Econ 384 Intermediate Microeconomics II

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Econ 384Intermediate Microeconomics II
Lorne Priemaza, M.A. Lorne.priemaza_at_ualberta.ca
Various material courtesy of Wiley Sons INC.
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Chapter 13

• 13.1 Market Structure
• 13.2 Homogeneous Oligopoly
• 13.3 Dominant Firm Markets
• 13.4 Oligopoly with Horizontally Differentiated
  Products
• 13.5 Monopolistic Competition
• Appendix

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13.1 Market Structure

• Market structure depends upon two spectrums
• Number of firms in market
• 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.
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13.1 Market Structure
Number of Sellers
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13.1 Market Structure

• Perfect Competition
• Many Firms
• Homogeneous Products
• examples Lemonade stands, fries
• B) Monopolistic Competition
• Many Firms
• Differentiated Products
• Examples dry cleaning, socks, burgers

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13.1 Market Structure

• C) Homogeneous Products Oligopoly
• Few Firms
• Homogeneous Products
• Examples Convenience Store, Apples
• D) Differentiated Products Oligopoly
• Few Firms
• Differentiated Products
• Examples Cola, Breakfast Cereals

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13.1 Market Structure

• E) Dominant Firm
• One Large Firm, many small firms
• Homogeneous Products
• Examples Ketchup, MP3 Players
• F) Monopoly
• One Firm
• One Product
• Examples Canadian Uranium, Canadian Health
  Insurance (government monopoly)

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13.1 Measuring Market Structure

• 1) Four-firm Concentration Ratio (4CR)
• -Sum of the top 4 sales revenue (in percentage
  terms) in an industry
• ie1) Internet Shaw (50) and Telus (50)
• 4CR 5050100
• ie2) French Fries New York (10), McDonalds
  (7), Wendys (4), Red Robin (3)
• 4CR 1074324
• Note Values are assumptions

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13.1 Measuring Market Structure

• 2) Herfindahl-Hirschman Index (HHI)
• -?(Market Share)2
• ie1) Monopoly HHI100210,000
• ie2) 100 Identical Firms HHI100(1)2100
• -HHI ranges from 0 (infinite firms) to 10,000
  (one firm)
• Note that the textbook calculations are
  inconsistent for HHI

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13.1 Measuring Market Structure

• -TYPICALLY
• -Industries closer to perfect competition or
  monopolistic competition have low 4CRs and HHIs
• -Oligopolies have intermediate 4CRs and HHIs
• -Industries closer to monopolies and dominant
  firms have high 4CRs and HHIs
• -This is a GENERALIZATION (there are deviations)

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13.1 Measuring Market Structure
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13.2 Homogeneous Oligopoly

• In perfect competition, each firm can ignore all
  other firms.
• Oligopoly markets feature COMPETITIVE
  INDERDEPENDENCE firm As decisions affect the
  profits of other firms.
• ex) if Firm A overproduces, price falls and
  Firm Bs profits decrease
• How does this close interdependence affect firm
  behavior?

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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.

Chapter Thirteen
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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
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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 firms are
QUANTITY TAKERS (v. price takers in Perfect
Competition) Note We will initially assume only
2 firms, a DUOPOLY
Chapter Thirteen
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Residual Demand
Price
Residual Marginal Revenue when q2 10
10 units
Residual Demand when q2 10
MC
Demand
0
Quantity
q1
Best response to q2 10
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Best Response/Reaction Function
Best Response- The point where (residual)
marginal revenue equals marginal cost gives ONE
best response of firm i to its rival's
action. Reaction Function- The graph of all
possible best responses to rival actions
Chapter Thirteen
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Reaction Functions
q2
Reaction Function of Firm 1

q2
Reaction Function of Firm 2
0
q1
q1
Chapter Thirteen
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Cournot Equilibrium
Equilibrium No firm has an incentive to deviate
in equilibrium each firm is maximizing profits
given its rival's output Each Firms output is a
BEST RESPONSE to each other firms output.
Chapter Thirteen
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Cournot Equilibrium Example
P 100 - Q1 - Q2 MC AC 10 What is firm 1's
profit-maximizing output when firm 2 produces
50? Residual demand P (100 - Q1) 50 50
- Q1 TRPQ 50Q1 - Q12 MR50 ?TR/ ?Q1 50 -
2Q1 Since profit is maximized when MRMC, MR50
MC 50 - 2Q1 10 40 2Q 20 Q
Chapter Thirteen
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Cournot Equilibrium Example

• P 100 - Q1 - Q2 MC AC 10
• What is the equation of firm 1's reaction
  function?
• Residual demand P (100 - Q2) - Q1
• TR PQ1 100Q1 - Q2 Q1 - Q12
• MRr ?TR/ ?Q1 100 - Q2 - 2Q1
• MRr MC ? 100 - Q2 - 2Q1 10
• Q1r 45 - Q2/2 firm 1's reaction function
• Similarly, Q2r 45 - Q1/2

