Download 06.03.2012 1 Elasticity Elasticity and applications Two demand

06.03.2012
Elasticity and applications
 Law of demand: “The demand curve is downward-sloping. As
price rises quantity demanded falls, [as price falls quantity
demanded rises].”
Elasticity
 Two markets: public transportation vs movie theaters
In 1984, the City of Chicago wanted to attract more transit riders with lower
fares. J. L. Shofer, research director at Northwestern University’s
Transportation Center, wrote:
“Lower fares never make up for loss of revenues. Even when losing riders by
increasing fares, revenue usually goes up. It’s a law of economics.”
 The law of demand is too general and not useful in analyzing the
case above. We often need more (precise) information.
Two demand curves
Price elasticity of demand
 As P decreases from P1 to P2,
QD increases along both
demand curves Da and Db.
P
 However, an equal decrease in
price results
 in a smaller increase in QD
in demand curve Da,
 in a larger increase in QD
for demand curve Db.
P1
P2
Db
 Demand Curve
Da
Q1
Q2
Q3
Q
Da
is relatively
less responsive to price
changes whereas Demand
curve Db is relatively more
responsive.
 Price elasticity of demand is a measure of how much the quantity
demanded of a good responds to a change in the price of that
good.
 Price elasticity of demand is the percentage change in quantity
demanded given a percent change in the price.
 If the amount of any good that people purchase changes a lot in
response to a small price change, we say “DEMAND IS ELASTIC”
 If a large price change results in a small change in the amount that
people purchase, we say “DEMAND IS INELASTIC”
1
06.03.2012
Price elasticity of demand
 The determinants of the price elasticity of demand:
 Availability of Close Substitutes
How to compute the price elasticity of
demand?
 The price elasticity of demand is computed as the percentage
change in the quantity demanded divided by the percentage
change in price.
 Necessities versus Luxuries
 Definition of the Market
 Time Horizon
 Demand tends to be more elastic:
 If there are a large number of close substitutes.
 If the good is a luxury.
Price elasticity of demand (EP )
 If the market is more narrowly defined (food versus milk).
 If we consider a longer time period after the price change.
Price elasticity of demand: Examples
10 % increase in the price of eggs leads to 5% reduction in
the number of eggs sold. What is the price elasticity of
demand? Answer: Price elasticity of demand for eggs is -.5
2. If the (price) elasticity of red apples is -0.8, then a one
percent increase in the price of red apples will lead to a
0.8 percent decrease (or, 0.8 % decrease) in the quantity
of red apples demanded.
If the (price) elasticity of red apples is -0.8, then a 5
percent increase in the price of red apples, will lead to a
5 x 0.8 = 4 percent decrease in the quantity of red apples
demanded.
Percentage change in quantity demand
Percentage change inprice
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.
BUT, slope is not elasticity!!
How to Calculate Percentage Changes in the
Elasticity formula (the midpoint method)?
1.
Price elasticity of demand (EP )
 The midpoint formula is preferable when calculating the
price elasticity of demand because it gives the same
answer regardless of the direction of the change.
(Q2 - Q1) / [(Q2 + Q1) / 2]
Price elasticity of demand (EP)
=
(P2 - P1) / [(P2 + P1) / 2]
Percentage change in quantity demand
Percentage change inprice
2
06.03.2012
Example using the Midpoint Method
•
Point A:
Point B:
Price = $4
Price = $6
Quantity = 120
Quantity = 80
 From Point A to Point B: Price rise = 50% and Quantity fall = 33%
From Point B to Point A: Price fall = 33% and Quantity rise = 50%
(80 - 120) / [(80 + 120)/ 2]
Price elasticity of demand (EP) =
Mid point method
= -
(6 - 4) / [(6 + 4)/ 2]
1
Elastic versus inelastic demand curves
 Roughly,
 Inelastic Demand
 Quantity demanded does not respond strongly to price changes.
 Price elasticity of demand is less than one.
 Elastic Demand
 Quantity demanded responds strongly to changes in price.
 Price elasticity of demand is greater than one.
 Formally,
 If | EP | > 1, demand is (price) elastic.
 If | EP | < 1, demand is (price) inelastic.
 If | EP | = 1, demand is (price) unit elastic.
 A very important remark: Because price and quantity are negatively
related along the (typical) demand curve, EP is (always) negative.
Remark on elasticity calculation
Elasticity calculation can be tricky, because there are many
(simultaneous) influences on demand and supply. (See the
example below.) Consider a demand curve drawn on the Pvs. Q graph. EP is a measure that corresponds to movements
up and down the demand curve. But changes in other
variables (shown as shifts in the P vs. Q graph) also impact
price and quantity. To calculate EP correctly, we have to make
sure that all else is held constant.
Remark on elasticity calculation
The following data show the prices of X and Y, the annual income of the
consumer, and the quantities of X consumed during the last 6 years.
