Download Elasticity - Iowa State University Department of Economics

Elasticity
Elasticity and Its
Application
“Ratio of Percentage
Changes”
Chapter 5
i.e. The percentage change in
something over the percentage
change in something.
Copyright © 2001 by Harcourt, Inc.
All rights reserved. Requests for permission to make copies of any part of the
work should be mailed to:
Permissions Department, Harcourt College Publishers,
6277 Sea Harbor Drive, Orlando, Florida 32887-6777.
Elasticity . . .
… is a measure of how much buyers and
sellers respond to changes in market
conditions
u
… allows us to analyze supply and
demand with greater precision.
u
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Price Elasticity of Demand
n
Demand for a good is said to be elastic if
the quantity demanded responds
substantially to a change in price.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Price Elasticity of Demand
u Price elasticity of demandis
the
percentage change in quantity demanded
given a percent change in the price.
u It
is a measure of how much the quantity
demanded of a good responds to a change
in the price of that good.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Determinants of
Price Elasticity of Demand
u Necessities
versus Luxuries
u Availability
n
Demand is said to be inelastic if the
quantity demanded responds only slightly
to changes in the price.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
u Definition
u Time
of Close Substitutes
of the Market
Horizon
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
1
Availability of Close
Substitutes
Necessities vs. Luxuries
n
Necessities tend to have inelastic
demands.
n
Goods with close substitutes tend to have
a more elastic demand because it is easier
for consumers to switch from that good.
n
Ex. Butter vs. Margarine.
Ex. Going to the doctor.
n
Luxuries tend to have elastic demands.
äA small increase in the price of butter
(assuming the price of margarine stays fixed)
could cause a significant decline in the
quantity of butter purchased.
Ex. Buying a yacht.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Definition of the Market
n
n
The elasticity of demand depends on how we
draw the boundaries of the market.
Narrowly defined markets tend to be more
elastic.
ä Ex. The market for white Adidas running shoes.
n
Broadly defined markets tend to be more
inelastic.
ä Ex. The market for shoes.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
The price elasticity of demand is computed
as the percentage change in the quantity
demanded divided by the percentage
change in price.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
n
Goods tend to have more elastic demand
over longer time horizons.
n
Ex. Gas prices rise. In the short run,
people will probably buy somewhat less
gas. However, in the long run, people
may purchase more fuel efficient cars or
move closer to work.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Computing the Price Elasticity
of Demand
Price Elasticity of
of Demand =
Time Horizon
Percentage Change
in Quantity Demanded
Percentage Change
in Price
Computing the Price Elasticity
of Demand
Price elasticity of demand =
Percentage change in quatity 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 percent
10
=
=2
( 2.20 − 2. 00)
10 percent
× 100
2.00
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
2
Computing the Price Elasticity of
Demand Using the Midpoint
Formula
The midpoint formula is preferable when
calculating the price elasticity of demand
because it gives the same answer regardless
of the which point we start at.
(Q2 − Q1 )/[(Q 2 + Q 1 )/2]
Price Elasticity of Demand=
(P2 − P1 )/[(P2 + P1 )/2]
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Ranges of Elasticity
Inelastic Demand
uQuantity demanded does not respond strongly to
price changes.
uPrice elasticity of demand is less thanone.
Elastic Demand
uQuantity demanded responds strongly to changes
in price.
uPrice elasticity of demand is greater thanone.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Computing the Price Elasticity
of Demand
Price
ED =
$5
4
Demand
=
(100- 50)
(100+ 50)/2
(4.00- 5.00)
(4.00+ 5.00)/2
50
100
n
Here are two points of a demand curve.
Calculate the elasticity between these two
points and determine if the elasticity is
elastic, unit elastic, or inelastic.
n
Pt A: P=5, Q=2
Pt B: P=2, Q=4
67 percent
= -3
- 22percent
Demand is price elastic
0
Elasticity Example
Quantity
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
A Variety of Demand Curves
n
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Ranges of Elasticity
u Perfectly
Because the price elasticity
of demand measures how
much quantity demanded
responds to the price, it is
closely related to the slope of
the demand curve.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Inelastic
Quantity demanded does not respond to price
changes.
u Perfectly Elastic
Quantity demanded changes infinitely with any
change in price.
u Unit Elastic
Quantity demanded changes by the same
percentage as the price.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
3
Inelastic Demand
Perfectly Inelastic Demand
- Elasticity is less than 1
- Elasticity equals 0
Price
Price
Demand
1. An
$5
increase
in price... 4
1. A 22% $5
increase
in price... 4
Demand
Quantity
100
2. ...leaves the quantity demanded unchanged.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Quantity
90 100
2. ...leads to a 11% decrease in quantity.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Elastic Demand
Unit Elastic Demand
- Elasticity is greater than 1
- Elasticity equals 1
Price
Price
1. A 22% $5
increase
in price... 4
1. A 22% $5
increase
in price... 4
Demand
Demand
Quantity
80
100
2. ...leads to a 22% decrease in quantity.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Perfectly Elastic Demand
- Elasticity equals infinity
Price
Demand
2. At exactly $4,
consumers will
buy any quantity.
