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Elasticity and Its
Applications
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5
The Laws of Supply and Demand . .
.
• … tell us the DIRECTION that quantities will
move in response to price (or other) changes.
• Often, though, we want to know more precisely
HOW MUCH quantities will change.
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Elasticity . . .
• … allows us to analyze supply and demand
with greater precision.
• … is a measure of how much buyers and sellers
respond to changes in market conditions
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THE ELASTICITY OF DEMAND
• Price elasticity of demand is a measure of how
much the quantity demanded of a good
responds to a change in the price of that good.
• Price elasticity of demand is the percentage
change in quantity demanded given a percent
change in the price.
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The Price Elasticity of Demand and Its
Determinants
•
•
•
•
Availability of Close Substitutes
Necessities versus Luxuries
Definition of the Market
Time Horizon
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The Price Elasticity of Demand and Its
Determinants
• Demand tends to be more elastic :
•
•
•
•
the larger the number of close substitutes.
if the good is a luxury.
the more narrowly defined the market.
the longer the time period.
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Computing the Price Elasticity of Demand
• The price elasticity of demand is computed as
the percentage change in the quantity demanded
divided by the percentage change in price.
Price elasticity of demand =
Percentage change in quantity demanded
Percentage change in price
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Computing the Price Elasticity of Demand
Price elasticity of demand =
Percentage change in quantity demanded
Percentage change in price
• Example: If the price of an ice cream cone
increases from $2.00 to $2.20 and the amount
you buy falls from 10 to 8 cones, then your
elasticity of demand would be calculated as:
(10  8)
 100
20%
10

2
(2.20  2.00)
 100 10%
2.00
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Two Slight Complications
• Note: Although the Law of Demand says that
quantities fall as prices rise, by convention, we write
price elasticity of demand as positive.
• Thus although a 10% increase in price might be
expected to lead to a negative percentage change in
quantity, (say 15%) we would still write this as
• Price elasticity =15/10=1.5 instead of -15/10=-1.5.
• We have to be careful about this issue with other
elasticities like income and cross-price elasticities.
• And we have one other problem...
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Computing the Price Elasticity of Demand
Price elasticity of demand =
Percentage change in quantity demanded
Percentage change in price
• Reverse Example: If the price of an ice cream
cone decreases from $2.20 to $2.00 and the
amount you buy falls from 10 to 8 cones, then
your elasticity of demand COULD be
calculated as: (8  10)
100
25%
8

 2.75%
(2.00  2.20)
100 9%
2.20
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Computing Elasticities
• Having a measure of sensitivity that is different
depending on whether you raise price or lower
price is not a good thing.
• Therefore, we usually compute the percentage
by using the MIDPOINT METHOD……
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The Midpoint Method: A Better Way to
Calculate Percentage Changes and
Elasticities
• The midpoint formula is preferable when
calculating the price elasticity of demand
because it gives the same answer regardless of
the direction of the change.
(Q2  Q1 ) / [(Q2  Q1 ) / 2]
Price elasticity of demand =
(P2  P1 ) / [(P2  P1 ) / 2]
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The Midpoint Method: A Better Way to
Calculate Percentage Changes and
Elasticities
• Example: If the price of an ice cream cone
increases from $2.00 to $2.20 and the amount
you buy falls from 10 to 8 cones, then your
elasticity of demand, using the midpoint
formula, would be calculated as:
(10  8)
22%
(10  8) / 2

 2.32
(2.20  2.00)
9.5%
(2.00  2.20) / 2
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The Variety of Demand Curves
• Inelastic Demand
• Quantity demanded does not respond strongly to
price changes.
• Price elasticity of demand is less than one.
• Elastic Demand
• Quantity demanded responds strongly to changes in
price.
• Price elasticity of demand is greater than one.
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Computing the Price Elasticity of Demand
(100-50)
ED 
Price
$5
4
0
(4.00  5.00)/2
67 percent

 (-?)3
(-?)22 percent
Demand
50
(4.00-5.00)
(100  50)/2
100 Quantity
Demand is price elastic
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The Variety of Demand Curves
• Perfectly Inelastic
• Quantity demanded does not respond to price
changes.
