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Chapter 13
Market
Structure
And
Competition
1
Chapter Thirteen Overview
1. Introduction: Cola Wars
2. A Taxonomy of Market Structures
3. Monopolistic Competition
4. Oligopoly – Interdependence of Strategic Decisions
•
Bertrand with Homogeneous and Differentiated Products
5. The Effect of a Change in the Strategic Variable
•
•
•
•
Theory vs. Observation
Cournot Equilibrium (homogeneous)
Comparison to Bertrand, Monopoly
Reconciling Bertrand, and Cournot
6. The Effect of a Change in Timing: Stackelberg Equilibrium
Chapter Thirteen
2
Market Structures
• The number of sellers
• The number of buyers
• Entry conditions
• The degree of product differentiation
Chapter Thirteen
3
Product Differentiation
Definition:
Product
Differentiation
between two or more products exists
when the products possess attributes
that, in the minds of consumers, set the
products apart from one another and
make them less than perfect substitutes.
Examples: Pepsi is sweeter than Coke,
Brand Name batteries last longer than
"generic" batteries.
Chapter Thirteen
4
Product Differentiation
• "Superiority" (Vertical Product Differentiation)
i.e. one product is viewed as unambiguously
better than another so that, at the same price, all
consumers would buy the better product
• "Substitutability" (Horizontal Product
Differentiation) i.e. at the same price, some
consumers would prefer the characteristics of
product A while other consumers would prefer
the characteristics of product B.
Chapter Thirteen
5
Types of Market Structures
Degree of
Product
Differentiation
Firms produce
identical
products
Firms produce
differentiated
products
Number of Firms
Many
Few
One
Dominant
One
Perfect
Oligopoly with Dominant Monopoly
Competition homogeneous firm
products
Monopolistic Oligopoly with
Competition differentiated
------------ -----------products
Chapter Thirteen
6
Oligopoly
Assumptions:
• Many Buyers and Few Sellers
• Each firm faces downward-sloping
demand because each is a large producer
compared to the total market size
• There is no one dominant model of
oligopoly. We will review several.
Chapter Thirteen
7
Cournot Oligopoly
Assumptions
• Firms set outputs (quantities)*
• Homogeneous Products
• Simultaneous
• Non-cooperative
*Definition: In a Cournot game, each firm sets its output
(quantity) taking as given the output level of its competitor(s),
so as to maximize profits.
Price adjusts according to demand.
Residual Demand: Firm i's guess about its rival's output
determines its residual demand.
Chapter Thirteen
8
Simultaneously vs. Non-cooperatively
Definition: Firms act simultaneously if
each firm makes its strategic decision at the
same time, without prior observation of the
other firm's decision.
Definition: Firms act non-cooperatively if
they set strategy independently, without
colluding with the other firm in any way
Chapter Thirteen
9
Residual Demand
Definition: The relationship between the
price charged by firm i and the demand
firm i faces is firm is residual demand
In other words, the residual demand of
firm i is the market demand minus the
amount of demand fulfilled by other
firms in the market: Q1 = Q - Q2
Chapter Thirteen
10
Residual Demand
Price
10 units
Residual Marginal Revenue when q2 = 10
Residual Demand when q2 = 10
MC
Demand
0
Quantity
q1*
Chapter Thirteen
11
Profit Maximization
Profit Maximization: Each firm acts as a
monopolist on its residual demand curve,
equating MRr to MC.
MRr = p + q1(p/q) = MC
Best Response Function:
The point where (residual) marginal revenue equals marginal cost
gives the best response of firm i to its rival's (rivals') actions.
For every possible output of the rival(s), we can determine firm i's
best response. The sum of all these points makes up the best
response (reaction) function of firm i.
Chapter Thirteen
12
Profit Maximization
q2
Example: Reaction Functions, Quantity Setting
Reaction Function of Firm 1
q2*
0
•
q1*
Reaction Function of Firm 2
q1
Chapter Thirteen
13
Equilibrium
Equilibrium: No firm has an incentive to deviate in equilibrium in the sense
that each firm is maximizing profits given its rival's output
What is the equation of firm 1's
reaction function?
P = 100 - Q1 - Q2
MC = AC = 10
What is firm 1's profit-maximizing
output when firm 2 produces 50?