3. At a price below $4,
quantity demanded is infinite.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Elasticity and Total Revenue
Total revenue is the amount paid by buyers
and received by sellers of a good.
u TR = Price * Quantity
u Another term that has a very similar meaning
is total expenditures. Total revenue equals
total expenditures.
u Revenue is the term used from the sellers
perspective
u Expenditures is the term used from the buyers
perspective.
u
1. At any price
above $4, quantity
demanded is zero.
$4
Quantity
50
100
2. ...leads to a 67% decrease in quantity.
Quantity
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
4
Elasticity and Total Revenue
Elasticity and Total Revenue
Price
$4
P x Q = $400
(total revenue)
P
0
Demand
100
Q
Quantity
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Elasticity and Total Revenue:
Inelastic Demand
Price
With an inelastic demand
curve, an increase in price
leads to a decrease in quantity
that is proportionately
smaller. Thus, total revenue
increases.
Price
Elasticity and Total Revenue
…leads to an increase
in total revenue
from$100 to $240
An increase in price
from $1 to $3...
$3
With an elastic demand curve,
an increase in the price leads to
a decrease in quantity demanded
that is proportionately larger.
Thus, total revenue decreases.
Revenue = $240
$1
Demand
Revenue = $100
0
100
Quantity
Demand
0
80
Quantity
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Elasticity and Total Revenue:
Elastic Demand
Price
Elasticity and Total Revenue
…leads to a decrease
in total revenue
from$200 to $100
Price
An increase in price
from $4 to $5...
$5
$4
Demand
Demand
Revenue = $200
0
50
Quantity
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
How Total Revenue is Affected by a Change in Price
Price ↑
Price ↓
Elastic
(E D,P > 1)
↓
↑
Unit Elastic
(E D,P = 1)
No Change
No Change
Inelastic
(E D,P < 1)
↑
↓
Revenue = $100
0
20
Quantity
Ex. As price increases for an elastic demand, total
revenue decrease.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
5
Computing the Elasticity of a
Linear Demand Curve
Price
$0
1
2
3
4
5
6
7
Quantity
14
12
10
8
6
4
2
0
Total Revenue
(Price x
Percent Change
Quantity)
in Price
$0
200%
12
67
20
40
24
29
24
22
20
18
12
15
0
Percent
Change
in Quantity
15%
18
22
29
40
67
200
Class Example
The price of a cd player rises from $100 to
$150, while the quantity demanded falls from
1200 to 900.
Elasticity
0.1
0.3
0.6
1
1.8
3.7
13
Description
Inelastic
Inelastic
Inelastic
Unit elastic
elastic
elastic
elastic
n
n
n
n
Calculate the price elasticity of demand.
Is demand elastic, unit elastic, or inelastic.
Calculate total revenue before and after the
price rise.
Calculate the % change in quantity demanded
if price rises another 5%.
ä Remember: E D,P = % ? Q / % ? P
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Class Example - Solutions
n
n
n
n
n
Price elasticity of demand = .71
Demand is inelastic.
TR when P = 100: $120,000
TR when P = 150: $135,000
If P rises by 5%, we would expect to see
Q decrease by 3.55%
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Percentage Change
in Quantity Demanded
Income Elasticity
=
of Demand
Percentage Change
in Income
n
Elasticity of demand with respect to
income.
ED,I
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
u Income
elasticity of demandmeasures
how much the quantity demanded of a
good responds to a change in consumers’
income.
u It is computed as the percentage change
in the quantity demanded divided by the
percentage change in income.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Computing Income
Elasticity
n
Income Elasticity of Demand
Income Elasticity
- Types of Goods u Normal
Goods
Goods
u Higher income raises the quantity
demanded for normal goods but lowers
the quantity demanded for inferior
goods .
u Inferior
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
6
Income Elasticity
n
Normal goods will have an income
elasticity that is greater than zero.
Why?
Income Elasticity Example
n
(Q A-Q B )(IA+IB ) / (Q A+Q B)(IA-IB )
n
When your income = $10,000, your demand for
mac & cheese is 20.
When your income = $30,000, your demand for
mac & cheese is 15.
n
n
Inferior goods will have an income
elasticity that is less than zero.
n
Why?
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Income Elasticity
Income Elasticity
- Types of Goods u Goods
consumers regard as necessities
tend to be income inelastic
Examples include food, fuel, clothing, utilities,
and medical services.
u Goods consumers regard as luxuries tend
Calculate the income elasticity and determine if
mac & cheese is a normal or inferior good.
n
Necessities will have an income elasticity
that is less than 1.
n
Luxuries will have an income elasticity
that is greater than 1.
to be income elastic.
Examples include sports cars, furs, and
expensive foods.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Income Elasticity Example
n
n
n
When your income = $10,000, your
quantity demanded for concerts is 1.
When your income = $30,000, your
quantity demanded for concerts is 12.
Calculate income elasticity and determine
if concert tickets are a necessity or luxury
to you.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Cross Price Elasticity
n
This is a measure of how much the quantity
demanded of one good responds to a change in
the price of another good.
n
Cross Price Elasticity is calculated as the
percentage change in quantity demanded of the
first good divided by the percentage change in
the price of the second good.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
7
Cross Price Elasticity
n
n
n
Whether cross price elasticity is positive
or negative depends on whether the two
goods are substitutes or complements.