• Perfectly Elastic
• Quantity demanded changes infinitely with any
change in price.
• Unit Elastic
• Quantity demanded changes by the same percentage
as the price.
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Testing Your Understanding:
Order these goods from most to least
elastic
•
•
•
•
•
•
1. Beef
2. Salt
3. European Vacation
4. Steak
5. Honda Accord
6. Dijon Mustard.
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Testing Your Understanding:
Order these goods from most to least
elastic
• A “Typical” Ranking (There is no “right”
answer here without data.)
• 1. European Vacation (Luxury,substitutes, cost)
• 2. Honda Accord (cost, substitutes)
• 3. Steak (Luxury, close Beef substitutes)
• 4. Dijon Mustard (luxury, taste specific)
• 5. Beef (moderate expense, chicken, pork sub)
• 6. Salt (inexpensive, necessity, no substitute?)
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The Variety of Demand Curves
• Because the price elasticity of demand
measures how much quantity demanded
responds to the price, it is related to the slope of
the demand curve.
• However, the slope and elasticity ARE NOT
THE SAME.
• A linear Demand Curve always has the same
slope but it can have DIFFERENT elasticity at
different parts.
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Elasticity of a Linear Demand Curve
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Figure 1 The Price Elasticity of Demand
(a) Perfectly Inelastic Demand: Elasticity Equals 0
Price
Demand
$5
4
1. An
increase
in price . . .
0
100
Quantity
2. . . . leaves the quantity demanded unchanged.
Copyright©2003 Southwestern/Thomson Learning
Figure 1 The Price Elasticity of Demand
(b) Inelastic Demand: Elasticity Is Less Than 1
Price
$5
4
1. A 22%
increase
in price . . .
Demand
0
90
100
Quantity
2. . . . leads to an 11% decrease in quantity demanded.
Figure 1 The Price Elasticity of Demand
(c) Unit Elastic Demand: Elasticity Equals 1
Price
$5
4
Demand
1. A 22%
increase
in price . . .
0
80
100
Quantity
2. . . . leads to a 22% decrease in quantity demanded.
Copyright©2003 Southwestern/Thomson Learning
Figure 1 The Price Elasticity of Demand
(d) Elastic Demand: Elasticity Is Greater Than 1
Price
$5
4
Demand
1. A 22%
increase
in price . . .
0
50
100
Quantity
2. . . . leads to a 67% decrease in quantity demanded.
Figure 1 The Price Elasticity of Demand
(e) Perfectly Elastic Demand: Elasticity Equals Infinity
Price
1. At any price
above $4, quantity
demanded is zero.
$4
Demand
2. At exactly $4,
consumers will
buy any quantity.
0
3. At a price below $4,
quantity demanded is infinite.
Quantity
A Policy Application of Supply and
Demand
• The summer of 2005 experienced one of the worst
hurricane seasons in the nation’s history.
• Aside from the tremendous human cost, hurricanes are
also often followed by some predictable economic
‘disruptions’.
• For example, the prices of bottled water and gasoline
both tend to rise sharply.
• Given that hurricanes if anything reduce the demand for
gasoline (people travel less not more) why should the price
of gasoline rise?
• Given that hurricanes do not destroy stocks of bottled water,
why should the price of bottled water rise?
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Gasoline Market Effects
• Hurricanes tend to disrupt supply chains of
refined gas with predictable impacts on shortS’
run supply...
P’
S
P
D
D’
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Bottled Water Market Effects
• Hurricanes tend to disrupt public infrastructure
such as water supplies with predictable impacts
on short-run demand for bottled water...
P’
D’
P
D
S
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Price Gouging?
• In the aftermath of a hurricane comes the inevitable clash over
"price gouging". Florida's Attorney General Charlie Crist
complained:
• Hurricane Charley is the worst natural disaster to befall our
state in a dozen years, and it is unthinkable that anyone
would try to take advantage of neighbors at a time like this.
• “We must enact a national federal price gouging law to
prevent exorbitant prices for food, water, housing, and gas.”
From www.housedemocrat.gov, Sept 6, 2005. (just after
Hurricane Katrina).
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Price Gouging?
• What would be the effect of banning “price
gouging” (putting a price ceiling) in the bottled
water market?