Firm 1's residual demand:
• P = (100 - 50) - Q1
• MR50 = 50 - 2Q1
• MR50 = MC  50 - 2Q1 = 10
Firm 1's residual demand:
• P = (100 - Q2) - Q1
• MRr = 100 - Q2 - 2Q1
• MRr = MC  100 - Q2 - 2Q1 = 10
• Q1r = 45 - Q2/2 firm 1's reaction
function
•Similarly, one can compute that
Q2r = 45 - Q1/2
Chapter Thirteen
14
Profit Maximization
Now, calculate the Cournot equilibrium.
• Q1 = 45 - (45 - Q1/2)/2
• Q1* = 30
• Q2* = 30
• P* = 40
• 1* = 2* = 30(30) = 900
Chapter Thirteen
15
Bertrand Oligopoly (homogeneous)
Assumptions:
• Firms set price*
• Homogeneous product
• Simultaneous
• Non-cooperative
*Definition: In a Bertrand
oligopoly, each firm sets its
price, taking as given the
price(s) set by other firm(s),
so as to maximize profits.
Chapter Thirteen
16
Setting Price
• Homogeneity implies that consumers will
buy from the low-price seller.
• Further, each firm realizes that the demand
that it faces depends both on its own price
and on the price set by other firms
• Specifically, any firm charging a higher
price than its rivals will sell no output.
• Any firm charging a lower price than its
rivals will obtain the entire market demand.
Chapter Thirteen
17
Residual Demand Curve – Price Setting
Price
Market Demand
Residual Demand Curve
•
(thickened line segments)
Quantity
0
Chapter Thirteen
18
Residual Demand Curve – Price Setting
• Assume firm always meets its residual demand
(no capacity constraints)
• Assume that marginal cost is constant at c per
unit.
• Hence, any price at least equal to c ensures nonnegative profits.
Chapter Thirteen
19
Best Response Function
Each firm's profit maximizing response to the other
firm's price is to undercut (as long as P > MC)
Definition: The firm's profit maximizing action as a
function of the action by the rival firm is the firm's
best response (or reaction) function
Example:
2 firms
Bertrand competitors
Firm 1's best response function is P1=P2- e
Firm 2's best response function is P2=P1- e
Chapter Thirteen
20
Equilibrium
If we assume no capacity constraints and
that all firms have the same constant
average and marginal cost of c then:
For each firm's response to be a best
response to the other's each firm must
undercut the other as long as P> MC
Where does this stop? P = MC (!)
Chapter Thirteen
21
Equilibrium
1. Firms price at marginal cost
2. Firms make zero profits
3. The number of firms is irrelevant to the price
level as long as more than one firm is present:
two firms is enough to replicate the perfectly
competitive outcome.
Essentially, the assumption of no capacity
constraints combined with a constant average and
marginal cost takes the place of free entry.
Chapter Thirteen
22
Stackelberg Oligopoly
Stackelberg model of oligopoly is a situation in which one firm acts as a
quantity leader, choosing its quantity first, with all other firms acting as
followers.
Call the first mover the “leader” and the second mover the “follower”.
The second firm is in the same situation as a Cournot firm: it takes the
leader’s output as given and maximizes profits accordingly, using its
residual demand.
The second firm’s behavior can, then, be summarized by a Cournot
reaction function.
Chapter Thirteen
23
Stackelberg Equilibrium vs. Cournot
q2
A
Profit for firm 1 at A…0
at B…0
at C…1012.5
at Cournot Eq…900
•
Former Cournot Equilibrium
•
•
C
B
(q1= 90)
Chapter Thirteen
•
Follower’s Cournot
Reaction Function
q1
24
Dominant Firm Markets
A single company with an
overwhelming market share (a
dominant firm) competes against
many
small
producers
(competitive fringe), each of
whom has a small market share.
Limit Pricing – a strategy
whereby the dominant firm
keeps its price below the level
that maximizes its current profit
in order to reduce the rate of
expansion by the fringe.
Chapter Thirteen
25
Bertrand Competition – Differentiated
Assumptions:
Firms set price*
Differentiated product
Simultaneous
Non-cooperative
*Differentiation means that lowering price
below your rivals' will not result in capturing
the entire market, nor will raising price mean
losing the entire market so that residual
demand decreases smoothly
Chapter Thirteen
26
Bertrand Competition – Differentiated
Q1 = 100 - 2P1 + P2 "Coke's demand"
Q2 = 100 - 2P2 + P1 "Pepsi's demand"
MC1 = MC2 = 5
What is firm 1's residual demand when
Firm 2's price is $10? $0?
