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4
Elasticity
A fter studying this chapter,
y ou will be able to:
Define, calculate, and explain the factors that influence
the price elasticity of demand
Define, calculate, and explain the factors that influence
the cross elasticity of demand and the income elasticity of
demand
Define, calculate, and explain the factors that influence
the elasticity of supply
What are the effects of a high gas price on buying
plans? You can see some of the biggest effects at car dealers
such a large scale that we end up cutting our expenditure on
lots, where SUVs and other gas guzzlers remain unsold while
gas?
sub-compacts and hybrids sell in greater quantities. But how
This chapter introduces you to elasticity: a tool that
big are these effects? When the price of gasoline doubles, as it
addresses these quantitative questions. At the end of the
has done over the past few years, by how much does the quan-
chapter, in Reading Between the Lines, well use the concept
tity of SUVs sold decrease, and by how much does the quantity
of elasticity to explain what was happening in the markets
of sub-compacts sold increase?
for gasoline and automobiles in 2008. But well explain and
And what about gasoline purchases? Do we keep filling our
tanks and spending more on gas? Or do we find substitutes on
illustrate elasticity by studying another familiar market: the
market for pizza.
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You know that when supply increases, the equilibrium
price falls and the equilibrium quantity increases. But
does the price fall by a large amount and the quantity
increase by a little? Or does the price barely fall and the
quantity increase by a large amount?
The answer depends on the responsiveness of the
quantity demanded to a change in price. You can see
why by studying Fig. 4.1, which shows two possible
scenarios in a local pizza market. Figure 4.1(a) shows
one scenario, and Fig. 4.1(b) shows the other.
In both cases, supply is initially S0. In part (a), the
demand for pizza is shown by the demand curve DA.
In part (b), the demand for pizza is shown by the
demand curve DB. Initially, in both cases, the price is
$20 a pizza and the equilibrium quantity is 10 pizzas
an hour.
Now a large pizza franchise opens up, and the supply of pizza increases. The supply curve shifts rightward to S1. In case (a), the price falls by an enormous
$15 to $5 a pizza, and the quantity increases by only
3 to 13 pizzas an hour. In contrast, in case (b), the
price falls by only $5 to $15 a pizza and the quantity
increases by 7 to 17 pizzas an hour.
The different outcomes arise from differing degrees
of responsiveness of the quantity demanded to a change
in price. But what do we mean by responsiveness? One
possible answer is slope. The slope of demand curve DA
is steeper than the slope of demand curve DB.
In this example, we can compare the slopes of the
two demand curves, but we cant always make such
a comparison. The reason is that the slope of a
demand curve depends on the units in which we
measure the price and quantity. And we often must
compare the demand for different goods and services that are measured in unrelated units. For example, a pizza producer might want to compare the
demand for pizza with the demand for soft drinks.
Which quantity demanded is more responsive to a
price change? This question cant be answered by
comparing the slopes of two demand curves. The
units of measurement of pizza and soft drinks are
unrelated. The question can be answered with a
measure of responsiveness that is independent of
units of measurement. Elasticity is such a measure.
The price elasticity of demand is a units-free measure
of the responsiveness of the quantity demanded of a
good to a change in its price when all other influences on buying plans remain the same.
FIGURE 4.1
Price (dollars per pizza)
Price Elasticity of Demand
How a Change in Supply
Changes Price and Quantity
40.00
S0
An increase
in supply
brings ...
S1
30.00
... a large
fall in price ...
20.00
10.00
... and a small
increase in quantity
5.00
DA
0
5
10
13 15
20
25
Quantity (pizzas per hour)
(a) Large price change and small quantity change
Price (dollars per pizza)
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40.00
An increase
S0 in supply
brings ...
S1
30.00
20.00
15.00
10.00
0
DB
... a small
fall in
price ...
5
... and a
large increase
in quantity
10
15 17
20
25
Quantity (pizzas per hour)
(b) Small price change and large quantity change
Initially, the price is $20 a pizza and the quantity sold is 10
pizzas an hour. Then supply increases from S0 to S1. In part
(a), the price falls by $15 to $5 a pizza, and the quantity
increases by 3 to 13 pizzas an hour. In part (b), the price
falls by only $5 to $15 a pizza, and the quantity increases
by 7 to 17 pizzas an hour. The price change is smaller and
the quantity change is larger in case (b) than in case (a).
The quantity demanded is more responsive to the change in
the price in case (b) than in case (a).
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Price Elasticity of Demand
Calculating Price Elasticity of Demand
To use this formula, we need to know the quantities
demanded at different prices when all other influences on buying plans remain the same. Suppose we
have the data on prices and quantities demanded of
pizza and we calculate the price elasticity of demand
for pizza.
Figure 4.2 zooms in on the demand curve for
pizza and shows how the quantity demanded
responds to a small change in price. Initially, the
price is $20.50 a pizza and 9 pizzas an hour are
soldthe original point in the figure. The price then
falls to $19.50 a pizza, and the quantity demanded
increases to 11 pizzas an hourthe new point in the
figure. When the price falls by $1 a pizza, the quantity demanded increases by 2 pizzas an hour.
To calculate the price elasticity of demand, we
express the changes in price and quantity demanded as
percentages of the average price and the average quantity. By using the average price and average quantity,
we calculate the elasticity at a point on the demand
curve midway between the original point and the new
point. The original price is $20.50 and the new price is
$19.50, so the average price is $20. The $1 price
decrease is 5 percent of the average price. That is,
P> Pave = 1$1> $202 * 100 = 5%.
The original quantity demanded is 9 pizzas and
the new quantity demanded is 11 pizzas, so the average quantity demanded is 10 pizzas. The 2 pizza
increase in the quantity demanded is 20 percent of
the average quantity. That is,
Q> Qave = 12> 102 * 100 = 20%.
So the price elasticity of demand, which is the percentage change in the quantity demanded (20 percent) divided by the percentage change in price (5
percent) is 4. That is,
%Q
Price elasticity of demand =
%P
20%
=
= 4.
5%
Price (dollars per pizza)
Price elasticity of
demand
Percentage change
in quantity demanded
.
Percentage change in price
Calculating the Elasticity
of Demand
FIGURE 4.2
Original
point
20.50
We calculate the price elasticity of demand by using
the formula:
83
P = $1
Elasticity = 4
20.00
Pave = $20
New
point
19.50
D
Q = 2
Qave = 10
0
9
10
11
Quantity (pizzas per hour)
The elasticity of demand is calculated by using the
formula:*
Price elasticity of demand =
Percentage change
in quantity demanded
Percentage change in price
%Q
=
%P
=
Q> Qave
=
2> 10
P> Pave
1> 20
= 4.
This calculation measures the elasticity at an average price of
$20 a pizza and an average quantity of 10 pizzas an hour.
* In the formula, the Greek letter delta () stands for change in and
% stands for percentage change in.
animation
Average Price and Quantity Notice that we use the
average price and average quantity. We do this
because it gives the most precise measurement of
elasticityat the midpoint between the original
price and the new price. If the price falls from
$20.50 to $19.50, the $1 price change is 4.9 percent
of $20.50. The 2 pizza change in quantity is 22.2
percent of 9 pizzas, the original quantity. So if we
use these numbers, the price elasticity of demand is
22.2 divided by 4.9, which equals 4.5. If the price
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a negative number. But it is the magnitude, or
absolute value, of the price elasticity of demand that
tells us how responsive the quantity demanded is. So
to compare price elasticities of demand, we use the
magnitude of the elasticity and ignore the minus sign.
rises from $19.50 to $20.50, the $1 price change is
5.1 percent of $19.50. The 2 pizza change in quantity is 18.2 percent of 11 pizzas, the original quantity. So if we use these numbers, the price elasticity
of demand is 18.2 divided by 5.1, which equals 3.6.
By using percentages of the average price and average quantity, we get the same value for the elasticity
regardless of whether the price falls from $20.50 to
$19.50 or rises from $19.50 to $20.50.
Inelastic and Elastic Demand
Figure 4.3 shows three demand curves that cover
the entire range of possible elasticities of demand.