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Cournot Equilibrium Example
P 100 - Q1 - Q2 MC AC 10 Q1r 45 - Q2/2
Q2r 45 - Q1/2 Calculate the Cournot
equilibrium. Q1 45 - Q2/2 Q1 45 - (45 -
Q1/2)/2 Q1 30 Q2 30 P 100 - Q1 - Q2 100
- 30 - 30 40 ?1 ?2 TR TC
(P-MC)Q ?1 ?2 (40-10)(30) 900
Chapter Thirteen
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Cournot Solving Steps

• Calculate Residual Demand
• Calculate (residual) MR
• MRMC to find reaction functions
• Use reaction functions to solve for Qs
• Use Qs to solve for P
• -Remember that Q1Q2QM
• Solve for ?
• Summarize

Chapter Thirteen
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How do firms achieve Cournot Equilibria?
q2

1. Each firm can calculate Reaction Functions

2) Firm 2 will never produce over A
3) Knowing this, Firm 1 will never produce under B
4) Knowing this, Firm 2 will never produce over C
5) This reasoning continues until point Z
A

C
Z
q2
Reaction Function of Firm 2
0
q1
q1
B
Chapter Thirteen
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Cournot vs. Monopoly vs. PC

• Since Pcournot gt MC, Cournot prices are higher
  than perfect competition prices
• Cournot firms have market power
• BUT, a Cournot market produces more than a
  Monopoly, and at a lower price.
• Each firms pursuit of individual self-interest
  does not typically maximize the industrys
  profits.
• Each firm wishes the other would decrease
  quantity
• Monopoly profits are possible if firms collude
  (which is illegal)

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PC vs. Cournot vs. Monopoly
Consider the following outcomes using our above
example of P100-Q
The outcome changes greatly with number of firms.
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Cournot Equilibrium, Many Firms
P a-bQ MC c N identical firms Find Cournot
Equilibrium Quantity Residual demand P a-b(Q1
Qother) TR PQ aQ1-bQ12 bQotherQ1 MR
?TR/ ?Q a-2bQ1 bQother Since profit is
maximized when MRMC, MR MC a-2bQ1 bQother
c Q1(a-c)/2b (1/2)Qother
Since Qother (N-1) Q1, Q1(a-c)/2b
(1/2)(N-1)Q1 Since Q1Q
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Cournot Equilibrium, Many Firms
P a-bQ MC c N identical firms Find Cournot
Equilibrium Market Price Since there are N
firms,
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Cournot Solving Steps Multi-Firm

• Calculate Residual Demand
• Calculate (residual) MR
• MRMC to find reaction functions
• New 3b) Remember that Qother (N-1) Q1
• 4) Use reaction functions to solve for Qs
• 5) Use Q to solve for P
• -Remember that ?QiQM
• 6) Solve for ?
• 7) Summarize

Chapter Thirteen
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Outcome comparisons
Given the relationship Pa-bQ and MCc,
Chapter Thirteen
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13.2 Bertrand Oligopoly (Homogeneous Products)

• Cournot Oligopoly Firms compete on QUANTITY
• Bertrand Oligopoly Firms compete on PRICES
• -Goods must be homogeneous/identical
• -A firms residual demand depends on the other
  firms price
• Zero demand at prices higher than the other firm
• Market demand at prices lower than the other firm

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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.
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Residual Demand Curve Price Setting
Price
Market Demand
Firm 1s Residual Demand Curve

P2
Quantity
0
Chapter Thirteen
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13.2 Bertrand Oligopoly (Homogeneous Products)

• Firm A must undercut firm Bs price to sell
  anything
• This will force firm B to undercut Firm A
• ...
• This will continue until neither firm can
  decrease price further, PMC
• The Perfect Competition Result!

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Bertrand Equilibrium Example
P 100 - QT MC AC 10 What is the Bertrand
Equilibrium? P MC10 P 100 QT 10 100
QT 90 QT ?TR-TC ?(P-MC)Q ?(10-10)90 0
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Bertrand vs. Cournot

• Cournot Long-Run Competition (Firms choose
  output capacity)
• Bertrand Short-Run Competition (Firms have
  excess output)
• --------------------------------------------------
  ----------------
• Cournot Firms can quickly adjust their price,
  so price competition is useless
• Bertrand Firms can only slowly adjust price, so
  firms believe a price cut can temporarily
  increase profits

