Outline

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Outline
1. Introduction Cola Wars
2. A Taxonomy of Market Structures
3. Monopolistic Competition Product
Differentiation with Many Buyers and Sellers

• 4. Oligopoly Interdependence of strategic
  Decisions
• Bertrand with Homogeneous Products
• Bertrand with Differentiated Products

• 5. The effect of a change in strategic
• variable
• Theory vs. Observation
• Cournot Equilibrium (Homogeneous)
• Comparison to Bertrand, Monopoly
• Reconciling Bertrand and Cournot

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A Taxonomy of Market Structures
Market structures differ on three important
dimensions 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.
The number of sellers The number of buyers
Entry conditions The degree of product
differentiation
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• Two types of 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.

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• (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.

Example Restaurants, Local markets for doctors
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• Monopolistic Competition in the Short Run
  (fixed number of firms)
• 1. Each firm is small gt 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

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Price
Example Perceived Demand and Actual Demand
d (PA20)
Quantity
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Price
Example Perceived Demand and Actual Demand
Demand assuming no price matching
d (PA50)
d (PA20)
Quantity
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Price
Example Perceived Demand and Actual Demand
Demand (assuming price matching by all firms)

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Demand assuming no price matching
d (PA50)
d (PA20)
Quantity
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• 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

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Example Short Run Chamberlinian Equilibrium
Price
d(PA43)
Quantity
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Example Short Run Chamberlinian Equilibrium
Price


Demand assuming no price matching
d (PA50)
d(PA43)
Quantity
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MR43
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Example Short Run Chamberlinian Equilibrium
Price
Demand (assuming price matching by all firms PPA)


Demand assuming no price matching
d (PA50)
d(PA43)
Quantity
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Example Short Run Chamberlinian Equilibrium
Price
Demand (assuming price matching by all firms PPA)

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Demand assuming no price matching
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d (PA50)
15
mc
d(PA43)
Quantity
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MR43
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Example Computing A 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
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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 gt Qd 140 - 80 60 QD
100 - 40 60 c. For any given average price,
PA, find a typical firm's profit maximizing
quantity
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• Inverse (perceived) demand
• P 50 - (1/2)Q (1/2)PA
• MR 50 - Q (1/2)PA
• MR MC gt 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

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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
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• Monopolistic Competition in the Long Run
• At the short run equilibrium P gt 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

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Price
Example Long Run Chamberlinian Equilibrium
Residual Demand shifts in as entry occurs
P
P
Average Cost
Quantity
q
q
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Price
Example Long Run Chamberlinian Equilibrium
P
Marginal Cost
P
Average Cost
Quantity
q
q
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Price
Example Long Run Chamberlinian Equilibrium
Residual Demand shifts in as entry occurs
P
Marginal Cost
P
Average Cost
Quantity
q
q
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Oligopoly

• Assume Many Buyers
• 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.

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1. Bertrand Oligopoly (Homogeneous)
Assume Firms set price
Homogeneous product Simultaneous
Noncooperative
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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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
noncooperatively if they set strategy
independently, without colluding with the other
firm in any way
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• How will each firm set 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.

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Definition The relationship between the price
charged by firm i and the demand firm i faces is
firm i's 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
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Price
Example Residual Demand Curve, Price Setting
Market Demand
Residual Demand Curve (thickened line segments)

Quantity
0
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• 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
  non-negative profits.

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Price charged by firm 2
Reaction function of firm 1
Reaction function of firm 2
Example Reaction Functions, Price Setting and
Homogeneous Products
p2
Price charged by firm 1
0
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Price charged by firm 2
45 line
Reaction function of firm 1
Reaction function of firm 2
Example Reaction Functions, Price Setting and
Homogeneous Products

p2
Price charged by firm 1
p1
0
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Price charged by firm 2
45 line
Reaction function of firm 1
Reaction function of firm 2
Example Reaction Functions, Price Setting and
Homogeneous Products