In Fig. 4.3(a), the quantity demanded is constant
regardless of the price. If the quantity demanded
remains constant when the price changes, then the
price elasticity of demand is zero and the good is said
to have a perfectly inelastic demand. One good that has
a very low price elasticity of demand (perhaps zero
over some price range) is insulin. Insulin is of such
importance to some diabetics that if the price rises or
falls, they do not change the quantity they buy.
If the percentage change in the quantity demanded
equals the percentage change in the price, then the
price elasticity equals 1 and the good is said to have a
unit elastic demand. The demand in Fig. 4.3(b) is an
example of a unit elastic demand.
Between the cases shown in Fig. 4.3(a) and Fig.
4.3(b) is the general case in which the percentage
change in the quantity demanded is less than the
percentage change in the price. In this case, the price
elasticity of demand is between zero and 1 and the
good is said to have an inelastic demand. Food and
shelter are examples of goods with inelastic demand.
Percentages and Proportions Elasticity is the ratio of
two percentage changes. So when we divide one percentage change by another, the 100s cancel. A percentage change is a proportionate change multiplied by 100.
The proportionate change in price is P/Pave, and the
proportionate change in quantity demanded is
Q/Qave. So if we divide Q/Qave by P/Pave we get the
same answer as we get by using percentage changes.
A Units-Free Measure Now that youve calculated a
price elasticity of demand, you can see why it is a
units-free measure. Elasticity is a units-free measure
because the percentage change in each variable is
independent of the units in which the variable is
measured. And the ratio of the two percentages is a
number without units.
Minus Sign and Elasticity When the price of a good
rises, the quantity demanded decreases. Because a positive change in price brings a negative change in the
quantity demanded, the price elasticity of demand is
D1
Price
Price
Price
Inelastic and Elastic Demand
FIGURE 4.3
Elasticity = 0
Elasticity =
Elasticity = 1
12
12
12
6
6
6
D3
D2
0
Quantity
(a) Perfectly inelastic demand
0
1
(b) Unit elastic demand
Each demand illustrated here has a constant elasticity. The
demand curve in part (a) illustrates the demand for a good
that has a zero elasticity of demand. The demand curve in
animation
2
3
Quantity
0
Quantity
(c) Perfectly elastic demand
part (b) illustrates the demand for a good with a unit elasticity of demand. And the demand curve in part (c) illustrates
the demand for a good with an infinite elasticity of demand.
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Price Elasticity of Demand
If the quantity demanded changes by an infinitely large percentage in response to a tiny price
change, then the price elasticity of demand is infinity and the good is said to have a perfectly elastic
demand. Figure 4.3(c) shows a perfectly elastic
demand. An example of a good that has a very
high elasticity of demand (almost infinite) is a soft
drink from two campus machines located side by
side. If the two machines offer the same soft drinks
for the same price, some people buy from one
machine and some from the other. But if one
machines price is higher than the others, by even
a small amount, no one will buy from the machine
with the higher price. Soft drinks from the two
machines are perfect substitutes. The demand for a
good that has a perfect substitute is perfectly elastic.
Between the cases in Fig. 4.3(b) and Fig. 4.3(c)
is the general case in which the percentage change in
the quantity demanded exceeds the percentage change
in price. In this case, the price elasticity of demand is
greater than 1 and the good is said to have an elastic
demand. Automobiles and furniture are examples of
goods that have elastic demand.
=
Price elasticity of demand =
Q> Qave
P> Pave
20> 10
10> 20
= 4.
That is, the price elasticity of demand at an average
price of $20 a pizza is 4.
Next, suppose that the price falls from $15 to $10 a
pizza. The quantity demanded increases from 20 to 30
pizzas an hour. The average price is now $12.50 a
pizza, and the average quantity is 25 pizzas an hour. So
5> 12.50
20> 40
10> 5
= 1> 4.
That is, the price elasticity of demand at an average
price of $5 a pizza is 1/4.
Youve now seen how elasticity changes along a
straight-line demand curve. At the midpoint of the
curve, demand is unit elastic. Above the midpoint,
demand is elastic. Below the midpoint, demand is
inelastic.
Price (dollars per pizza)
Elasticity and slope are not the same, but they are
related. To understand how they are related, lets
look at elasticity along a straight-line demand
curvea demand curve that has a constant slope.
Figure 4.4 illustrates the calculation of elasticity
along a straight-line demand curve. First, suppose the
price falls from $25 to $15 a pizza. The quantity
demanded increases from zero to 20 pizzas an hour.
The average price is $20 a pizza, and the average
quantity is 10 pizzas. So
10> 25
= 1.
That is, the price elasticity of demand at an average
price of $12.50 a pizza is 1.
Finally, suppose that the price falls from $10 to
zero. The quantity demanded increases from 30 to 50
pizzas an hour. The average price is now $5 a pizza,
and the average quantity is 40 pizzas an hour. So
Elasticity Along a StraightLine Demand Curve
FIGURE 4.4
Elasticity Along a Straight-Line
Demand Curve
Price elasticity of demand =
Price elasticity of demand =
85
25.00
Elasticity = 4
20.00
Elastic
15.00
Elasticity = 1
12.50
Inelastic
10.00
/
Elasticity =14
5.00
0
10
20 25
30
40
50
Quantity (pizzas per hour)
On a straight-line demand curve, elasticity decreases as the
price falls and the quantity demanded increases. Demand is
unit elastic at the midpoint of the demand curve (elasticity is
1). Above the midpoint, demand is elastic; below the midpoint, demand is inelastic.
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CHAPTER 4 Elasticity
The total revenue from the sale of a good equals the
price of the good multiplied by the quantity sold.
When a price changes, total revenue also changes.
But a cut in the price does not always decrease total
revenue. The change in total revenue depends on the
elasticity of demand in the following way:
If demand is elastic, a 1 percent price cut increases
the quantity sold by more than 1 percent and total
revenue increases.
If a price cut increases total revenue, demand is
elastic.
If a price cut decreases total revenue, demand is
inelastic.
If a price cut leaves total revenue unchanged,
demand is unit elastic.
25.00
Elastic
demand
20.00
Unit
elastic
15.00
12.50
10.00
If demand is inelastic, a 1 percent price cut
increases the quantity sold by less than 1 percent
and total revenue decreases.
If demand is unit elastic, a 1 percent price cut
increases the quantity sold by 1 percent and total
revenue does not change.
In Fig. 4.5(a), over the price range from $25 to
$12.50, demand is elastic. Over the price range from
$12.50 to zero, demand is inelastic. At a price of
$12.50, demand is unit elastic.
Figure 4.5(b) shows total revenue. At a price of
$25, the quantity sold is zero, so total revenue
is zero. At a price of zero, the quantity demanded
is 50 pizzas an hour and total revenue is again zero.
A price cut in the elastic range brings an increase in
total revenuethe percentage increase in the quantity demanded is greater than the percentage
decrease in price. A price cut in the inelastic range
brings a decrease in total revenuethe percentage
increase in the quantity demanded is less than the
percentage decrease in price. At unit elasticity, total
revenue is at a maximum.
Figure 4.5 shows how we can use this relationship between elasticity and total revenue to estimate elasticity using the total revenue test. The
total revenue test is a method of estimating the price
elasticity of demand by observing the change in
total revenue that results from a change in the
price, when all other influences on the quantity
sold remain the same.
Elasticity and Total Revenue
FIGURE 4.5
Price (dollars per pizza)
Total Revenue and Elasticity
Inelastic
demand
5.00
25
0
50
Quantity (pizzas per hour)
(a) Demand
Total revenue (dollars)
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350.00
Maximum
total revenue
312.50
250.00
200.00
150.00
100.00
50.00
When demand
is elastic, a
price cut
increases
total revenue
0
When demand
is inelastic, a
price cut
decreases
total revenue
25
50
Quantity (pizzas per hour)
(b) Total revenue
When demand is elastic, in the price range from $25 to
$12.50, a decrease in price (part a) brings an increase in
total revenue (part b). When demand is inelastic, in the
price range from $12.50 to zero, a decrease in price (part
a) brings a decrease in total revenue (part b). When
demand is unit elastic, at a price of $12.50 (part a), total
revenue is at a maximum (part b).