Q1(10) = 100 - 2P1 + 10 = 110 - 2P1
Q1(0) = 100 - 2P1 + 0 = 100 - 2P1
Chapter Thirteen
27
Key Concepts
Residual Demand, Price Setting, Differentiated Products
Coke’s
Price
100
Each firm maximizes profits based on its residual demand by
setting MR (based on residual demand) = MC
Pepsi’s price = $0 for D0 and $10 for D10
MR0
0
Coke’s Quantity
Chapter Thirteen
28
Key Concepts
Residual Demand, Price Setting, Differentiated Products
Coke’s
Price
110
100
Each firm maximizes profits based on its residual demand by
setting MR (based on residual demand) = MC
Pepsi’s price = $0 for D0 and $10 for D10
D10
D0
0
Coke’s Quantity
Chapter Thirteen
29
Key Concepts
Residual Demand, Price Setting, Differentiated Products
Coke’s
Price
110
100
Each firm maximizes profits based on its residual demand by
setting MR (based on residual demand) = MC
Pepsi’s price = $0 for D0 and $10 for D10
MR10
0
MR0
D10
D0
Coke’s Quantity
Chapter Thirteen
30
Key Concepts
Residual Demand, Price Setting, Differentiated Products
Coke’s
Price
110
100
Each firm maximizes profits based on its residual demand by
setting MR (based on residual demand) = MC
Pepsi’s price = $0 for D0 and $10 for D10
D10
5
0
MR10
MR0
D0
Coke’s Quantity
Chapter Thirteen
31
Key Concepts
Residual Demand, Price Setting, Differentiated Products
Coke’s
Price
110
100
Each firm maximizes profits based on its residual demand by
setting MR (based on residual demand) = MC
Pepsi’s price = $0 for D0 and $10 for D10
30
27.5
D10
MR10
5
0
45
50 MR0
D0
Coke’s Quantity
Chapter Thirteen
32
Key Concepts
Residual Demand, Price Setting, Differentiated Products
Each firm maximizes profits based on its residual demand by
setting MR (based on residual demand) = MC
Example:
MR1(10) = 55 - Q1(10) = 5
Q1(10) = 50
P1(10) = 30
Therefore, firm 1's best response to a price of
$10 by firm 2 is a price of $30
Chapter Thirteen
33
Key Concepts
Residual Demand, Price Setting, Differentiated Products
Each firm maximizes profits based on its residual demand by
setting MR (based on residual demand) = MC
Example:
• Solving for firm 1's reaction function for
any arbitrary price by firm 2
P1 = 50 - Q1/2 + P2/2
MR = 50 - Q1 + P2/2
MR = MC => Q1 = 45 + P2/2
Chapter Thirteen
34
Key Concepts
Residual Demand, Price Setting, Differentiated Products
Each firm maximizes profits based on its residual demand by
setting MR (based on residual demand) = MC
And, using the demand curve, we have:
• P1 = 50 + P2/2 - 45/2 - P2/4 or
• P1 = 27.5 + P2/4 the reaction function
Chapter Thirteen
35
Equilibrium and Reaction Functions
Pepsi’s
Price (P2)
Price Setting and Differentiated Products
P2 = 27.5 + P1/4
(Pepsi’s R.F.)
27.5
Coke’s
Price (P1)
Chapter Thirteen
36
Equilibrium and Reaction Functions
Pepsi’s
Price (P2)
Price Setting and Differentiated Products
P1 = 27.5 + P2/4
(Coke’s R.F.)
P2 = 27.5 + P1/4
(Pepsi’s R.F.)
•
27.5
27.5
P1 = 110/3
Chapter Thirteen
Coke’s
Price (P1)
37
Equilibrium and Reaction Functions
Pepsi’s
Price (P2)
P2 =
110/3
Price Setting and Differentiated Products
P1 = 27.5 + P2/4
(Coke’s R.F.)
Bertrand
Equilibrium
P2 = 27.5 + P1/4
(Pepsi’s R.F.)
•
27.5
27.5
P1 = 110/3
Chapter Thirteen
Coke’s
Price (P1)
38
Equilibrium
Equilibrium occurs when all
firms simultaneously choose
their best response to each
others' actions.
Graphically, this amounts to
the point where the best
response functions cross.
