13.4 product differentiation

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13.4 Product DifferentiationWhen 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 DifferentiationHorizontal 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.

(Small price change =>Small demand change)

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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 productSimultaneous 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

5Chapter Thirteen

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

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

Bertrand Competition – Differentiated

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110100

D0

D10

Chapter Thirteen

Residual Demand

Pepsi’s price = $0 for D0 and $10 for D10

Coke’s Price

Coke’s Quantity

7Coke’s Quantity

MR0

D0

0

MR10

110100

D10

Chapter Thirteen

Marginal Revenue (from Residual Demand)

Pepsi’s price = $0 for D0 and $10 for D10

Each firm maximizes profits based on its residual demand by setting MR (based on residual demand) = MC

Coke’s Price

5

8

5

27.5

MR0

D0

0

D10

MR10

30

45 50

110100

Chapter Thirteen

Optimal Price and Quantity

When MC=MR, we calculate price and quantityCoke’s

Price

Coke’s Quantity

Example: MR=MC

MRR(10) = 55 - Q1(10) = 5

Q1(10) = 50P1(10) = 30

Therefore, firm 1's best response to a price of $10 by firm 2 is a price of $30

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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 + P2/2MR = 50 - Q1 + P2/2MR = MC => 5 = 50 - Q1 + P2/2Q1 = 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 = 5Q1 = 45 + P2/2

Continue Solving for the reaction function

Q1 = Q1

100 - 2P1 + P2 = 45 + P2/2P1 = 27.5 + P2/4 Likewise, P2 = 27.5 + P1/4

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P1 = 27.5 + P2/4, P2 = 27.5 + P1/4Q1 = 100 - 2P1 + P2 "Coke's demand"Q2 = 100 - 2P2 + P1 "Pepsi's demand"

Solving for price and quantity:P1 = 27.5 + P2/4P1 = 27.5 + (27.5 + P1/4 )/44P1 = 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)

Equilibrium

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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)

Equilibrium

Both Coke and Pepsi make profits of 2005.55 when they produce 63.3 each at a price of $36.67 each.

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P2 = 110/3 •

BertrandEquilibrium

27.5

Chapter Thirteen

Pepsi’sPrice (P2)

Coke’s Price (P1)

P2 = 27.5 + P1/4(Pepsi’s R.F.)

P1 = 27.5 + P2/4 (Coke’s R.F.)

Equilibrium and Reaction Functions

P1 = 110/327.5

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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.

15Chapter Thirteen

Horizontal Differentiation Solving Steps

1) Use Residual Demand (given)2) Calculate (residual) MR3) MR=MC and demand to find reaction functions

(in terms of Prices)4) Use reaction functions to solve for P’s5) Use P’s to solve for Q`s 6) Solve for `s7) Summarize

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13.5 Monopolistic Competition

Assumptions:

Firms set priceDifferentiated productsMany buyers and sellersFree 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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Average Cost

Quantity

Price

Short-Run Profit

q*

P*

MRChapter Thirteen

13.5 Short Run Monopolistic Competition

D

Marginal Cost

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Monopolistic Competition ExampleP = 100 - Q TC = 10+Q2

Calculate Equilibrium price and QuantityTR = PQ = 100Q – Q2 MR = ∂TR/ ∂Q = 100 - 2Q

MC = ∂TC/ ∂Q =2QMR = MC 100 - 2Q = 2QQ* = 25

P = 100 – QP = 100 – 25P* = 75

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Monopolistic Competition Example

P = 100 - Q Q* = 25TC = 10+Q2 P* = 75

Calculate ProfitsAC = 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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Average Cost

Quantity

Price

Short-Run Profit

25

75

MRChapter Thirteen

13.5 Short Run Monopolistic Competition Example

D

Marginal Cost

25.4

21Chapter Thirteen

Monopolistic Competition, Short-RunSolving Steps

1) Use Residual Demand (given)2) Calculate (residual) MR3) MR=MC to solve for P4) No Step (Take a bread, eat a sandwich)5) Use P to solve for Q 6) Solve for `s7) Summarize

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Long-Run Monopolistic CompetitionIn the short run, profit is availableThere is free entry and exit

THEREFOREFirms will enter, decreasing individual residual demand until:

P=AC (profits=0)

Note: P≠MC since MC ≠ AC in these examples

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Average Cost

Quantity

Price

Marginal Cost

q*

P*=AC

MRChapter Thirteen

Monopolistic Competition Long Run Equilibrium

Dnew Dold

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Chapter 13 Conclusions1) 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 Conclusions4) 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 Conclusions7) 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