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Price Elasticity of Demand
Your Expenditure and Your Elasticity
When a price changes, the change in your expenditure
on the good depends on your elasticity of demand.
If your demand is elastic, a 1 percent price cut increases the quantity you buy by more than 1 percent and your expenditure on the item increases.
If your demand is inelastic, a 1 percent price cut
increases the quantity you buy by less than 1 percent and your expenditure on the item decreases.
If your demand is unit elastic, a 1 percent price
cut increases the quantity you buy by 1 percent
and your expenditure on the item does not change.
So if you spend more on an item when its price
falls, your demand for that item is elastic; if you spend
the same amount, your demand is unit elastic; and if
you spend less, your demand is inelastic.
The Factors That Influence the
Elasticity of Demand
Some Real-World Elasticities
of Demand
Elastic and Inelastic Demand
The real-world elasticities of demand in the table range
from 1.52 for metals, the item with the most elastic
demand in the table, to 0.05 for oil, the item with the
most inelastic demand in the table.
Oil and food, which have poor substitutes and inelastic demand, might be classified as necessities. Furniture
and motor vehicles, which have good substitutes and
elastic demand, might be classified as luxuries.
Price Elasticities of Demand
Good or Service
Elasticity
Elastic Demand
Metals
1.52
What makes the demand for some goods elastic and
the demand for others inelastic? The elasticity of
demand for a good depends on
The closeness of substitutes
The proportion of income spent on the good
The time elapsed since the price change
Electrical engineering products
1.39
Professional services
1.09
Closeness of Substitutes The closer the substitutes for a
Transportation services
1.03
good or service, the more elastic is the demand for it.
For example, oil from which we make gasoline has substitutes but none that are currently very close (imagine
a steam-driven, coal-fueled car). So the demand for oil
is inelastic. Plastics are close substitutes for metals, so
the demand for metals is elastic.
The degree of substitutability between two
goods also depends on how narrowly (or broadly)
we define them. For example, a personal computer
has no really close substitutes, but a Dell PC is a
close substitute for a Hewlett-Packard PC. So the
elasticity of demand for personal computers is
lower than the elasticity of demand for a Dell or a
Hewlett-Packard.
In everyday language we call goods such as food
and shelter necessities and goods such as exotic vacations luxuries. A necessity is a good that has poor substitutes and that is crucial for our well-being. So
generally, a necessity has an inelastic demand.
A luxury is a good that usually has many substitutes, one of which is not buying it. So a luxury generally has an elastic demand.
87
Mechanical engineering products
1.30
Furniture
1.26
Motor vehicles
1.14
Instrument engineering products
1.10
Inelastic Demand
Gas, electricity, and water
0.92
Chemicals
0.89
Drinks (all types)
0.78
Clothing
0.64
Tobacco
0.61
Banking and insurance services
0.56
Housing services
0.55
Agricultural and fish products
0.42
Books, magazines, and newspapers
0.34
Food
0.12
Oil
0.05
Sources of data: Ahsan Mansur and John Whalley, Numerical
Specification of Applied General Equilibrium Models: Estimation,
Calibration, and Data, in Applied General Equilibrium Analysis, eds.
Herbert E. Scarf and John B. Shoven (New York: Cambridge University
Press, 1984), 109, and Henri Theil, Ching-Fan Chung, and James L.
Seale, Jr., Advances in Econometrics, Supplement I, 1989, International
Evidence on Consumption Patterns (Greenwich, Conn.: JAI Press Inc.,
1989), and Geoffrey Heal, Columbia University, Web site.
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Proportion of Income Spent on the Good Other
things remaining the same, the greater the proportion
of income spent on a good, the more elastic is the
demand for it.
Think about your own elasticity of demand for
chewing gum and housing. If the price of chewing
gum doubles, you consume almost as much gum as
before. Your demand for gum is inelastic. If apartment
rents double, you shriek and look for more students
Price Elasticities of Demand for Food
How Inelastic?
As the average income in a country increases and the
proportion of income spent on food decreases, the
demand for food becomes more inelastic.
The figure shows that the price elasticity of demand
for food (green bars) is greatest in the poorest countries.
The larger the proportion of income spent on food, the
larger is the price elasticity of demand for food. In
Tanzania, a nation where the average income is onethirtieth that of the United States and where 62 percent
of income is spent on food, the price elasticity of
demand for food is 0.77. In contrast, in the United
States, where 12 percent of income is spent on food,
the price elasticity of demand for food is 0.12.
Food budget
(percentage of income)
Country
Tanzania
62
India
to share accommodation with you. Your demand for
housing is not as inelastic as your demand for gum.
Why the difference? Housing takes a large proportion
of your budget, and gum takes only a tiny proportion.
You dont like either price increase, but you hardly
notice the higher price of gum, while the higher rent
puts your budget under severe strain.
Time Elapsed Since Price Change The longer the
time that has elapsed since a price change, the more
elastic is demand. When the price of oil increased by
400 percent during the 1970s, people barely changed
the quantity of oil and gasoline they bought. But
gradually, as more efficient auto and airplane engines
were developed, the quantity bought decreased. The
demand for oil has become more elastic as more time
has elapsed since the huge price hike. Similarly, when
the price of a PC fell, the quantity of PCs demanded
increased only slightly at first. But as more people
have become better informed about the variety of
ways of using a PC, the quantity of PCs bought has
increased sharply. The demand for PCs has become
more elastic.
Review Quiz
1
2
56
Korea
40
Brazil
35
Greece
31
3
Spain
28
France
17
Germany
15
Canada
14
United States
12
4
0
0.2
0.4
0.6
0.8
1.0
Price elasticity of demand
Price Elasticities in 10 Countries
Source of data: Henri Theil, Ching-Fan Chung, and James L. Seale, Jr.,
Advances in Econometrics, Supplement 1, 1989, International Evidence
on Consumption Patterns (Greenwich, Conn.: JAI Press, Inc., 1989).
5
6
Why do we need a units-free measure of the
responsiveness of the quantity demanded of a
good or service to a change in its price?
Define the price elasticity of demand and show
how it is calculated.
Why, when we calculate the price elasticity of
demand, do we express the change in price as a
percentage of the average price and the change in
quantity as a percentage of the average quantity?
What is the total revenue test? Explain how it
works.
What are the main influences on the elasticity
of demand that make the demand for some
goods elastic and the demand for other goods
inelastic?
Why is the demand for a luxury generally more
elastic than the demand for a necessity?
Work Study Plan 4.1
and get instant feedback.
Youve now completed your study of the price
elasticity of demand. Two other elasticity concepts tell
us about the effects of other influences on demand.
Lets look at these other elasticities of demand.
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More Elasticities of Demand
Back at the pizzeria, you are trying to work out how
a price rise by the burger shop next door will affect
the demand for your pizza. You know that pizzas
and burgers are substitutes. And you know that
when the price of a substitute for pizza rises, the
demand for pizza increases. But by how much?
You also know that pizza and soft drinks are complements. And you know that if the price of a complement of pizza rises, the demand for pizza decreases. So
you wonder, by how much will a rise in the price of a
soft drink decrease the demand for your pizza?
To answer these questions, you need to calculate
the cross elasticity of demand. Lets examine this elasticity measure.
Cross Elasticity of Demand
We measure the influence of a change in the price of
a substitute or complement by using the concept of
the cross elasticity of demand. The cross elasticity of
demand is a measure of the responsiveness of the
demand for a good to a change in the price of a substitute or complement, other things remaining the
same. We calculate the cross elasticity of demand by
using the formula:
Cross elasticity
of demand
The change in the price of a burger, a substitute for
pizza, is +$1the new price, $2.50, minus the original
price, $1.50. The average price is $2 a burger. So the
price of a burger rises by 50 percent. That is,
P> Pave = 1 + 1> 22 * 100 = + 50%.
So the cross elasticity of demand for pizza with
respect to the price of a burger is
+ 20%
= 0.4.
