Transcript Slide 1

Lecture 9
Elasticities
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Elasticities are measures of responsiveness
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The response of one variable to changes in another
Can be positive or negative
If “close” to zero, relative unresponsive
If “far” from zero, relatively responsive
Calculated as the ratio of two percentage changes:
E = (%∆Y)/(%∆X)
– This is said to be “the elasticity of Y with respect to X”
Consider this hypothetical
relationship
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The elasticity of grades
with respect to
Study Time/week
time spent studying
– Likely positive
– Ε = (%∆G)/(%∆S) > 0
– If E > 1, we say “elastic”
(relatively responsive)
– If E < 1, we say “inelastic”
(relatively unresponsive)
0
Grade
Another hypothetical example
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The elasticity of grades
with respect to
alcohol consumption
Alcohol Consumption/week
– Likely negative
– E = (%∆G)/(%∆W) < 0
– If |E| >1, we say “elastic”
(relatively responsive)
– If |E| < 1, we say “inelastic”
(relatively unresponsive)
0
Grades
Real elasticity computation regarding alcohol: a 10% price
increase leads to a 5.8% decline in traffic fatalities.
The (own) Price Elasticity of Demand
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Measures the responsiveness of quantity demanded
to changes in the price of the good itself
– Defined thus:
 ε = [(%∆in quantity demanded)/(%∆ in price)]
 Or ε = [(%∆Qd)/(%∆P)]
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Note that ε must be negative (Law of Demand)
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Sometimes convenient to refer to the absolute
value |ε| so we can ignore the negative sign
Examples of demand elasticities
Suppose a 10% rise in the price of a good causes a
20% reduction in the quantity demanded in a
measured time period
ε = -20%/+10% = -2
Suppose a 15% decline in the price of a good causes
a 10% increase quantity demanded in a measured
time period
ε = +10%/-15% = -0.67
Categories of demand elasticities
“Elastic” demand
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Elastic demand
– |ε| > 1
Price
– Qd relatively responsive to price
Demand
– Price change leads to spending
change in opposite direction
– Thus,
 Higher price → lower spending
 Lower price → higher spending
Q/time
When is a good likely to
have sensitive elasticity?
If a product is not unique so it has many
close substitutes and consumers know
about the alternatives.
When buyers’ expenditures are a large
part of their income so they shop
more carefully.
The product is an input in production
that is price sensitive, so the producer
will keep close watch on input prices.
Demand elasticity . . .
“Inelastic” demand
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Inelastic demand
– |ε| < 1
Price
– Qd relatively unresponsive to price
– Price change leads to spending
change in same direction
– Thus,
 Higher price → higher spending
 Lower price → lower spending
Demand
Q/time
When is elasticity likely to
be less sensitive?
When comparisons to substitutes is difficult.
Door-to-door sales. Complex products that are
hard to compare.
When consumers pay only a fraction of the
cost—when insurance covers most of the bill.
When the cost of switching would be high—
when the consumer has developed expertise in
using a product.
When a product is used with another product
that the consumer is committed to—such as
ink cartridges.
No close substitutes?
In 2006 SCI, the largest player in the funeral business,
with 14% of total industry revenue saw its average
revenue per service (its product price) rise by 9%.
At the same time, the number of funeral services
performed fell by 5.8 percent.
The price elasticity of demand for its services is –
(-5.8/9) = 0.64. Its price and quantity demanded
suggest that its demand is inelastic—and we thus
know from this calculation that its total revenue
increased from these services increases.
Some uses of demand elasticities
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More Accurate Pricing
– Use of UPC bar codes to aid in pricing products
(e.g., Wal-Mart and other retailers data)
Trying to Maximize Profits
– A higher price is no guarantee of higher revenue
(will study below)
Plan ahead
– If you think you know about future trends —
plan more precisely (hotels and conventions)
Real World Elasticities
(all negative numbers)
Product or Service
Lamb
Bread
Coffee
Tires
Auto Repairs
Theatre & Opera
Movies
Foreign Travel by U.S. Residents
Public Transportation
Electricity
Jewelry & Watches
Alcohol and Tobacco
Recreation
Estimated Elasticity
Short Run
Long Run
2.65
0.15
0.16
0.8
1.4
0.2
0.9
0.1
0.6
0.1
0.4
0.3
1.1
---1.2
2.4
0.3
3.7
1.8
1.2
1.8
0.6
0.9
3.5
Example
The Macon Telegraph sponsored a road
race for charity. Entry fee was $12 per
runner. 1,600 runners participated.
Fees were $19,200.
To raise more money, fee raised to $20
the next year. Same weather. 900
runners participated. Fees $18,000.
Price elasticity (arc) of demand? 1.12
Example
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ESPN football videogame:
2003 price: $40
2004 price: $20 (50% decrease)
2003 Qd: 400,000
2004 Qd: 2.7 million (575% increase)
E = 575%/50% = 11.5
Note: major competitor, Madden football,
did not change price; its sales rose less than
10% from 2003 to 2004
Example
Kelkoo.com, owned by Yahoo!, is 3rd largest retail
website in UK; 10 million users per month.
Data for sales of PDAs in 100 days in 2003:
18 models sold by 19 retailers. If click on one
model, may get prices offered by 12 retailers.
Price elasticities of demand for various models
offered by different retailers ranged from -1.75
to -14.7. Average was -4.6.
Lowest price retailer saw demand rise 60.4%.
Cross-price elasticities
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Cross-price elasticity of demand
– Measure of responsiveness of
demand to changes in prices of
substitutes and complements:
(%∆ Dx) / (%∆ Py)
– If positive, goods are substitutes, by
definition
– If negative, goods are complements,
by definition
Estimates of Cross Elasticities
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These are estimates of cross elasticities of various
goods (goods that are substitutes) in the U.S.:
Electricity and natural gas
Beef and Pork
Natural gas and fuel oil
Margarine and butter
0.20 (weak substitutes)
0.20
0.44
0.81 (strong substitutes)
Income Elasticity
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Income elasticity of demand
– Measure of responsiveness of demand to
changes in income:
(%∆ Dx) / (%∆ l)
– If positive, good is normal, by definition
(>1, superior)
– If negative, good is inferior, by definition
Estimates of Income Elasticities
Estimates of income elasticities from different
studies in the U.S.:
Flour
-0.36 (inferior good)
Margarine
-0.20 (inferior good)
Milk and cream
0.07 (little change)
Beef
0.51 to 1.05
Apples
1.32
Dental Services
1.41 (highly responsive to
Restaurant meals
1.48 income increases)
Personal air travel 1.8
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Endless Elasticities
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Many measures of elasticity can be
performed simultaneously.
The demand for cans of Coke varies
across state. Even when price is the
same, sales are higher in Southern states
(Georgia has highest consumption)
compared to Northern (ND lowest).
What factors could you consider?
Elasticity
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A study of gasoline sales found that
price elasticity for regular gasoline was
-.6 and for premium gasoline was -.3.
What does that mean?