Chapter Thirteen
39
Equilibrium
Example: Firm 1 and Firm 2, continued
• P1 = 27.5 + P2/4
• P2 = 27.5 + P1/4
Solving these two equations in two
unknowns.
• P1* = P2* = 110/3
Plugging these prices into demand, we have:
• Q1* = Q2* = 190/3
• 1* = 2* = 2005.55
•  = 4011.10
Chapter Thirteen
40
Equilibrium
Profits are positive in equilibrium since
both prices are above marginal cost!
Even if we have no capacity constraints,
and constant marginal cost, a firm cannot
capture all demand by cutting price.
This blunts price-cutting incentives and
means that the firms' own behavior does
not mimic free entry
Chapter Thirteen
41
Equilibrium
Only if I were to let the number of firms
approach infinity would price approach
marginal cost.
Prices need not be equal in equilibrium if
firms not identical (e.g. Marginal costs
differ implies that prices differ)
The reaction functions slope upward:
"aggression => aggression"
Chapter Thirteen
42
Cournot, Bertrand, and Monopoly Equilibriums
P > MC for Cournot competitors, but P < PM:
If the firms were to act as a monopolist (perfectly
collude), they would set market MR equal to MC:
• P = 100 - Q
• MC = AC = 10
• MR = MC => 100 - 2Q = 10 => QM = 45
• PM = 55
• M= 45(45) = 2025
• c = 1800
Chapter Thirteen
43
Cournot, Bertrand, and Monopoly Equilibriums
A perfectly collusive industry takes into account that an increase in
output by one firm depresses the profits of the other firm(s) in the
industry. A Cournot competitor takes into account the effect of the
increase in output on its own profits only.
Therefore, Cournot competitors "overproduce" relative to the collusive
(monopoly) point. Further, this problem gets "worse" as the number of
competitors grows because the market share of each individual firm
falls, increasing the difference between the private gain from increasing
production and the profit destruction effect on rivals.
Therefore, the more concentrated the industry in the Cournot case, the
higher the price-cost margin.
Chapter Thirteen
44
Cournot, Bertrand, and Monopoly Equilibriums
Homogeneous product Bertrand resulted in
zero profits, whereas the Cournot case resulted
in positive profits. Why?
The best response functions in the Cournot
model slope downward. In other words, the
more aggressive a rival (in terms of output),
the more passive the Cournot firm's response.
The best response functions in the Bertrand
model slope upward. In other words, the
more aggressive a rival (in terms of price) the
more aggressive the Bertrand firm's response.
Chapter Thirteen
45
Cournot, Bertrand, and Monopoly Equilibriums
Cournot: Suppose firm j raises its
output…the price at which firm i can sell
output falls. This means that the incentive
to increase output falls as the output of
the competitor rises.
Bertrand: Suppose firm j raises price the
price at which firm i can sell output rises.
As long as firm's price is less than firm's,
the incentive to increase price will depend
on the (market) marginal revenue.
Chapter Thirteen
46
Chamberlinian Monopolistic Competition
Market Structure
• Many Buyers
• Many Sellers
• Free entry and Exit
• (Horizontal) Product Differentiation
When firms have horizontally differentiated
products, they each face downward-sloping
demand for their product because a small
change in price will not cause ALL buyers to
switch to another firm's product.
Chapter Thirteen
47
Monopolistic Competition – Short Run
1. Each firm is small each takes the observed "market
price" as given in its production decisions.
2. Since market price may not stay given, the firm's
perceived demand may differ from its actual demand.
3.If all firms' prices fall the same amount, no
customers switch supplier but the total market
consumption grows.