+ 50%
Figure 4.6 illustrates the cross elasticity of demand.
Pizza and burgers are substitutes. Because they are substitutes, when the price of a burger rises, the demand
for pizza increases. The demand curve for pizza shifts
rightward from D0 to D1. Because a rise in the price of a
burger brings an increase in the demand for pizza, the
cross elasticity of demand for pizza with respect to the
price of a burger is positive. Both the price and the
quantity change in the same direction.
FIGURE 4.6
Cross Elasticity of Demand
Price of pizza
More Elasticities of Demand
Price of a burger,
a substitute, rises.
Positive cross elasticity
Percentage change
in quantity demanded
.
Percentage change in price of
a substitute or complement
The cross elasticity of demand can be positive or
negative. It is positive for a substitute and negative for
a complement.
Substitutes Suppose that the price of pizza is constant and people buy 9 pizzas an hour. Then the price
of a burger rises from $1.50 to $2.50. No other influence on buying plans changes and the quantity of
pizzas bought increases to 11 an hour.
The change in the quantity demanded is +2
pizzasthe new quantity, 11 pizzas, minus the original quantity, 9 pizzas. The average quantity is 10
pizzas. So the quantity of pizzas demanded increases
by 20 percent. That is,
Q> Qave = 1 + 2> 102 * 100 = + 20%.
89
Price of a soft drink,
a complement,
rises. Negative
cross elasticity
0
D1
D0
D2
Quantity of pizza
A burger is a substitute for pizza. When the price of a
burger rises, the demand for pizza increases and the
demand curve for pizza shifts rightward from D0 to D1. The
cross elasticity of demand is positive.
A soft drink is a complement of pizza. When the price
of a soft drink rises, the demand for pizza decreases and
the demand curve for pizza shifts leftward from D0 to D2.
The cross elasticity of demand is negative.
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Complements Now suppose that the price of pizza is
constant and 11 pizzas an hour are bought. Then the
price of a soft drink rises from $1.50 to $2.50. No
other influence on buying plans changes and the
quantity of pizzas bought falls to 9 an hour.
The change in the quantity demanded is the
opposite of what weve just calculated: The quantity
of pizzas demanded decreases by 20 percent (20%).
The change in the price of a soft drink, a
complement of pizza, is the same as the percentage
change in the price of a burger that weve just calculated. The price rises by 50 percent (+50%). So the
cross elasticity of demand for pizza with respect to
the price of a soft drink is
- 20%
= - 0.4.
+ 50%
Because pizza and soft drinks are complements,
when the price of a soft drink rises, the demand for
pizza decreases. The demand curve for pizza shifts
leftward from D0 to D2. Because a rise in the price of
a soft drink brings a decrease in the demand for pizza,
the cross elasticity of demand for pizza with respect
to the price of a soft drink is negative. The price and
quantity change in opposite directions.
The magnitude of the cross elasticity of demand
determines how far the demand curve shifts. The
larger the cross elasticity (absolute value), the greater
is the change in demand and the larger is the shift in
the demand curve.
If two items are close substitutes, such as two
brands of spring water, the cross elasticity is large. If
two items are close complements, such as movies and
popcorn, the cross elasticity is large.
If two items are somewhat unrelated to each other,
such as newspapers and orange juice, the cross elasticity is smallperhaps even zero.
The income elasticity of demand is calculated by
using the formula:
Income elasticity
of demand
Percentage change
in quantity demanded
.
Percentage change in income
Income elasticities of demand can be positive or
negative and they fall into three interesting ranges:
Greater than 1 (normal good, income elastic)
Positive and less than 1 (normal good, income
inelastic)
Negative (inferior good)
Income Elastic Demand Suppose that the price of
pizza is constant and 9 pizzas an hour are bought.
Then incomes rise from $975 to $1,025 a week. No
other influence on buying plans changes and the
quantity of pizzas sold increases to 11 an hour.
The change in the quantity demanded is +2 pizzas.
The average quantity is 10 pizzas, so the quantity
demanded increases by 20 percent. The change in
income is +$50 and the average income is $1,000, so
incomes increase by 5 percent. The income elasticity
of demand for pizza is
20%
= 4.
5%
The demand for pizza is income elastic. The percentage increase in the quantity of pizza demanded
exceeds the percentage increase in income. When the
demand for a good is income elastic, the percentage of
income spent on that good increases as income increases.
Income Elasticity of Demand
Income Inelastic Demand If the income elasticity of
demand is positive but less than 1, demand is income
inelastic. The percentage increase in the quantity
demanded is positive but less than the percentage
increase in income. When the demand for a good is
income inelastic, the percentage of income spent on that
good decreases as income increases.
Suppose the economy is expanding and people are
enjoying rising incomes. This prosperity brings an
increase in the demand for most types of goods and
services. But by how much will the demand for pizza
increase? The answer depends on the income elasticity
of demand, which is a measure of the responsiveness
of the demand for a good or service to a change in
income, other things remaining the same.
Inferior Goods If the income elasticity of demand is
negative, the good is an inferior good. The quantity
demanded of an inferior good and the amount spent
on it decrease when income increases. Goods in this
category include small motorcycles, potatoes, and
rice. Low-income consumers buy most of these
goods.
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More Elasticities of Demand
Income Elasticities of Demand
Necessities and Luxuries
The table shows estimates of some real-world
income elasticities of demand. The demand for a
necessity such as food or clothing is income inelastic, while the demand for a luxury such as transportation, which includes airline and foreign travel,
is income elastic.
But what is a necessity and what is a luxury
depends on the level of income. For people with a
low income, food and clothing can be luxuries. So
the level of income has a big effect on income elasticities of demand. The figure shows this effect on
the income elasticity of demand for food in 10
countries. In countries with low incomes, such as
Tanzania and India, the income elasticity of demand
for food is high. In countries with high incomes,
such as the United States, the income elasticity of
91
demand for food is low. That is as income increases,
the income elasticity of demand for food decreases.
Low-income consumers spend a larger percentage of
any increase in income on food than do highincome consumers.
Country
Income
(percentage of U.S. income)
Tanzania
3.3
India
5.2
Korea
20.4
Brazil
36.8
Greece
41.3
Spain
55.9
Japan
61.6
France
81.1
Canada
99.2
United States
100.0
Some Real-World Income Elasticities of Demand
0
0.2
0.4
0.6
0.8
1.0
Income elasticity of demand
Income Elastic Demand
Airline travel
5.82
Movies
3.41
Foreign travel
3.08
Electricity
1.94
Restaurant meals
1.61
Income Elasticities in 10 Countries
Review Quiz
Local buses and trains
1.38
1
Haircuts
1.36
2
Automobiles
1.07
3
Income Inelastic Demand
Tobacco
0.86
Alcoholic drinks
0.62
Furniture
0.53
Clothing
0.51
Newspapers and magazines
0.38
Telephone
0.32
Food
0.14
Sources of data: H.S. Houthakker and Lester D. Taylor, Consumer
Demand in the United States (Cambridge, Mass.: Harvard University
Press, 1970), and Henri Theil, Ching-Fan Chung, and James L.
Seale, Jr., Advances in Econometrics, Supplement 1, 1989,
International Evidence on Consumption Patterns (Greenwich, Conn.:
JAI Press, Inc., 1989).
4
5
What does the cross elasticity of demand measure?
What does the sign (positive versus negative) of
the cross elasticity of demand tell us about the
relationship between two goods?
What does the income elasticity of demand
measure?
What does the sign (positive versus negative) of
the income elasticity of demand tell us about a
good?
Why does the level of income influence the
magnitude of the income elasticity of demand?
Work Study Plan 4.2
and get instant feedback.
Youve now completed your study of the cross
elasticity of demand and the income elasticity of
demand. Lets look at the other side of the market
and examine the elasticity of supply.
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CHAPTER 4 Elasticity
You know that when demand increases, the equilibrium price rises and the equilibrium quantity
increases. But does the price rise by a large amount
and the quantity increase by a little? Or does the
price barely rise and the quantity increase by a large
amount?