Substitutes will have a cross price
elasticity that is greater than zero.
Complements will have a cross price
elasticity that is less than zero.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Cross Price Elasticity Ex.
n
n
n
Suppose the percentage change for the quantity
demanded for good X decreased 25% while the
percentage change in the price of good Y
increase by 50%
What is the cross price elasticity and are the
goods substitutes or complements?
Cross price elasticity = -.5 => Complements
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Determinants of
Elasticity of Supply
Price Elasticity of Supply
u Price elasticity of supply is
the
percentage change in quantity supplied
resulting from a percent change in price.
u It is a measure of how much the quantity
supplied of a good responds to a change
in the price of that good.
uAbility of sellers to change the amount of
the good they produce.
u Beach -front land is inelastic.
u Books,
cars, or manufactured goods are
elastic.
uTime period.
uSupply is more elastic in the long run.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
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 S
Supplied
upplied
Elasticity of Supply
Supply =
Percentage Change
Change
in Price
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Ranges of Elasticity
u Perfectly Elastic
ES = ∞
u Relatively Elastic
ES > 1
u Unit
Elastic
ES = 1
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
8
Perfectly Inelastic Supply
Ranges of Elasticity
- Elasticity equals 0
Price
u Relatively Inelastic
ES < 1
Supply
1. An
$5
increase
in price... 4
u Perfectly Inelastic
ES = 0
Quantity
100
2. ...leaves the quantity supplied unchanged.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Inelastic Supply
Unit Elastic Supply
- Elasticity is less than 1
Price
- Elasticity equals 1
Price
Supply
Supply
1. A 22% $5
increase
in price... 4
1. A 22% $5
increase
in price... 4
Quantity
100 110
2. ...leads to a 10% increase in quantity.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Quantity
100
125
2. ...leads to a 22% increase in quantity.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Elastic Supply
Perfectly Elastic Supply
- Elasticity is greater than 1
Price
- Elasticity equals infinity
Price
1. At any price
above $4, quantity
supplied is infinite.
Supply
1. A 22% $5
increase
in price...
4
Supply
$4
2. At exactly $4,
producers will
supply any quantity.
100
200 Quantity
2. ...leads to a 67% increase in quantity.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
3. At a price below $4,
quantity supplied is zero.
Quantity
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
9
Application of Elasticity
uCan
good news for farming be bad news for
farmers?
uWhat happens to wheat farmers and the market
for wheat when university agronomists discover a
new wheat hybridthat is more productive than
existing varieties?
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Application of Elasticity
u Examine whether the supply or demand
curve shifts.
u Determine the direction of the shift of the
curve.
u Use the supply-and-demand diagram to
see how the market equilibrium changes.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
An Increase in Supply in the
Market for Wheat
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
An Increase in Supply in the
Market for Wheat
Price of
Wheat
Price of
Wheat
1. When demand is inelastic,
an increase in supply...
S1
S1
$3
Demand
Demand
0
100
Quantity of Wheat
Compute Elasticity
100 - 110
ED =
S2
2. ...leads $3
to a large
2
fall in
price...
3.00 - 2.00
(100 + 110)/2
0
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
110
Quantity of Wheat
Does Drug Interdiction Increase or
Decrease Drug Related Crime?
n
(3.00 + 2.00)/2
- 0.095
=
≈ -0.24
0.4
100
3. ...and a proportionately smaller
increase in quantity sold. As a result,
revenue falls from $300 to $220.
n
One adverse effect of drug use is that
drug addicts often turn to robbery and
other violent crimes to obtain the money
needed to support their habit.
The government spends billions of dollars
each year to reduce the flow of drugs into
this country. Let’s see how this works.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
10
Does Drug Interdiction Increase or
Decrease Drug Related Crime?
n
n
When the government stops some drugs
from entering the country and arrests
more smugglers, it raises the cost of
selling drugs. How does this affect
supply?
Do you think that the demand for drugs
is elastic or inelastic?
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Does Drug Interdiction Increase or
Decrease Drug Related Crime?
n
n
An increase in total expenditures means
that the drug addicts now have to spend
more for their drugs and this may lead to
even more crime, when we the
government was trying to reduce crime.
In the long run, this may encourage
people to break their habit and also
discourage the number of new users.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Compute Elasticity
100 - 110
ED =
=
3.00 - 2.00
(100 + 110)/2
(3.00 + 2.00)/2
- 0.095
≈ -0.24
0.4
Demand is inelastic
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Summary
uPrice
elasticity of demand measures
how much the quantity demanded
responds to changes in the price.
uIf a demand curve is elastic, total
revenue falls when the price rises.
uIf it is inelastic, total revenue rises as
the price rises.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
Summary
uThe
price elasticity of supply measures
how much the quantity supplied
responds to changes in the price.
uIn most markets, supply is more elastic
in the long run than in the short run.
Harcourt, Inc. items and derived items copyright © 2001 by Harcourt, Inc.
11