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```Lecture 3
Prof. Jura Liaukonyte
1
Dyson
Plan of the Lecture
 Other Elasticities
 Measures of Market Concentration
 Relationship between Advertising and Market structure:
 Dorfman-Steiner Condition
 Advertising to sales ratios across different industries
2
Dyson
Price Elasticity of Supply
 Measures the sensitivity of quantity supplied given a change
in price
 Measures the percentage change in quantity supplied resulting
from a 1 percent change in price
%Q S
E 
%P
S
P
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Dyson
Income Elasticity of Demand
Definition
Formula
 Measures how much quantity
demanded changes with a
change in income
EI >0 implies normal good.
EI <0 implies inferior good.
 Normal goods may be necessity
or luxury.
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Dyson
Q/Q
I Q
EI 

I/I
Q I
Cross Price Elasticity
Definition
Formula
 Measures the percentage change in
the quantity demanded of one good
that results from a one percent
change in the price of another good


Complements: Cars and Tires
 Cross-price elasticity of demand is
negative
 Price of cars increases, quantity
demanded of tires decreases
Substitutes: Butter and Margarine
 Cross-price elasticity of demand is
positive
 Price of butter increases, quantity of
margarine demanded increases
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Dyson
EQb Pm 
Qb Qb Pm Qb

Pm Pm Qb Pm
Size of shift in Demand
Assume Psubst Increases
EXY>1
Price
Price
EXY<1
D
D’
Demand for Product
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Dyson
D D’
Demand for Product
Example: The Cross-Price Elasticity of Demand for
Cars
Sentra Escort LS400 735i
Sentra -6.528 0.454
0.000
0.000
Escort 0.078
-6.031 0.001
0.000
LS400 0.000
0.001
-3.085 0.032
735i
0.001
0.093
0.000
-3.515
 Source: Berry, Levinsohn and Pakes, "Automobile Price in Market Equilibrium,"
Econometrica 63 (July 1995), 841-890.
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Dyson
 Measures the sensitivity of demand given a change in
%Q
Q A

%A
A Q
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Dyson
 Ad-inelastic demand curve: Demand does not shift much
 Example:
 Concrete: Consumers’ purchasing decisions are mostly
based on price and related terms of sale.
 Ad-elastic demand curve: Demand is relatively responsive to
 Example:
 Soda: Consumers’ purchasing decisions can be easily
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Dyson
 Two key results from advertising
 The marginal gain from advertising expenditures is greater the
more sensitive the demand curve is to advertising expenditures.
 Firms should advertise more when the demand curve is more
10
Dyson
Lerner Index
 Lerner Index:
L = (p - MC)/p = 1/|EP|
 The higher the number, the more pricing power the firm
has.
 Mark-up power reflects monopoly power.
 PUNCHLINE: If elasticity increases, mark-up will
decline. If the product becomes less elastic, markup will increase.
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Dyson
What are Sources of Monopoly Power?
• Low elasticity of demand
• We just showed this using Lerner Index.
• Possibly due to strong product differentiation.
• High barriers to entry
• e.g., ownership of necessary raw materials, patents and
regulatory barriers, scale economies, product diff.
• Number of other competitors in market.
• Interactions between firms: Compete or
cooperate?
12
Dyson
Product Differentiation
 Products are different if there is some objective
characteristic or property, real or perceived, that provides
a basis for buyers to choose one over the other.
 Product differentiation may lead to reduced own -price
elasticity. As the degree of differentiation increases, the
price elasticity will decrease.
13
Dyson
Product Differentiation, cont.
 Ways in which products are differentiated.





Product Brand
Packaging
Conditions of Sale
Service Provided
Location
 Product Differentiation as an Entry Strategy
 Product differentiation to create a niche market.
 Product differentiation to deter entry.
14
Dyson
 Assume a firm faces a downward-sloping demand
inverse curve but one that shifts depending on the
amount of advertising A that the firm does
 P=P(Q, A)
Recall, the Lerner Index, LI
L = (p - MC)/p = 1/|EP|
Where |EP| is the price elasticity of demand
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Dyson
 Recall, the elasticity of output demand with respect to advertising A
Q / Q
A Q
EA 