The answer depends on the responsiveness of the
quantity supplied to a change in price. You can see
why by studying Fig. 4.7, which shows two possible
scenarios in a local pizza market. Figure 4.7(a) shows
one scenario, and Fig. 4.7(b) shows the other.
In both cases, demand is initially D0. In part (a),
supply is shown by the supply curve In SA. part (b),
supply is shown by the supply curve SB. Initially, in
both cases, the price is $20 a pizza and the equilibrium quantity is 10 pizzas an hour.
Now increases in incomes and population increase
the demand for pizza. The demand curve shifts rightward to D1. In case (a), the price rises by $10 to $30
a pizza, and the quantity increases by only 3 to 13
pizzas an hour. In contrast, in case (b), the price rises
by only $1 to $21 a pizza, and the quantity increases
by 10 to 20 pizzas an hour.
The different outcomes arise from differing degrees
of responsiveness of the quantity supplied to a change
in price. We measure the degree of responsiveness by
using the concept of the elasticity of supply.
FIGURE 4.7
Price (dollars per pizza)
Elasticity of Supply
40.00
How a Change in Demand
Changes Price and Quantity
An increase in
demand brings ...
SA
30.00
20.00
... a large
price rise ...
D1
10.00
D0
... and a small
quantity increase
0
5
10
13 15
20
25
Quantity (pizzas per hour)
(a) Large price change and small quantity change
Price (dollars per pizza)
92
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40.00
An increase
in demand
brings ...
30.00
21.00
20.00
SB
D1
... a small
price rise ...
Calculating the Elasticity of Supply
The elasticity of supply measures the responsiveness of
the quantity supplied to a change in the price of a
good when all other influences on selling plans remain
the same. It is calculated by using the formula:
Elasticity
of supply
Percentage change in
quantity supplied
.
Percentage change in price
We use the same method that you learned when you
studied the elasticity of demand. (Refer back to p.
87 to check this method.) Lets calculate the elasticity of supply along the supply curves in Fig. 4.7.
In Fig. 4.7(a), when the price rises from $20 to
$30, the price rise is $10 and the average price is $25,
so the price rises by 40 percent of the average price.
The quantity increases from 10 to 13 pizzas an hour,
10.00
D0
... and a large
quantity increase
0
5
10
15
20
25
Quantity (pizzas per hour)
(b) Small price change and large quantity change
Initially, the price is $20 a pizza, and the quantity sold is 10
pizzas an hour. Then the demand for pizza increases. The
demand curve shifts rightward to D1. In part (a), the price rises
by $10 to $30 a pizza, and the quantity increases by 3 to 13
pizzas an hour. In part (b), the price rises by only $1 to $21 a
pizza, and the quantity increases by 10 to 20 pizzas an hour.
The price change is smaller and the quantity change is larger
in case (b) than in case (a). The quantity supplied is more
responsive to a change in the price in case (b) than in case (a).
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Elasticity of Supply
The Factors That Influence the
Elasticity of Supply
so the increase is 3 pizzas, the average quantity is 11.5
pizzas an hour, and the quantity increases by 26 percent. The elasticity of supply is equal to 26 percent
divided by 40 percent, which equals 0.65.
In Fig. 4.7(b), when the price rises from $20 to
$21, the price rise is $1 and the average price is
$20.50, so the price rises by 4.9 percent of the average price. The quantity increases from 10 to 20 pizzas
an hour, so the increase is 10 pizzas, the average
quantity is 15 pizzas, and the quantity increases by
67 percent. The elasticity of supply is equal to 67
percent divided by 4.9 percent, which equals 13.67.
Figure 4.8 shows the range of elasticities of supply.
If the quantity supplied is fixed regardless of the
price, the supply curve is vertical and the elasticity of
supply is zero. Supply is perfectly inelastic. This case
is shown in Fig. 4.8(a). A special intermediate case
occurs when the percentage change in price equals
the percentage change in quantity. Supply is then
unit elastic. This case is shown in Fig. 4.8(b). No
matter how steep the supply curve is, if it is linear
and passes through the origin, supply is unit elastic.
If there is a price at which sellers are willing to offer
any quantity for sale, the supply curve is horizontal
and the elasticity of supply is infinite. Supply is perfectly elastic. This case is shown in Fig. 4.8(c).
The elasticity of supply of a good depends on
Resource substitution possibilities
Time frame for the supply decision
Resource Substitution Possibilities Some goods and
services can be produced only by using unique or
rare productive resources. These items have a low,
perhaps even a zero, elasticity of supply. Other
goods and services can be produced by using commonly available resources that could be allocated to
a wide variety of alternative tasks. Such items have a
high elasticity of supply.
A Van Gogh painting is an example of a good with
a vertical supply curve and a zero elasticity of supply.
At the other extreme, wheat can be grown on land
that is almost equally good for growing corn, so it is
just as easy to grow wheat as corn. The opportunity
cost of wheat in terms of forgone corn is almost constant. As a result, the supply curve of wheat is almost
horizontal and its elasticity of supply is very large.
Similarly, when a good is produced in many different
countries (for example, sugar and beef ), the supply of
the good is highly elastic.
S1
Price
Inelastic and Elastic Supply
Price
Price
FIGURE 4.8
93
S 2A
Elasticity of
supply =
Elasticity of
supply = 0
Elasticity of
supply = 1
S3
S 2B
0
Quantity
(a) Perfectly inelastic supply
0
(b) Unit elastic supply
Each supply illustrated here has a constant elasticity. The
supply curve in part (a) illustrates the supply of a good that
has a zero elasticity of supply. The supply curve in part (b)
illustrates the supply of a good with a unit elasticity of
animation
Quantity
0
Quantity
(c) Perfectly elastic supply
supply. All linear supply curves that pass through the origin
illustrate supplies that are unit elastic. The supply curve in
part (c) illustrates the supply of a good with an infinite elasticity of supply.
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CHAPTER 4 Elasticity
The supply of most goods and services lies
between these two extremes. The quantity produced
can be increased but only by incurring a higher cost.
If a higher price is offered, the quantity supplied
increases. Such goods and services have an elasticity
of supply between zero and infinity.
Time Frame for the Supply Decision To study the
influence of the amount of time elapsed since a price
change, we distinguish three time frames of supply:
1. Momentary supply
2. Long-run supply
3. Short-run supply
When the price of a good rises or falls, the momentary supply curve shows the response of the quantity
supplied immediately following the price change.
Some goods, such as fruits and vegetables, have a
perfectly inelastic momentary supplya vertical supply curve. The quantities supplied depend on cropplanting decisions made earlier. In the case of
oranges, for example, planting decisions have to be
made many years in advance of the crop being available. The momentary supply curve is vertical because,
on a given day, no matter what the price of oranges,
producers cannot change their output. They have
picked, packed, and shipped their crop to market,
and the quantity available for that day is fixed.
In contrast, some goods have a perfectly elastic
momentary supply. Long-distance phone calls are an
example. When many people simultaneously make a
call, there is a big surge in the demand for telephone
cables, computer switching, and satellite time, and
the quantity supplied increases. But the price remains
constant. Long-distance carriers monitor fluctuations
in demand and reroute calls to ensure that the quantity supplied equals the quantity demanded without
changing the price.
The long-run supply curve shows the response of
the quantity supplied to a price change after all the
technologically possible ways of adjusting supply
have been exploited. In the case of oranges, the long
run is the time it takes new plantings to grow to full
maturityabout 15 years. In some cases, the longrun adjustment occurs only after a completely new
production plant has been built and workers have
been trained to operate ittypically a process that
might take several years.
The short-run supply curve shows how the quantity
supplied responds to a price change when only some
of the technologically possible adjustments to production have been made. The short-run response to a
price change is a sequence of adjustments. The first
adjustment that is usually made is in the amount of
labor employed. To increase output in the short run,
firms work their labor force overtime and perhaps
hire additional workers. To decrease their output in
the short run, firms either lay off workers or reduce
their hours of work. With the passage of time, firms
can make additional adjustments, perhaps training
additional workers or buying additional tools and
other equipment.
The short-run supply curve slopes upward because
producers can take actions quite quickly to change
the quantity supplied in response to a price change.