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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 leaders output as
given and maximizes profits accordingly, using
its residual demand. The second firms behavior
can, then, be summarized by a Cournot reaction
function.
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Stackelberg Leader Choice
The Stackelberg leader knows the followers
reaction function, and can use that to choose its
production
P 100 - QL - QF MC AC 10 What is the
equation of the followers reaction
function? Residual demand P (100 - QL) -
QF TR PQF 100QF - QF QL - QF2 MRFr ?TR/
?Q1 100 - QL - 2QF MRFr MC ? 100 - QL - 2QF
10 QFr 45 - QL/2 followers reaction function
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Stackelberg Leader Choice
P 100 - QL - QF MC AC 10 QFr 45 -
QL/2 Calculate the Stackelberg equilibrium. P
100 - QL - QF 100 - QL (45 - QL/2 ) P 55
QL/2 TR PQL 55QL QL2/2 MRL ?TR/ ?QL
55 QL MRL MC ? 55 QL 10 QL 45
Chapter Thirteen
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Stackelberg Leader Choice
P 100 - QL - QF MC AC 10 QFr 45 -
QL/2 QL 45 Continue Calculating the
Stackelberg equilibrium. QFr 45 - QL/2 45 -
45/2 QFr 22.5 P 100 - QL - QF 100 -
45 22.5 32.5 ?L TR TC (P-MC)QL
(32.5-10)45 1,012.5 ?F TR TC (P-MC)QF
(32.5-10)22.5 506.25
Chapter Thirteen
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Stackelberg Leader Choice
With a Stackelberg leader, price is 32.50, with
the leader producing 45 units for a profit of
1,012.50 and the following producing 22.5 units
for a profit of 506.25.

• Notice that
• Price is lower than the Cournot equilibrium
• Leader profits are higher than the cournot
  equilibrium
• Follower profits are lower than the Cournot
  equilibrium
• There is an advantage to moving first

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Stackelberg Solving Steps

• Calculate Leaders Residual Demand
• Calculate Leaders (residual) MR
• Leaders MRMC to find QL
• Use QL to solve for QF
• Use Qs to solve for P
• -Remember that QLQFQM
• Solve for ?s
• Summarize

Chapter Thirteen
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13.3 Dominant Firm Model

• The dominant firm model features
• A single company with an overwhelming market
  share (a dominant firm), D
• many small producers (competitive fringe), each
  of whom has a small market share, F
• The dominant firm faces market demand, and
  residual demand that takes into account the
  competitive fringes supply

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Dominant Firm
The dominant firms residual demand (DR) is
market demand minus competitive fringe supply (in
terms of Q)
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Dominant Firm Example
P 100 - QT SF P 10QF or QF P - 10 MCD
AC 10 What is the equation of the Dominant
Firms Residual Demand? QR QT QF QR 100-P
(P-10) QR 110-2P P 55-QR/2
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Dominant Firm Example
P 100 - QT SF P 10QF or QF P - 10 MCD
AC 10 QR 90-2P (P 55-QR/2) Calculate
Dominant Firm Quantities and Price TRDR PQD
55QD-QD2/2 MRL ?TR/ ?QL 55 QD MRL MC ? 55
QD 10 QD 45 P 55-QR/2 P 55-45/2 32.5
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Dominant Firm Example
P 100 - QT SF P 10QF or QF P - 10 MCD
AC 10 QR 90-2P (P 55-QR/2) Calculate and
check Competitive Fringe Quantities SF P
10QF 32.5 10QF QF 22.5 QT QD QF QT
45 22.5 67.5 P 100 QT 32.5 100 67.5
32.5
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Dominant Firm Example
P 100 - QT SF P 10QF or QF P - 10 MCD
AC 10 QR 90-2P (P 55-QR/2) QF 22.5, QD
45, P32.5 Calculate market share and dominant
firm profit D Market Share QD/ QT
45/67.5100 66.6 F Market Share QD/ QT
22.5/67.5100 33.3 ?D TR TC (P-MC)QD
(32.5-10)45 1,012.5

• At a price of 32.50, the dominant firm produces
  45 units for a profit of 1,012.50, and fringe
  firms produce 22.5 total.

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Dominant Firm Solving Steps

• Calculate Dominant Firms Residual Demand
• Calculate Dominant Firms (residual) MR
• Leaders MRMC to find QD
• Use QD to solve for P
• Use P to solve for QF
• -Remember that QDQFQM
• Solve for ? and Market Share
• Summarize

Chapter Thirteen
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Aside Calculating SF

• Recall
• A competitive firms supply comes from its MC
  curve
• Identical firms supply can be summed (through q)

Fringe Firm MC520q, 40 firms Calculate Fringe
Supply MC520q q(P-5)/20 QF40(P-5)/20 QF2P-10

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Growing Fringe

• As the size of the fringe grows, the price, and
  the production and profits of the dominant firm
  decreases (next slide)
• There is therefore an incentive for the dominant
  firm to practice limit pricing (illegal in
  Canada)
• 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

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