• A) in the market after Katrina?
• B) in bottled water markets after the next
hurricane?
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Short Run Effects of a Price Ceiling
• Forcing the price below the new equilibrium creates a
situation of excess demand. How will it be determined
who gets the available water?
P’
D’
P
D
S
Qs
Qd
Excess Demand
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Long Run Effects of a Price Ceiling
• Why might a ban on ‘price gouging’ cause the short
run supply curve (after the NEXT hurricane) to move
left?
P’’
P’
D’
P
D
S
Qs
Qd
Excess Demand
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Total Revenue and the Price Elasticity of
Demand
• Total revenue is the amount paid by buyers and
received by sellers of a good.
• Computed as the price of the good times the quantity
sold.
TR = P x Q
• Suppose you were operating a business and was
considering raising the price by 10%.
• Would your revenues rise or fall?
• How could you use elasticity of demand to help you
guess right?
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Figure 2 Total Revenue
Price
$4
P × Q = $400
(revenue)
P
0
Demand
100
Quantity
Q
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Elasticity and Total Revenue along a Linear
Demand Curve
• At an inelastic part of the demand curve, an
increase in price leads to a decrease in quantity
that is proportionately smaller. Thus, total
revenue increases.
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Figure 3 How Total Revenue Changes When Price
Changes: At an inelastic part of the Demand Curve
Price
Price
… leads to an Increase in
total revenue from $100 to
$240
An Increase in price from $1
to $3 …
$3
Revenue = $240
$1
Demand
Revenue = $100
0
100
Quantity
Demand
0
80
Quantity
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Elasticity and Total Revenue along a Linear
Demand Curve
• At an elastic part of the demand curve, an
increase in the price leads to a decrease in
quantity demanded that is proportionately
larger. Thus, total revenue decreases.
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Figure 3A How Total Revenue Changes When Price
Changes: At an ELASTIC part of the Demand Curve
Price
Price
… leads to an Increase in
total revenue from $210 to
$240
Revenue =$210
A Decrease in price
from $6 to $3 …
$3
Revenue = $240
Demand
0
35
Quantity
Demand
0
80
Quantity
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Figure 4 How Total Revenue Changes When Price
Changes: Elastic Demand
Price
Price
… leads to an decrease in
total revenue from $200 to
$100
An Increase in price from $4
to $5 …
$5
$4
Demand
Demand
Revenue = $200
0
50
Revenue = $100
Quantity
0
20
Quantity
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Income Elasticity of Demand
• Income elasticity of demand measures how
much the quantity demanded of a good
responds to a change in consumers’ income.
• It is computed as the percentage change in the
quantity demanded divided by the percentage
change in income.
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Computing Income Elasticity
Percentage change
in quantity demanded
Income elasticity of demand =
Percentage change
in income
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Income Elasticity
• Types of Goods
• Normal Goods
• Inferior Goods
• Higher income raises the quantity demanded for
normal goods but lowers the quantity demanded
for inferior goods.
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Income Elasticity
• Goods consumers regard as necessities tend to
be income inelastic
• Examples include food, fuel, clothing, utilities, and
medical services.
• Goods consumers regard as luxuries tend to be
income elastic.
• Examples include sports cars, furs, and expensive
foods.
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Testing Your Understanding:
Substitutes or Complements?
Good A
Left shoe
Coffee
Honda Accord
Classical Music
Movies
Football
Tattoos
Airplanes
Beef
Good B
Right shoe
Tea
Toyota Camry
Rock and Roll
TV Shows
Beer
Clothes
Bicycles
Broccoli
S, C or Independent?
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Cross-Price Elasticity
• Since demand for Good A can depend on prices of
other goods, we also have the notion of cross-price
elasticity.
• Recall that Good B is a substitute for Good A if
demand for Good A rises when the price of Good B
rises.
• As in the case of income elasticity, the SIGN of a
cross-price elasticity conveys vital information.
• The sign of the cross price elasticity between Goods A
and B is positive if the two goods are substitutes.
• What is the sign if they are complements?
Copyright © 2004 South-Western/Thomson Learning
Computing Cross-Price Elasticity
Cross-price elasticity of demand for A with respect to B
Percentage change
in quantity demanded of A
=
.