For example, if the price of oranges falls, growers can
stop picking and leave oranges to rot on the trees. Or
if the price rises, they can use more fertilizer and
improved irrigation to increase the yields of their
existing trees. In the long run, they can plant more
trees and increase the quantity supplied even more in
response to a given price rise.
Review Quiz
1
2
3
4
5
Why do we need a units-free measure of the
responsiveness of the quantity supplied of a
good or service to a change in its price?
Define the elasticity of supply and show how it
is calculated.
What are the main influences on the elasticity
of supply that make the supply of some goods
elastic and the supply of other goods inelastic?
Provide examples of goods or services whose elasticities of supply are (a) zero, (b) greater than zero
but less than infinity, and (c) infinity.
How does the time frame over which a supply
decision is made influence the elasticity of
supply? Explain your answer.
Work Study Plan 4.3
and get instant feedback.
You have now learned about the elasticities of
demand and supply. Table 4.1 summarizes all the elasticities that youve met in this chapter. In the next chapter,
we study the efficiency of competitive markets. But first
study Reading Between the Lines on pp. 9697, which
puts the elasticity of demand to work and looks at the
markets for gasoline and automobiles.
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Elasticity of Supply
TABLE 4.1
95
A Compact Glossary of Elasticities
P rice Elasticities of Demand
A relationship is described as
When its magnitude is
Which means that
Perfectly elastic
Infinity
Elastic
Less than infinity
Unit elastic
1
Inelastic
Greater than zero
but less than 1
Zero
The smallest possible increase in price causes an
infinitely large decrease in the quantity demanded*
The percentage decrease in the quantity demanded
but greater than 1 exceeds the percentage increase
in price
The percentage decrease in the quantity demanded
equals the percentage increase in price
The percentage decrease in the quantity demanded
is less than the percentage increase in price
The quantity demanded is the same at all prices
A relationship is described as
When its value is
Which means that
Close substitutes
Large
Substitutes
Positive
Unrelated goods
Zero
Complements
Negative
The smallest possible increase in the price of one
good causes an infinitely large increase in the
quantity demanded of the other good
If the price of one good increases, the quantity
demanded of the other good also increases
If the price of one good increases, the quantity
demanded of the other good remains the same
If the price of one good increases, the quantity
demanded of the other good decreases
Perfectly inelastic
Cross Elasticities of Demand
Income Elasticities of Demand
A relationship is described as
When its value is
Which means that
Income elastic
(normal good)
Income inelastic
(normal good)
Greater than 1
Negative
(inferior good)
Less than zero
The percentage increase in the quantity demanded is
greater than the percentage increase in income
The percentage increase in the quantity demanded is
greater than zero less than the percentage increase
in income
When income increases, quantity demanded
decreases
Less than 1 but
Elasticities of Supply
A relationship is described as
When its magnitude is
Which means that
Perfectly elastic
Infinity
Elastic
Less than infinity but
greater than 1
Greater than zero but
less than 1
Zero
The smallest possible increase in price causes an
infinitely large increase in the quantity supplied
The percentage increase in the quantity supplied
exceeds the percentage increase in the price
The percentage increase in the quantity supplied is
less than the percentage increase in the price
The quantity supplied is the same at all prices
Inelastic
Perfectly inelastic
*
In each description, the directions of change may be reversed. For example, in this case, the smallest possible decrease in price causes an
infinitely large increase in the quantity demanded.
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READING BETWEEN THE LINES
The Elasticities of Demand for Gasoline,
SUVs, and Subcompacts
As Gas Costs Soar, Buyers Are Flocking to Small Cars
Soaring gas prices have turned the steady migration by Americans to smaller cars
into a stampede.
http://www.nytimes.com
May 2, 2008
Sales of Toyotas subcompact Yaris increased 46 percent, and Hondas tiny Fit had a record
month. Fords compact Focus model jumped 32 percent in April from a year earlier. All those
models are rated at more than 30 miles per gallon for highway driving. ...
Sales of traditional SUVs are down more than 25 percent this year. In April, for example,
sales of G.M.s Chevrolet Tahoe fell 35 percent.
Full-size pickup sales have fallen more than 15 percent this year, with Fords industry-leading
F-Series pickup dropping 27 percent in April alone. Sales of pickups, though, are expected to
strengthen with the economy, because of their use as commercial vehicles.
How the downsizing of Americas vehicle fleet will affect fuel consumption is still largely unknown. When gas prices rise, as they are now, many drivers simply drive less to save money.
But there are some indications that the trend toward smaller vehicles will reduce the nations fuel use. In California, motorists bought 4 percent less gasoline in January than they
did the year before, a drop of more than 58 million gallons, according to the Oil Price
Information Service.
That is an incredible year-over-year drop, said Tom Kloza, the organizations chief oil analyst. Some of it clearly has to do with changes in the vehicle fleet.
Copyright 2008 The New York Times Company. Reprinted with permission. Further reproduction prohibited.
Essence of the Story
Faced with high gas prices, Americans are substituting
smaller cars for SUVs.
Toyota Yaris sales increased 46 percent and Ford
Focus sales increased 32 percent in April 2008 from a
year earlier.
96
Sales of SUVs decreased by more than 25 percent in
2008 and Chevrolet Tahoe sales fell 35 percent.
Full-size pickup sales decreased more than 15 percent
in 2008 and Ford F-Series pickup sales decreased by
27 percent in April 2008.
The effect of a downsized vehicle fleet on fuel consumption is unknown.
In California, gasoline consumption decreased by 4
percent in January 2008 from a year earlier.
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Economic Analysis
Using data provided in this news article and by the Energy Information Administration, and assuming that no other
influences on buying plans changed, we can estimate the
price elasticity of demand for gasoline in California.
Price (dollars per gallon)
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Table 1 summarizes the gasoline price and quantity
data and, using the midpoint method, calculates the
price elasticity of demand.
3.50
New point
3.09
Elasticity = 0.14
P = 0.80
2.69
Original point
Pave
2.29
Q = 58
Table 1 Price Elasticity of Demand for Gasoline in California
January-07
January-08
Change
Average
% change
Elasticity
1450
1392
58
1421
4.1
2.29
3.09
0.80
2.69
29.7
0.14
Figure 1 illustrates the changes in price and quantity
and the elasticity calculation.
Table 2 Cross Elasticities of Demand for
Vehicles in the United States
Vehicle
Toyota Yaris
Ford Focus
Chevrolet Tahoe
Ford F-Series
Price of gasoline
Apr-07 Apr-08
% Cross elasticity
Number
change of demand
7,323
16,626
10,980
56,692
2.89
11,434
23,850
8,139
44,813
3.51
43.8
35.7
29.7
23.4
19.4
2.3
1.8
1.5
1.2
The cross elasticities of demand are calculated using
the formula on p. 93.
The cross elasticities of demand for the Yaris and Focus
are positive and large. A rise in the price of gasoline
increases the demand for these vehicles. A small car
and gasoline are substitutesa smaller car is used in
place of a large gas bill. Figure 2 illustrates the cross
elasticity of demand for small vehicles.
Positive cross elasticity:
price of gasoline rises
and demand for small
cars increases
14,000
D0
0
7,323
11,434
Quantity (cars per month)
Figure 2 Cross elasticity: Yaris and price of gasoline
55,000
Negative cross elasticity:
price of gasoline rises
and demand for large
vehicles decreases
35,000
D0
D1
(dollars per gallon)
24,000
D1
The estimated price elasticity of demand for gasoline in
California is 0.14, which means that the demand is inelastic. A large percentage change in price brings a
small percentage change in the quantity of gasoline
demanded.
Table 2 shows the quantities sold of four vehicles and
the price of gasoline in April 2007 and April 2008
and calculates some cross elasticities of demand.
