome
• If both firms charge the same price, consumers
will be indifferent between firms and each firm
will supply half the market.
Criticism of Bertrand
Model – Homogenous Good
Case
•
When firms produce a homogenous
good, it is more natural to compete by
setting quantities rather than prices
(bringing us back to the Cournot
model)
Price Competition –
Differentiated Products
• Determining Prices and Output
– Firm 1: If P2 is fixed:
Firm 1' s profit maximizing price 
 1 P1  12  4 P1  P2  0
Firm 1' s reaction curve 
P1  3  1 4 P2
Firm 2' s reaction curve 
P2  3  1 4 P1
Bertrand Model –
Heterogeneous Good Case
P1
Firm 2’s Reaction Curve
Collusive Equilibrium
$6
$4
Firm 1’s Reaction Curve
Nash Equilibrium
$4
$6
P2
Competition Versus Collusion:
The Prisoners’ Dilemma
• Assume:
FC  $20 and VC  $0
Firm 1' s demand : Q  12  2 P1  P2
Firm 2' s demand : Q  12  2 P2  P1
Nash Equilibriu m : P  $4
Collusion :
P  $6
  $12
  $16
Competition Versus Collusion:
The Prisoners’ Dilemma
• Possible Pricing Outcomes:
–
If both charge $6,   $16
–
If P1  $6 and P2  $4
then  2  P2Q2  20
 (4)12  (2)( 4)  6  20  $20
 1  P1Q1  20
 (6)12  (2)(6)  4  20  $4
Payoff Matrix for Pricing
Game
Firm 2
Charge $4
Charge $4
Charge $6
$12, $12
$20, $4
$4, $20
$16, $16
Firm 1
Charge $6
Competition Versus Collusion:
The Prisoners’ Dilemma
• These two firms are playing a noncooperative game.
– Each firm independently does the best it
can taking its competitor into account.
• An example in game theory, called the
Prisoners’ Dilemma, illustrates the
problem oligopolistic firms face.
The Prisoners’ Dilemma
• Scenario
– Two prisoners have been accused
of collaborating in a crime.
– They are in separate jail cells and
cannot communicate.
– Each has been asked to confess to
the crime.
Payoff Matrix for
Prisoners’ Dilemma
Prisoner B
Confess
Confess
Don’t confess
-5, -5
-1, -10
-10, -1
-2, -2
Prisoner A
Don’t
confess
Implications of the Prisoners’
Dilemma for Oligipolistic Pricing
• In some oligopoly markets, pricing behavior
in time can create a predictable pricing
environment and implied collusion may
occur.
• In other oligopoly markets, the firms are
very aggressive and collusion is not
possible.
• Firms are reluctant to change price because of the
likely response of their competitors.
• In this case prices tend to be relatively rigid, leading
to a kinked-demand curve model
The Kinked Demand Curve
Model
$/Q
So long as marginal cost is in the
vertical region of the marginal
revenue curve, price and output
will remain constant.
Price rise
matched
Price rise
unmatched
MC’
P*
MC
Price cut
unmatched
Price cut
matched
D
Quantity
Q*
MR
Price Signaling and Price
Leadership
• Price Signaling
– Implicit collusion in which a firm
announces a price increase in the hope
that other firms will follow suit
• Price Leadership
– Pattern of pricing in which one firm
regularly announces price changes that
other firms then match
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.
Price Setting by a Dominant
Firm
Price
SF
D
The dominant firm’s demand
curve is the difference between
market demand (D) and the supply
of the fringe firms (SF).
P1
MCD
P*
DD
P2
QF QD
QT
MRD
At this price, fringe firms
sell QF, so that total
sales are QT.
Quantity
Cartels
• Characteristics
– Explicit agreements to set output and price
– May not include all firms
– Most often international
– Conditions for success
• Competitive alternative sufficiently deters
cheating
• Potential of monopoly power--inelastic demand
• Either the cartel must control nearly all of the
world’s supply or the supply of non-cartel
producers must not be price elastic
The OPEC Oil Cartel
Price
TD
SC
TD is the total world demand
curve for oil, and SC is the
competitive supply. OPEC’s
demand is the difference
between the two.
OPEC’s profits maximizing
quantity is found at the
intersection of its MR and
MC curves. At this quantity
OPEC charges price P*.
P*
DOPEC
MCOPEC
MROPEC
QOPEC
Quantity
Cartels
• About OPEC
–
–
–
–
Very low MC
TD is inelastic
Non-OPEC supply is inelastic
DOPEC is relatively inelastic
The CIPEC Copper Cartel
Price
•TD and SC are relatively elastic
•DCIPEC is elastic
•CIPEC has little monopoly power
•P* is closer to PC
TD
SC
MCCIPEC
DCIPEC
P*
PC
MRCIPEC
QCIPEC
QC
QT
Quantity