Percentage change
in price of B
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Cross-Price Elasticity: A Policy
Application
• When one firm attempts to buy another firm (a
“merger’) the purchase typically must be
approved by the U.S Department of Justice or
the Federal Trade Commission (FTC) to ensure
the market remains competitive.
• If there are only two firms in the market before
the merger, then the proposed transactions
would create a monopoly and is usually
prohibited.
• What determines the market though?
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Cross-Price Elasticity: A Policy
Application
• The U.S. government often uses cross-price
elasticities to decide if there are enough other
firms to maintain competitive discipline on
prices.
• To do this, they analyze cross-price elasticities.
• Suppose the newly merged firm were to raise its
price by 5%.
• Would it lose enough sales to substitute
products (more than 5% of its sales) so that the
price rise would not be profitable?
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Cross-Price Elasticity: A Policy
Application
• In a famous case, U.S. vs. Dupont, the government
tried to argue that Dupont had monopolised the
cellophane wrapper market.
• Since Dupont controlled more than 75% of the
cellophane market, this claim seemed strong.
• However, the Supreme Court held that Dupont’s
ability to price monopolistically was severely
constrained by the presence of manufacturers of
aluminum foil, Saran wrap, waxed paper, etc.
• The Court used evidence of high cross-price
elasticities of demand between these products to reach
their conclusions.
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Cross-Price Elasticity: A Policy
Application
• The reasoning of the Court remains a matter of
significant debate. However, the use of crossprice elasticities is still an important tool in
anti-trust investigations.
• The “Horizontal Merger Guidelines” illustrate
how extensive use of cross-price elasticities can
be used to determine whether a given market is
competitive or not.
• See
http://www.atrnet.gov/invest/mergers/mgrguide.
htm
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THE ELASTICITY OF SUPPLY
• Price elasticity of supply is a measure of how
much the quantity supplied of a good responds
to a change in the price of that good.
• Price elasticity of supply is the percentage
change in quantity supplied resulting from a
percent change in price.
Copyright © 2004 South-Western/Thomson Learning
Figure 6 The Price Elasticity of Supply
(a) Perfectly Inelastic Supply: Elasticity Equals 0
Price
Supply
$5
4
1. An
increase
in price . . .
0
100
Quantity
2. . . . leaves the quantity supplied unchanged.
Copyright©2003 Southwestern/Thomson Learning
Figure 6 The Price Elasticity of Supply
(b) Inelastic Supply: Elasticity Is Less Than 1
Price
Supply
$5
4
1. A 22%
increase
in price . . .
0
100
110
Quantity
2. . . . leads to a 10% increase in quantity supplied.
Copyright©2003 Southwestern/Thomson Learning
Figure 6 The Price Elasticity of Supply
(c) Unit Elastic Supply: Elasticity Equals 1
Price
Supply
$5
4
1. A 22%
increase
in price . . .
0
100
125
Quantity
2. . . . leads to a 22% increase in quantity supplied.
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Figure 6 The Price Elasticity of Supply
(d) Elastic Supply: Elasticity Is Greater Than 1
Price
Supply
$5
4
1. A 22%
increase
in price . . .
0
100
200
Quantity
2. . . . leads to a 67% increase in quantity supplied.
Copyright©2003 Southwestern/Thomson Learning
Figure 6 The Price Elasticity of Supply
(e) Perfectly Elastic Supply: Elasticity Equals Infinity
Price
1. At any price
above $4, quantity
supplied is infinite.
$4
Supply
2. At exactly $4,
producers will
supply any quantity.
0
3. At a price below $4,
quantity supplied is zero.
Quantity
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Determinants of Elasticity of Supply
• Ability of sellers to change the amount of the
good they produce.
• Beach-front land is inelastic.
• Books, cars, or manufactured goods are elastic.
• Time period.
• Supply is more elastic in the long run.
Copyright © 2004 South-Western/Thomson Learning
Computing the Price Elasticity of Supply
• The price elasticity of supply is computed as
the percentage change in the quantity supplied
divided by the percentage change in price.
Percentage change
in quantity supplied
Price elasticity of supply =
Percentage change in price
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APPLICATION of ELASTICITY
• Can good news for farming be bad news for
farmers?