1,392
1,421
1,450
Quantity (millions of gallons per month)
Figure 1 Price elasticity of demand for gasoline
Price (dollars per vehicle)
0
Price
(dollars per gallon)
Price (dollars per car)
Quantity
(millions of gallons)
D
Qave
0
8,139
10,980
Quantity (vehicles per month)
Figure 3 Cross elasticity: Tahoe and price of gasoline
The cross elasticity of demand for the Tahoe and
F-Series are negative and large. A rise in the price of
gasoline decreases the demand for these vehicles. A
large vehicle and gasoline are complements. Figure 3 illustrates the cross elasticity of demand for large vehicles.
97
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CHAPTER 4 Elasticity
SUMMARY
Key Points
Price Elasticity of Demand (pp. 8288)
Elasticity is a measure of the responsiveness of the
quantity demanded of a good to a change in its
price, other things remaining the same.
Price elasticity of demand equals the percentage
change in the quantity demanded divided by the
percentage change in the price.
The larger the magnitude of the price elasticity of
demand, the greater is the responsiveness of the
quantity demanded to a given price change.
If demand is elastic, a cut in price leads to an
increase in total revenue. If demand is unit elastic,
a cut in price leaves total revenue unchanged. And
if demand is inelastic, a cut in price leads to a
decrease in total revenue.
Price elasticity of demand depends on how easily
one good serves as a substitute for another, the
proportion of income spent on the good, and the
length of time elapsed since the price change.
More Elasticities of Demand (pp. 8991)
Elasticity of Supply (pp. 9295)
Cross elasticity of demand measures the responsiveness of the demand for one good to a change
in the price of a substitute or a complement, other
things remaining the same.
The cross elasticity of demand with respect to the
price of a substitute is positive. The cross elasticity
of demand with respect to the price of a complement is negative.
Income elasticity of demand measures the responsiveness of demand to a change in income, other
things remaining the same. For a normal good, the
income elasticity of demand is positive. For an
inferior good, the income elasticity of demand is
negative.
When the income elasticity of demand is greater
than 1 (income elastic), the percentage of
income spent on the good increases as income
increases.
When the income elasticity of demand is less than
1 (income inelastic and inferior), the percentage of
income spent on the good decreases as income
increases.
Elasticity of supply measures the responsiveness of
the quantity supplied of a good to a change in its
price, other things remaining the same.
The elasticity of supply is usually positive and
ranges between zero (vertical supply curve) and
infinity (horizontal supply curve).
Supply decisions have three time frames: momentary, long run, and short run.
Momentary supply refers to the response of the
quantity supplied to a price change at the instant
that the price changes.
Long-run supply refers to the response of the
quantity supplied to a price change when all the
technologically feasible adjustments in production
have been made.
Short-run supply refers to the response of the
quantity supplied to a price change after some of
the technologically feasible adjustments in production have been made.
Key Figures and Table
Figure 4.2 Calculating the Elasticity
of Demand, 83
Figure 4.3 Inelastic and Elastic Demand, 84
Figure 4.4 Elasticity Along a Straight-Line
Demand Curve, 85
Figure 4.5 Elasticity and Total Revenue, 86
Figure 4.6 Cross Elasticity of Demand, 89
Table 4.1 A Compact Glossary of
Elasticities, 95
Key Terms
Cross elasticity of demand, 89
Elastic demand, 85
Elasticity of supply, 92
Income elasticity of demand, 90
Inelastic demand, 84
Perfectly elastic demand, 85
Perfectly inelastic demand, 84
Price elasticity of demand, 82
Total revenue, 86
Total revenue test, 86
Unit elastic demand, 84
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PROBLEMS and APPLICATIONS
99
Work problems 112 in Chapter 4 Study Plan and get instant feedback.
Work problems 1426 as Homework, a Quiz, or a Test if assigned by your instructor.
1. Rain spoils the strawberry crop. As a result, the
price rises from $4 to $6 a box and the quantity
demanded decreases from 1,000 to 600 boxes a
week. Over this price range,
a. What is the price elasticity of demand?
b. Describe the demand for strawberries.
2. If the quantity of dental services demanded
increases by 10 percent when the price of dental
services falls by 10 percent, is the demand for dental services inelastic, elastic, or unit elastic?
3. The demand schedule for hotel rooms is
Price
Quantity demanded
(dollars per night)
(millions of rooms per night)
200
100
250
80
400
50
500
40
800
25
1,000
20
a. What happens to total revenue if the price falls
from $400 to $250 a night?
b. What happens to total revenue if the price falls
from $250 to $200 a night?
c. At what price is total revenue at a maximum?
Explain and interpret your answer.
d. Is the demand for hotel rooms elastic, unit elastic, or inelastic?
4. The Grip of Gas: Why Youll Pay Through the
Nose to Keep Driving
Drivers in the United States consistently rank as
the least sensitive to changes in gas prices. ... If
prices rose from $3 per gallon to $4 per gallon
and stayed there for a year purchases of gasoline in the United States would fall only about 5
percent.
Slate, September 27, 2005
a. Using the information provided, calculate the
price elasticity of demand for gasoline.
b. Does this measurement indicate that the
demand for gasoline is elastic, unit elastic,
or inelastic?
c. If the price of gasoline rises, will total revenue from gasoline sales increase or decrease? Explain.
5. In 2003, when music downloading first took off,
Universal Music slashed the price of a CD from
an average of $21 to an average of $15. The company said that it expected the price cut to boost
the quantity of CDs sold by 30 percent, other
things remaining the same.
a. What was Universal Musics estimate of the
price elasticity of demand for CDs?
b. Given your answer in a, if you were making
the pricing decision at Universal Music, would
you cut the price, raise the price, or not
change the price? Explain your decision.
6. Why the Tepid Response to Rising
Gasoline Prices?
Estimates of the long-run response to past movements in [gasoline] prices imply that a 10 percent
price rise causes 5 to 10 percent less consumption, other things being equal. ... The nationwide
average price of gasoline surged 53 percent from
1998 to 2004, after adjusting for inflation. Yet
consumption was up 10 percent in this period.
Of course, many other things changed in
this period. Perhaps most important,
[incomes] grew by 19 percent. ... This
would ordinarily be expected to push gasoline sales up about 20 percent ...
The New York Times, October 13, 2005
a. What does the above information tell us about
the responsiveness of the quantity of gasoline
demanded to a change in the price a long time
after the price change occurs?
b. Calculate the income elasticity of demand for
gasoline implied by the above information.
c. If other things remained the same except for the
increase in income and the rise in price, what
would the data for 1998 to 2004 imply about
the price elasticity of demand for gasoline?
d. List all the factors you can think of that might
bias the estimate of the price elasticity of demand for gasoline, using just the data for
1998 to 2004.
7. If a 12 percent rise in the price of orange juice
decreases the quantity of orange juice demanded
by 22 percent and increases the quantity of apple
juice demanded by 14 percent, calculate the
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a. Price elasticity of demand for orange juice.
b. Cross elasticity of demand for apple juice with
respect to the price of orange juice.
8. Swelling Textbook Costs Have College Students
Saying Pass
Textbook prices have been rising at double the rate
of inflation for the past two decades [and]
nearly 60 percent of students nationwide choose
not to buy all the course materials. For students
working to pay for school or for those whose parents sweat every increase in tuition, book prices can
be a nasty surprise. And plenty of students
come up with their own strategies: Hunting down
used copies and selling books back at the end of
the semester; buying online, which is sometimes
cheaper than the campus store; asking professors to
put a copy in the library and waiting around till its
free. Or borrowing, copying, taking careful notes
in classand gambling that the exam questions
dont come from the text.
Washington Post, January 23, 2006
Explain what this news clip implies about
a. The price elasticity of demand for college textbooks.
b. The income elasticity of demand for college
textbooks.
c. The cross elasticity of demand for college textbooks from the campus bookstore with respect
to the online price of a textbook.
9. Home Depot Earnings Hammered
As home prices slump across the country, fewer
people are spending money to renovate their
homes, and the improvements that they are making are not as expensive. People are spending
on small ticket types of repairs, not big ticket
renovations. With gas and food prices increasing people have less extra income to spend on
major home improvements.
CNN, May 20, 2008
a. What does this news clip imply about the income elasticity of demand for big-ticket
home-improvement items?
b. Would the income elasticity of demand be
greater or less than 1? Explain.