p2
Price charged by firm 1
p1
0
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Thus, each firm's profit maximizing response to
the other firm's price is to undercut (as long as
P gt 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
P1P2- e Firm 2's best response function is
P2P1- e
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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 Pgt
MC Where does this stop? P MC (!)
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So 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
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2. Bertrand Competition (Differentiated)
Assume Firms set price
Differentiated product Simultaneous
Noncooperative As before,
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
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Example 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? Q110 100 - 2P1 10
110 - 2P1 Q10 100 - 2P1 0 100 - 2P1
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Example Residual Demand, Price Setting,
Differentiated Products Each firm maximizes
profits based on its residual demand by setting
MR (based on residual demand) MC
Pepsis price 0 for D0 and 10 for D10
Cokes price
100
MR0
0
Cokes quantity
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Example Residual Demand, Price Setting,
Differentiated Products Each firm maximizes
profits based on its residual demand by setting
MR (based on residual demand) MC
Pepsis price 0 for D0 and 10 for D10
Cokes price
110
100
MR0
0
Cokes quantity
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Example Residual Demand, Price Setting,
Differentiated Products Each firm maximizes
profits based on its residual demand by setting
MR (based on residual demand) MC
Pepsis price 0 for D0 and 10 for D10
Cokes price
110
100
D0
MR10
MR0
0
Cokes quantity
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Example Residual Demand, Price Setting,
Differentiated Products Each firm maximizes
profits based on its residual demand by setting
MR (based on residual demand) MC
Pepsis price 0 for D0 and 10 for D10
Cokes price
110
100
30
27.5
D10
D0
MR10
5
MR0
0
Cokes quantity
45 50
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Example Residual Demand, Price Setting,
Differentiated Products Each firm maximizes
profits based on its residual demand by setting
MR (based on residual demand) MC
Pepsis price 0 for D0 and 10 for D10
Cokes price
110
100
30
27.5
D10
D0
MR10
5
MR0
0
Cokes quantity
45 50
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• Example
• MRc10 55 - Q110 5
• Qc10 50
• Pc10 30
• Therefore, firm 1's best response to a
• price of 10 by firm 2 is a price of 30

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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 gt Q1
45 P2/2
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And, using the demand curve, we have P1 50
P2/2 - 45/2 - P2/4 or P1 27.5 P2/4reaction
function
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Pepsis price (P2)
P2 27.5 P1/4 (Pepsis R.F.)
Example Equilibrium and Reaction Functions,
Price Setting and Differentiated Products
27.5
Cokes price (P1)
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P1 27.5 P2/4 (Cokes R.F.)
Pepsis price (P2)
P2 27.5 P1/4 (Pepsis R.F.)

Example Equilibrium and Reaction Functions,
Price Setting and Differentiated Products
27.5
Cokes price (P1)
27.5
P1 110/3
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P1 27.5 P2/4 (Cokes R.F.)
Pepsis price (P2)
P2 27.5 P1/4 (Pepsis R.F.)
Bertrand Equilibrium
P2 110/3

Example Equilibrium and Reaction Functions,
Price Setting and Differentiated Products
27.5
Cokes price (P1)
27.5
P1 110/3
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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...
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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
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• Notice that
• 1. 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

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• Only if I were to let the number of firms
  approach infinity would price approach marginal
  cost.
• 2. Prices need not be equal in equilibrium if
  firms not identical (e.g. Marginal costs differ
  implies that prices differ)
• 3. The reaction functions slope upward
  "aggression gt aggression"

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Theory vs. Observation
US Manufacturing Industries CR8
Average Profit Rate gt70
12.1 lt70
6.9
Source Bain, Joe S., "Relation of Profit Rate
to Industry Concentration American
Manufacturing, 1936-1940," Quarterly Journal of
Economics, v. 65 (August 1951), pp. 293-324 and
Barriers to New Competition (Cambridge Harvard
University Press, 1956).
Example Prices Rise With Industry Concentration
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Cournot Oligopoly
Assume Firms set outputs (quantities)
Homogeneous Products
Simultaneous Noncooperative Definit
ion 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. Recall our reasoning from the Bertrand
case Residual Demand Firm i's guess about its
rival's output determines its residual demand.
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Example Residual Demand
Price
Residual Marginal Revenue when q2 10
10 units
Residual Demand when q2 10
MC
Demand
Quantity
0
q1
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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.

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q2
Example Reaction Functions, Quantity Setting
Reaction function of firm 1
0
q1
q1
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q2
Example Reaction Functions, Quantity Setting
Reaction function of firm 1

q2
Reaction function of firm 2
0
q1
q1
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Equilibrium No firm has an incentive to deviate
in equilibrium in the sense that each firm is
maximizing profits given its rival's
output. Example 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 Q150
20
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b. What is the equation of firm 1's reaction
function? 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
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c. Similarly, one can compute that Q2r 45 -
Q1/2. Now, calculate the Cournot
equilibrium. Q1 45 - (45 - Q1/2)/2 Q1
30 Q2 30 P 40 ?1 ?2 30(30) 900
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Comparison of Cournot, Bertrand and Monopoly
Equilibria
a. P gt MC for Cournot competitors, but P lt
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 gt 100 - 2Q 10 gt QM 45
PM 55
?M 45(45) 2025
?c 1800
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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.
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2. 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.
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Cournot Suppose firm j raises its outputthe
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
pricethe price at which firm i can sell output
rises. As long as firm i's price is less than
firm j's, the incentive to increase price will
depend on the (market) marginal revenue.
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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.
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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.
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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). 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.