• What happens to wheat farmers and the market
for wheat when university agronomists discover
a new wheat hybrid that is more productive
than existing varieties?
Copyright © 2004 South-Western/Thomson Learning
THE APPLICATION OF SUPPLY,
DEMAND, AND ELASTICITY
• Examine whether the supply or demand curve
shifts.
• Determine the direction of the shift of the
curve.
• Use the supply-and-demand diagram to see how
the market equilibrium changes.
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Figure 8 An Increase in Supply in the Market for Wheat
Price of
Wheat
2. . . . leads
to a large fall
in price . . .
1. When demand is inelastic,
an increase in supply . . .
S1
S2
$3
2
Demand
0
100
110
Quantity of
Wheat
3. . . . and a proportionately smaller
increase in quantity sold. As a result,
revenue falls from $300 to $220.
Copyright©2003 Southwestern/Thomson Learning
Compute the Price Elasticity of DEMAND
(Note: error in slides online, they read
‘Supply’)
100  110
(100  110) / 2
ED 
3.00  2.00
(3.00  2.00) / 2
0.095

 0.24
0.4
Demand is inelastic
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Competitive Markets: A First Glance
• Although total revenue fell, farmers voluntarily
took up the new hybrid.
• Why?
• Individually, every farmer takes the price of
wheat as given.
• Individually, it is a profitable strategy for each
farmer to take up the invention.
• As a group, wheat producers may actually
prefer not to increase supply.
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Application
• Where does information about elasticity come
from?
• There are a variety of sources: for example, one
might be a history of data relating prices to
quantity.
• Example: Data may be available over the last
12 months on prices and sales of a CD:
Copyright © 2004 South-Western/Thomson Learning
Source 1:Data on Prices And
Quantity
Q
P
75.5
20
72.25
21
79.5
19
82.75
18.5
68.25
22
55.75
25
73.5
20.5
74
20.5
96.75
15
93.5
15.5
90.25
16.5
73.5
20.5
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Source 1:Scatter Plot
CD Demand
30
25
P
20
Series1
15
10
5
0
50
60
70
80
90
100
Q
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Source 1: Fitted Line (Estimation via
Econometrics)
30
25
P
20
15
Series1
10
5
0
g20:g31
Q (CDs)
Copyright © 2004 South-Western/Thomson Learning
Source 2:By Case Study
• In 2004, the federal government mandated a new
safety feature in gas water heaters called FVIR.
• It resulted in an industry wide cost rise of $30.
• The average gas water heater cost about $230.
• Thus, there was about a 12.25% increase in price
(using the midpoint method).
• If the change of quantity was, say, a fall in gas water
heater purchases of 10% (again using the midpoint
method) we could directly compute the elasticity.
• If the change in electric water heater purchases was an
increase in (say) 5%, we could also compute the cross
price elasticity.
Copyright © 2004 South-Western/Thomson Learning
Source 3:By Inference or
Introspection
• Suppose that we knew the price elasticity of
water heaters (gas and electric) was 1.1.
• What could we presume was the lower bound
on the elasticity of gas water heaters?
• Why?
Copyright © 2004 South-Western/Thomson Learning
Summary
• Price elasticity of demand measures how much
the quantity demanded responds to changes in
the price.
• Price elasticity of demand is calculated as the
percentage change in quantity demanded
divided by the percentage change in price.
• If a demand curve is elastic, total revenue falls
when the price rises.
• If it is inelastic, total revenue rises as the price
rises.
Copyright © 2004 South-Western/Thomson Learning
Summary
• The income elasticity of demand measures how
much the quantity demanded responds to
changes in consumers’ income.
• The cross-price elasticity of demand measures
how much the quantity demanded of one good
responds to the price of another good.
• The price elasticity of supply measures how
much the quantity supplied responds to changes
in the price. .
Copyright © 2004 South-Western/Thomson Learning
Summary
• In most markets, supply is more elastic in the
long run than in the short run.
• The price elasticity of supply is calculated as
the percentage change in quantity supplied
divided by the percentage change in price.
• The tools of supply and demand can be applied
in many different types of markets.
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