10. Spam Sales Rise as Food Costs Soar
Sales of Spamthat much maligned meatare
rising as consumers are turning more to lunch
meats and other lower-cost foods to extend their
already stretched food budgets. Consumers
are quick to realize that meats like Spam and
other processed foods can be substituted for costlier cuts as a way of controlling costs.
AOL Money & Finance, May 28, 2008
a. Is Spam a normal good or inferior good?
Explain.
b. Would the income elasticity of demand for
Spam be negative or positive? Explain.
11. Study Ranks Honolulu Third Highest for
Unaffordable Housing
[Study ranks] Honolulu number 3 in the world for
the most unaffordable housing market in urban
locations. Honolulu is listed only behind Los
Angeles and San Diego and is deemed severely
unaffordable. Where there are significant constraints on the supply of land for residential development, housing inflation has occurred.
Hawaii Reporter, September 11, 2007
a. Would the supply of housing in Honolulu be
elastic or inelastic?
b. Explain how the elasticity of supply plays an
important role in influencing how rapidly
housing prices in Honolulu rise.
12. The demand for illegal drugs is inelastic. Much
of the expenditure on illegal drugs comes from
crime. Assuming these statements to be correct,
a. How will a successful campaign that decreases
the supply of drugs influence the price of illegal drugs and the amount spent on them?
b. What will happen to the amount of crime?
c. What is the most effective way of decreasing
the quantity of illegal drugs bought and
decreasing the amount of drug-related crime?
13. Use the links on MyEconLab (Textbook
Resources, Chapter 4, Web links) to find the
number of gallons in a barrel of oil and the prices
of crude oil and gasoline in the summer of 2007
and 2008.
a. What are the other costs that make up the
total cost of a gallon of gasoline?
b. If the price of crude oil falls by 10 percent, by
what percentage do you expect the price of
gasoline to change, other things remaining the
same?
c. Which demand do you think is more elastic:
that for crude oil or gasoline? Why?
d. Use the concepts of demand, supply, and elasticity to explain recent changes in the prices of
crude oil and gasoline.
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Price (dollars per DVD)
14. With higher fuel costs, airlines raise their fares.
The average fare rises from 75 per passenger
mile to $1.25 per passenger mile and the number
of passenger miles decreases from 2.5 million a
day to 1.5 million a day. Over this price range,
a. What is the price elasticity of demand for air
travel?
b. Describe the demand for air travel.
15. The figure shows the demand for DVD rentals.
6
5
4
3
2
1
D
0
25
50
75
100
125 150
DVDs per day
a. Calculate the elasticity of demand when the
price rises from $3 to $5 a DVD.
b. At what price is the elasticity of demand for
DVDs equal to 1?
16. The demand schedule for computer chips is
Price
Quantity demanded
(dollars per chip)
(millions of chips per year)
200
250
300
350
400
50
45
40
35
30
a. What happens to total revenue if the price
falls from $400 to $350 a chip?
b. What happens to total revenue if the price
falls from $350 to $300 a chip?
c. At what price is total revenue at a maximum?
d. At an average price of $350, is the demand for
chips elastic, inelastic, or unit elastic? Use the
total revenue test to answer this question.
17. In problem 16, at $250 a chip, is the demand for
chips elastic or inelastic? Use the total revenue
test to answer this question.
18. Your price elasticity of demand for bananas is 4.
If the price of bananas rises by 5 percent, what is
101
a. The percentage change in the quantity of bananas you buy?
b. The change in your expenditure on bananas?
19. Why Gasoline Follows Oil Up but Not Down
If it seems like gasoline prices are quick to skyrocket when the price of oil goes up, but then
take their sweet ol time coming back down
when crude prices sink, the answer is simple:
They do. There is a rocket and feather
aspect. The service stations are still selling the
same amount of gasoline when wholesale prices
fall so theres no reason to drop. [Service
stations] typically react [to a spike in oil prices]
by pushing prices higher, even before they
replace their inventories. Eventually, the free
market steps in and prices begin going down
when other nearby stations reduce their price.
CNN, January 12, 2007
a. Explain the link between the elasticity of supply of gasoline and gas price fluctuations.
b. Explain the connection between the elasticity
of demand for gasoline and the rocket and
feather tendency of price fluctuations.
20. As Gasoline Prices Soar, Americans Slowly Adapt
in March, Americans drove 11 billion fewer
miles than in March 2007. People have
recognized that prices are not going down and
are adapting to higher energy cost.
Americans spend 3.7 percent of their disposable income on transportation fuels. At its lowest point, that share was 1.9 percent in 1998,
and at its highest it reached 4.5 percent in
1981. We actually have a lot of choices,
based on what car we drive, where we live, how
much time we choose to drive, and where we
choose to go. For many people, higher energy
costs mean fewer restaurant meals, deferred
weekend outings with the kids, less air travel
and more time closer to home.
International Herald Tribune, May 23, 2008
a. List and explain the elasticities of demand that
are implicitly referred to in the news clip.
b. Explain the factors identified in the news clip
that may make the demand for gasoline
inelastic.
21. When Alexs income increased from $3,000 to
$5,000, he increased his consumption of bagels
from 4 to 8 a month and decreased his consumption of donuts from 12 to 6 a month. Calculate
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Alexs income elasticity of demand for
a. Bagels.
b. Donuts.
22. Wal-Marts Recession-Time Pet Project
Wal-Mart is redefining the pets business in
its stores, including repositioning pet food and
supplies right in front of its other fast-growing
business, baby products. There lies the connection, according to retail industry experts, who
point out that kids and pets tend to be fairly
recession-resistant businesses. Even in a recession,
dogs will be fed and kids will get their toys.
CNN, May 13, 2008
a. What does this news clip imply about the income elasticity of demand for pet food and
baby products?
b. Would the income elasticity of demand be
greater or less than 1? Explain.
23. Netflix to Offer Online Movie Viewing
Online movie rental service Netflix introduced a
new feature Tuesday to allow customers to watch
movies and television series on their personal
computers. Netflix has been competing with
video rental retailer Blockbuster, which has
added an online rental service to the in-store
rental service.
CNN, January 16, 2007
a. How will the offering of online movie viewing
influence the price elasticity of demand for instore movie rentals?
b. Would the cross elasticity of demand for online movies and in-store movie rentals be negative or positive? Explain.
c. Would the cross elasticity of demand for online movies with respect to high-speed Internet service be negative or positive? Explain.
24. To Love, Honor, and Save Money
Nearly half of caterers and event planners surveyed said they were seeing declines in wedding spending in response to the economic slowdown; 12% even reported wedding cancellations
because of financial concerns.
Time, June 2, 2008
a. Based upon this news clip, are wedding events
a normal good or inferior good? Explain.
b. Are wedding events more of a necessity or luxury? Explain.
c. Given your answer to b, would that make the
income elasticity of demand greater than 1,
less than 1, or equal to 1?
25. The table gives the supply schedule of longdistance phone calls.
Price
Quantity supplied
(cents per minute)
(millions of minutes per day)
10
20
30
40
200
400
600
800
Calculate the elasticity of supply when
a. The price falls from 40 cents to 30 cents a
minute.
b. The average price is 20 cents a minute.
26. Study Reading Between the Lines on pp. 9697
and then answer the following questions.
a. What factors other than the price of gasoline
would you expect to influence California motorists planned purchases of gasoline?
b. In which directions would the factors that you
identified in a change the demand for gasoline
in California?
c. How would the changes in the demand for
gasoline have biased our estimate of the price
elasticity of demand for gasoline?
d. Given the influence of the price of gasoline on
the demand for small vehicles and large vehicles, how would you expect the prices of small
vehicles and large vehicles to have changed in
2008?
e. What elasticities do you need to know to predict the magnitude of the changes in the
prices of small vehicles and large vehicles?
f. If the prices of cars did change in 2008 in the
directions that you have predicted in d, how
would these changes impact our estimates of
the cross elasticities of demand for small vehicles and large vehicles with respect to the price
of gasoline?
g. How would you expect the demand for vehicles to change in the long run in response to a
permanent rise in the price of gasoline?