Download Econ 384 Chapter13b

13.4 Product Differentiation
When firms produce similar but differentiated
products, they can be differentiated in two ways:
Vertical Differentiation – consumers consider
one product vastly superior to another
ex) Processed Cheddar and Blue Cheese
ex) Flip Phone and Smart Phone
Horizontal Differentiation – consumers consider
one product a POOR substitute for the other,
and may pay more for the “better” product
ex) Swiss Cheese and Cheddar Cheese
ex) Iphone and Samsung Galaxy
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13.4 Product Differentiation
Horizontal Differentiation ≈ Brand Loyalty
Firms spend money on advertising and “exclusive
deals” to maintain horizontal differentiation
A product with WEAK horizontal differentiation
will be MORE sensitive to its own and rivals’ price
changes.
(Small price change =>Large demand change)
A product with STRONG horizontal differentiation
will be LESS sensitive to its own and rivals’ price
changes.
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(Small price change =>Small demand change)
13.4 Product Differentiation
Shift in demand is due to a change in rivals’ price.
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Bertrand Competition –
Horizontally Differentiated Products
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
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Bertrand Competition – Differentiated
Q1 = 100 - 2P1 + P2 "Coke's demand"
Q2 = 100 - 2P2 + P1 "Pepsi's demand"
MC1 = MC2 = 5
What is Coke’s residual demand when
Pepsi’s price is $10? $0?
Q1(10) = 100 - 2P1 + 10 = 110 - 2P1
Q1(0) = 100 - 2P1 + 0 = 100 - 2P1
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Chapter Thirteen
Residual Demand
Coke’s
Price
110
100
Pepsi’s price = $0 for D0 and $10 for D10
D10
D0
0
Coke’s Quantity
Chapter Thirteen
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Marginal Revenue (from Residual Demand)
Coke’s
Price
110
100
5
0
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
MR0
D10
D0
Coke’s Quantity
Chapter Thirteen
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Optimal Price and Quantity
Coke’s
Price
When MC=MR, we calculate price and
quantity
Example:
MR=MC
110
100
MRR(10) = 55 - Q1(10) = 5
30
27.5
D10
MR10
5
0
Q1(10) = 50
P1(10) = 30
MR0
45
50
D0
Therefore, firm 1's best
response to a price of $10
by firm 2 is a price of $30
Coke’s Quantity
Chapter Thirteen
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Reaction Functions
Q1 = 100 - 2P1 + P2 "Coke's demand"
Q2 = 100 - 2P2 + P1 "Pepsi's demand"
MC1 = MC2 = 5
Solve 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 => 5 = 50 - Q1 + P2/2
Q1 = 45 + P2/2
(continued)
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Reaction Functions
Q1 = 100 - 2P1 + P2 "Coke's demand"
Q2 = 100 - 2P2 + P1 "Pepsi's demand"
MC1 = MC2 = 5
Q1 = 45 + P2/2
Continue Solving for the reaction function
Q1 = Q1
100 - 2P1 + P2 = 45 + P2/2
P1 = 27.5 + P2/4
Likewise,
P2 = 27.5 + P1/4
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Equilibrium
P1 = 27.5 + P2/4,
P2 = 27.5 + P1/4
Q1 = 100 - 2P1 + P2 "Coke's demand"
Q2 = 100 - 2P2 + P1 "Pepsi's demand"
Solving for price and quantity:
P1 = 27.5 + P2/4
P1 = 27.5 + (27.5 + P1/4 )/4
4P1 = 110 + 27.5 + P1/4
3.75P1 =137.5
P1* = 110/3 = P2* (Due to symmetry)
Q1 = 100 - 2P1 + P2
Q1 = 100 - 110/3
Q1* = 190/3 = Q2* (by symmetry)
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Equilibrium
P1* = 110/3 = P2*
Q1* = 190/3 = Q2*
MC1 = MC2 = 5
Calculating Profits.