A / A
Q A
A
EA

P * Q | Ed |
Dorfman-Steiner Condition
For a profit-maximizing monopolist, the advertising-tosales ratio is equal to the ratio of the elasticity of
demand with respect to advertising relative to the
elasticity of demand with respect to price.
16
Dyson
Dorfman-Steiner
 The Dorfman-Steiner formula relates the sales ratio to pricecost margin and elasticity.
 The advertising-to-sales ratio is greater the greater the
advertising elasticity of demand and lower the price elasticity
of demand (or the greater the price-cost margin).
17
Dyson
Intuition Behind D-S
A
EA

P * Q | Ed |
 Recall: the greater the demand elasticity, the lower the
optimal price.
 Price-cost margin is smaller when elasticity is higher.
 Since the price-cost margin is smaller with elastic demand,
the gain from advertising is also smaller even if the increase
in quantity demanded is the same.
 The marginal gain from advertising is greater the greater the
price-cost margin.
18
Dyson
Example
 Suppose you have been hired to marker a new music
recording that is expected to have target sales of \$20
million for upcoming year
Scenario
 The marketing department has estimated that 1%
increase in advertising will translate to 0.5% increase in
sales
 And that 1% increase in the price of the recording would
reduce the number sold by about 2%
Question
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Dyson
 How much money should you commit to advertising the
recording in the coming year?
 This ratio varies between industries
 Salt industry: a-s-r = 0 to .5%
 Breakfast cereals industry: a-s-r= 8% to 13%
 The type of product
 Price elasticity of demand
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Dyson
Industry
PERFUME,COSMETIC,TOILET PREP
MOTION PIC, VIDEOTAPE PRODTN
DISTILLED AND BLENDED LIQUOR
RUBBER AND PLASTICS FOOTWEAR
FOOD AND KINDRED PRODUCTS
DOLLS AND STUFFED TOYS
EDUCATIONAL SERVICES
SPECIAL CLEAN,POLISH PREPS
SOAP,DETERGENT,TOILET PREPS
BOOKS: PUBG, PUBG & PRINTING
AMUSEMENT PARKS
WOMENS,MISSES,JRS OUTERWEAR
SPORTING & ATHLETIC GDS, NEC
GAMES,TOYS,CHLD VEH,EX DOLLS
BEVERAGES
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Dyson
SIC Code
as % of sales
2844
7812
2085
3021
2000
3942
8200
2842
2840
2731
7996
2330
3949
4833
3944
2080
20.1
19.4
14.4
12.5
11.5
10.1
9.8
9.8
9.2
8.8
8
8
7.8
7.4
6.8
6.1
as % of
margin
29.2
31.4
23.7
26.3
23.1
20
16.3
19.5
17.4
20.2
17
13.5
20.9
25.3
14.9
9.9
growth %
4
6.3
0.6
7.7
1.2
-4.8
9.2
3.8
2.3
-16.2
-0.9
0.2
-2
1.1
14
4.9
Industry
INDUSTRIAL ORGANIC CHEMICALS
OIL & GAS FIELD SERVICES,NEC
PETROLEUM REFINING
AIRCRAFT
COMPUTER COMMUNICATION EQUIP
PETROLEUM,EX BULK STATN-WHSL
STEEL WORKS & BLAST FURNACES
COMPUTER STORAGE DEVICES
COMPUTERS & SOFTWARE-WHSL
CONGLOMERATE
CONSTRUCTION MACHINERY & EQ
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Dyson
SIC Code
as % of sales
2860
1389
2911
3721
3576
5172
3312
3572
5045
9997
3531
0.1
0.1
0.1
0.2
0.2
0.2
0.2
0.3
0.3
0.3
0.3
as % of
margin
0.5
0.2
0.5
1.1
0.3
3.4
1
0.6
3.6
1.7
1.3
growth %
2.8
-6.2
0.1
-4.8
-1.6
23.3
-5.8
3.6
-1.2
3
1.6
Profit Maximization: MR=MC
Set Up
 profit(q)
 How
Optimization
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Dyson
= TR(q) – TC(q)
to maximize profit?
Profit Maximization: MR=MC