4. If only one firm's price falls, it steals customers
from other firms as well as increases total market
consumption
Chapter Thirteen
48
Perceived vs. Actual Demand
Price
d (PA=20)
Quantity
Chapter Thirteen
49
Perceived vs. Actual Demand
Price
Demand assuming no price
matching
d (PA=50)
d (PA=20)
Quantity
Chapter Thirteen
50
Perceived vs. Actual Demand
Price
Demand (assuming price matching by all firms)
50
•
Demand assuming no price
matching
d (PA=50)
d (PA=20)
Quantity
Chapter Thirteen
51
Market Equilibrium
The market is in equilibrium if:
• Each firm maximizes profit taking
the average market price as given
• Each firm can sell the quantity it
desires at the actual average market
price that prevails
Chapter Thirteen
52
Short Run Chamberlinian Equilibrium
Price
d(PA=43)
Quantity
Chapter Thirteen
53
Short Run Chamberlinian Equilibrium
Price
Demand assuming no price
matching
d (PA=50)
d(PA=43)
Quantity
Chapter Thirteen
54
Short Run Chamberlinian Equilibrium
Price
Demand (assuming price matching by all firms P=PA)
•
•
Demand assuming no price
matching
d (PA=50)
d(PA=43)
Quantity
Chapter Thirteen
55
Short Run Chamberlinian Equilibrium
Price
Demand (assuming price matching by all firms P=PA)
50
43
•
•
15
Demand assuming no price
matching
mc
57
MR43
Chapter Thirteen
d (PA=50)
d(PA=43)
Quantity
56
Short Run Monopolistically Competitive Equilibrium
Computing Short Run
Monopolistically Competitive Equilibrium
• MC = $15
• N = 100
• Q = 100 - 2P + PA
• Where: PA is the average market
price N is the number of firms
Chapter Thirteen
57
Short Run Monopolistically Competitive Equilibrium
A. What is the equation of d40? What is the equation of D?
• d40: Qd = 100 - 2P + 40 = 140 - 2P
• D: Note that P = PA so that
• QD = 100 - P
B. Show that d40 and D intersect at P = 40
• P = 40 => Qd = 140 - 80 = 60
QD = 100 - 40 = 60
C. For any given average price, PA, find a typical firm's profit
maximizing quantity
Chapter Thirteen
58
Inverse Perceived Demand
P = 50 - (1/2)Q + (1/2)PA
MR = 50 - Q + (1/2)PA
MR = MC => 50 - Q + (1/2)PA = 15
Qe = 35 + (1/2)PA
Pe = 50 - (1/2)Qe + (1/2)PA
Pe = 32.5 + (1/4)PA
Chapter Thirteen
59
Short Run Monopolistically Competitive Equilibrium
D. What is the short run equilibrium
price in this industry?
In equilibrium, Qe = QD at PA so that
100 - PA = 35 + (1/2)PA
PA = 43.33
Qe = 56.66
QD = 56.66
Chapter Thirteen
60
Monopolistic Competition in the Long Run
At the short run equilibrium P > AC so that
each firm may make positive profit.
Entry shifts d and D left until average
industry price equals average cost.
This is long run equilibrium is represented
graphically by:
MR = MC for each firm
D = d at the average market price
d and AC are tangent at average market
price
Chapter Thirteen
61
Long Run Chamberlinian Equilibrium
Price
Residual Demand shifts
in as entry occurs
P*
Marginal Cost
P**
Average Cost
q**
q*
MR
Chapter Thirteen
Quantity
62
Summary
1. Market structures are characterized by the number
of buyers, the number of sellers, the degree of product
differentiation and the entry conditions.
2. Product differentiation alone or a small number of
competitors alone is not enough to destroy the long run
zero profit result of perfect competition. This was
illustrated with the Chamberlinian and Bertrand models.
3. Chamberlinian) monopolistic competition assumes
that there are many buyers, many sellers, differentiated
products and free entry in the long run.
Chapter Thirteen
63
Summary
4. Chamberlinian sellers face downward-sloping demand but are
price takers (i.e. they do not perceive that their change in price will
affect the average price level). Profits may be positive in the short
run but free entry drives profits to zero in the long run.
5. Bertrand and Cournot competition assume that there are many
buyers, few sellers, and homogeneous or differentiated products.
Firms compete in price in Bertrand oligopoly and in quantity in
Cournot oligopoly.
6. Bertrand and Cournot competitors take into account their
strategic interdependence by means of constructing a best response
schedule: each firm maximizes profits given the rival's strategy.
Chapter Thirteen
64
Summary
7. Equilibrium in such a setting requires that all firms be on
their best response functions.
8.
If the products are homogeneous, the Bertrand
equilibrium results in zero profits. By changing the strategic
variable from price to quantity, we obtain much higher prices
(and profits). Further, the results are sensitive to the
assumption of simultaneous moves.
9. This result can be traced to the slope of the reaction
functions: upwards in the case of Bertrand and downwards in
the case of Cournot. These slopes imply that "aggressivity"
results in a "passive" response in the Cournot case and an
"aggressive" response in the Bertrand case.
Chapter Thirteen
65