1* = TR-TC
1* = (P1* - MC1) Q1*
1* = (110/3 - 5) 190/3
1* = 2005.55 = 2* (By symmetry)
Both Coke and Pepsi make profits of 2005.55
when they produce 63.3 each at a price of
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$36.67 each.
Equilibrium and Reaction Functions
Pepsi’s
Price (P2)
P2 =
110/3
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
Coke’s
Price (P1)
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Chapter Thirteen
Equilibrium Notes
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.
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.
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Horizontal Differentiation Solving Steps
1) Use Residual Demand (given)
2) Calculate (residual) MR
3) MR=MC and demand to find reaction functions
(in terms of Prices)
4) Use reaction functions to solve for P’s
5) Use P’s to solve for Q`s
6) Solve for `s
7) Summarize
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Chapter Thirteen
13.5 Monopolistic Competition
Assumptions:
Firms set price
Differentiated products
Many buyers and sellers
Free entry and exit
Products are ASSUMED to be imperfect substitutes for
each other.
Due to differentiated products, each firm has its own
residual demand curve and optimizes like a monopoly:
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13.5 Short Run Monopolistic Competition
Price
Short-Run Profit
Marginal Cost
P*
Average Cost
q* MR
D
Quantity
Chapter Thirteen
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Monopolistic Competition Example
P = 100 - Q
TC = 10+Q2
Calculate Equilibrium price and Quantity
TR = PQ = 100Q – Q2
MR = ∂TR/ ∂Q = 100 - 2Q
MC = ∂TC/ ∂Q =2Q
MR = MC  100 - 2Q = 2Q
Q* = 25
P = 100 – Q
P = 100 – 25
P* = 75
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Monopolistic Competition Example
P = 100 - Q
TC = 10+Q2
Q* = 25
P* = 75
Calculate Profits
AC = TC/Q = 10/Q+Q
* = TR – TC = (P-AC)Q* = (32.5-10)45 = 1,012.5
* = (75- [10/25+25])25
* = (75- [10/25+25])25
* = $1240
This firm will charge a price of $75 and sell 25
units for profits of $1240
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13.5 Short Run Monopolistic Competition Example
Price
Short-Run Profit
Marginal Cost
75
25.4
Average Cost
25 MR
D
Quantity
Chapter Thirteen
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Monopolistic Competition, Short-Run
Solving Steps
1)
2)
3)
4)
5)
6)
7)
Use Residual Demand (given)
Calculate (residual) MR
MR=MC to solve for P
No Step (Take a bread, eat a sandwich)
Use P to solve for Q
Solve for `s
Summarize
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Chapter Thirteen
Long-Run Monopolistic Competition
In the short run, profit is available
There is free entry and exit
THEREFORE
Firms will enter, decreasing individual residual
demand until:
P=AC (profits=0)
Note: P≠MC since MC ≠ AC in these examples
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Monopolistic Competition Long Run Equilibrium
Price
Marginal Cost
P*=AC
Average Cost
q* MR
Dnew
Chapter Thirteen
Dold
Quantity
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Chapter 13 Conclusions
1) Market structure is determined by:
a) Number of Firms
b) Product Differentiation
2) Market structure can be measured using
the 4-firm concentration ratio (4CR) or
the Herfindahl-Hirschman Index (HHI)
3) In a Cournot oligopoly firms choose
quantities and make profits
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Chapter 13 Conclusions
4) In a Bertrand Oligopoly firms choose
prices and make no profits (Perfect
Competition outcome)
5) In a Stackleberg Oligopoly one firm acts
first, for higher output and profits
6) A Dominant Firm works as a monopoly
once the fringe has been removed from
the demand
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Chapter 13 Conclusions
7) A Dominant Firm has incentives to keep
the competitive fringe small
8) Oligopolies with differentiated products
operate with their demand curves
SLIGHTLY affected by rivals
9) Monopolistic Competition works like a
monopoly, but free entry eliminates
profits.
10) Economics is awesome
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