Set Up
Optimization

Profit maximization: dprofit/dq = 0

This implies dTR(q)/dq - dTC(q)/dq = 0

But dTR(q)/dq = marginal revenue


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Dyson
profit(q) = TR(q) – TC(q)
dTC(q)/dq = marginal cost
So profit maximization implies MR = MC
Profit Maximization: Monopoly Condition
Derivation of the monopolist’s marginal revenue
\$/unit
1. Demand: P = A – B*Q
2. Total Revenue: TR = P*Q = A*Q – B*Q2
3. Marginal Revenue: MR = dTR/dQ
4. MR= A-2B*Q
A
Demand
With linear demand the marginal
revenue curve is also linear with
the same price intercept
…
but twice the slope
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Dyson
Quantity
MR
Market Concentration
 Numbers and size distributions of firms
Different Market
Structures
Measurements of
market structures
 Ready-to-eat breakfast cereals: high concentration
 Newspapers: low concentration



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Dyson
Concentration ratio,
Herfindahl-Hirschman Index (HHI)
Lerner Index (LI)
Industry Concentration
• Four-Firm Concentration Ratio
– The sum of the market shares of the top four firms in the defined
industry. Letting Si denote sales for firm i and ST denote total industry
sales
C4  w1  w2  w3  w4 , where w1 
Si
ST
• Herfindahl-Hirschman Index (HHI)
– The sum of the squared market shares of firms in a given industry,
multiplied by 10,000: HHI = 10,000  S wi2, where wi = Si/ST.
27
Dyson
Measure of concentration
Firm Rank
Squared Market
Share
1
25
625
2
25
625
3
25
625
4
5
25
5
5
25
6
5
25
7
5
25
8
5
25
Concentration Index
28
Market Share
(%)
Dyson
Measure of concentration
Market Share
(%)
Firm Rank
1
2
3
4
5
6
7
8
Concentration Index
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Dyson
Σ
25
25
25
5
5
5
5
5
Squared Market
Share
Σ
625
625
625
25
25
25
25
25
Measure of concentration
Market Share
(%)
Firm Rank
1
2
3
4
5
6
7
8
Concentration Index
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Dyson
Σ
25
25
25
5
5
5
5
5
CR4 = 80
Squared Market
Share
Σ
625
625
625
25
25
25
25
25
H = 2,000
Measure of concentration
Market Share
(%)
Firm Rank
1
2
3
4
5
6
7
8
Σ
Assume firms 4
and 5 merge
Concentration Index
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Dyson
25
25
25
5
5
5
5
5
Squared Market
Share
10
Σ
625
625
625
25
25
25
25
25
100
Measure of concentration
Market Share
(%)
Firm Rank
1
2
3
4
5
6
7
8
Σ
The
concentration
indices change
Concentration Index
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Dyson
25
25
25
5
5
5
5
5
Squared Market
Share
10
Σ
CR4 = 80 85
625
625
625
25
25
25
25
25
100
H = 2,000 2050
HHI
Definition
Properties
 The Herfindahl-Hirschman Index – the square of the percentage
market share of each firm summed over the largest 50 firms in the
industry (or all of the firms if there is less than 50)

In perfect competition, the HHI is small

In monopoly, the HHI is 10,000 (100 squared)

A popular measure with the Justice Dept in the 1980’s

Example
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Dyson

HHI < 1000 characterized competitive markets

HHI > 1800 would bring Justice Dept challenge to proposed
mergers
E.g. The cigarette industry is highly concentrated with only 8 firms
and a Herfindahl-Hirschman Index (HH1) of 2623
Example: Credit Card Industry
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Dyson
Market Definition
 All Credit Lending Institutions with their own card
 27.2% J.P. Morgan Chase & Co.
 19.2% Bank of America Corporation
 18.9% Citigroup Inc.
 17.2% American Express Company
 4.0% Capital One
 CR4: 83.2
 HHI: 1810-1850
 Total Number of Companies: 192
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Dyson
What is a Market?
 No clear consensus
 the market for automobiles
 should we include light trucks; pick-ups SUVs?
 the market for soft drinks
 what are the competitors for Coca Cola and Pepsi?
 With whom do McDonalds and Burger King compete?
 Presumably define a market by closeness in substitutability
of the commodities involved
 how close is close?
 how homogeneous do commodities have to be?
36
Dyson
Fast-Food Outlets
McDonald’s
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Dyson
Burger
King
Wendy’s
```
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