Year
1987
1988
1989
1990
1991
1992
PX ($)
100
110
90
100
100
100
QX
80
90
100
100
90
110
PY ($)
50
40
40
60
40
40
Income ($)
20,000
18,000
18,000
20,000
20,000
25,000
(a) Which pair of years would you use to calculate the price elasticity of demand
for X? Why?
(b) What is the price elasticity of demand for X?
3
06.03.2012
Perfectly Inelastic Demand
Particular demand curves
Price
Demand
E=0
 Perfectly Inelastic
 Quantity demanded does not respond to price changes.
 Perfectly Elastic
$5.00
 Quantity demanded changes infinitely with any change in price.
 Unit Elastic
$4.00
 Quantity demanded changes by the same percentage as the price.
1. An increase in
price…
0
100
Quantity
2. …leaves the quantity demanded unchanged.
Inelastic Demand
Price
Demand
Unit Elastic Demand
E<1
E=1
Price
Demand
$5.00
$5.00
$4.00
$4.00
1. A 22% increase
in price…
1. A 22% increase
in price…
0
90
100
2. … Leads to a 11% decrease in quantity demanded.
Quantity
0
80
100
Quantity
2. … Leads to a 22% decrease in quantity demanded.
4
06.03.2012
Elastic Demand
Perfectly Elastic Demand
E>1
Price
E=
Price
Demand
$5.00
1. At any price above $4, quantity demanded is
zero.
$4.00
Demand
$4.00
2. At exactly $4, consumers will buy any quantity.
1. A 22% increase
in price…
3. At any price below $4, quantity demanded is infinite.
0
50
100
0
Quantity
Quantity
2. … Leads to a 67% decrease in quantity demanded.
Total Revenue and the price elasticity
of demand
 Remember the quotation:
In 1984, the City of Chicago wanted to attract more transit riders with
lower fares. J. L. Shofer, research director at Northwestern
University’s Transportation Center, wrote:
“Lower fares never make up for loss of revenues. Even when losing riders
by increasing fares, revenue usually goes up. It’s a law of economics.”
Inelastic Demand: How does total revenue change
when prices change?
With an inelastic demand curve, an increase in the price leads to a decrease in quantity demanded
that is proportionately smaller. Thus, total revenue increases when price increases.
Price
$3.00
P x Q = $240
(revenue)
 Total revenue is the amount paid by buyers and received by
sellers of a good and computed as the price of the good times
the quantity sold.
TR = P x Q
$1.00
P x Q = $100
(revenue)
0
Demand
80
100
Quantity
5
06.03.2012
Elastic Demand: How does total revenue change
when prices change?
Elasticity along a linear demand curve
Price
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 when price increases.
Elasticity is
larger than 1.
7
6
Price
5
$5.00
4
$4.00
Elasticity is
smaller than
1.
3
Demand
2
Revenue = $100
1
Revenue = $200
0
0
20
50
2
4
6
8
10
12
14
Quantity
Quantity
Elasticity and Total Revenue along a Linear
Demand Curve
Income elasticity of demand
 Income elasticity of demand measures how much the quantity
demanded of a good responds to a change in consumers’
income.
 It is computed as the percentage change in the quantity
demanded divided by the percentage change in income.
Percentage change
in quantity demanded
Income elasticity of demand =
Percentage change
in income
6
06.03.2012
Income elasticity of demand
 Income elasticity of demand measures how much the quantity
demanded of a good responds to a change in consumers’
income.
 It is computed as the percentage change in the quantity
demanded divided by the percentage change in income.
Percentage change
in quantity demanded
Income elasticity of demand =
Percentage change
in income
Income elasticity of demand
 Goods consumers regard as necessities tend to be income
inelastic
 Examples include food, fuel, clothing, utilities, and medical
services.
 Goods consumers regard as luxuries tend to be income
elastic.
 Examples include sports cars, furs, and expensive foods.
Higher income raises the quantity demanded for normal goods but lowers the quantity
demanded for inferior goods. Thus, income elasticity of demand is positive for normal goods
and negative for inferior goods.
Cross price elasticity of demand
 Cross-Price elasticity of demand measures how much the quantity
demanded of a good responds to a change in the price of another
good.
 It is computed as the percentage change in the quantity demanded
divided by the percentage change in the price of the other good.
The cross elasticity of the demand for good X with respect to the
price of good Y is defined as:
Cross price elasticity of demand
 Cross-Price elasticity of demand measures how much the quantity
demanded of a good responds to a change in the price of another
good.
 It is computed as the percentage change in the quantity demanded
divided by the percentage change in the price of the other good.
The cross elasticity of the demand for good X with respect to the
price of good Y is defined as:
Percentage change in quantity
demanded of good X
Cross price elasticity of demand =
Percentage change in the
price of good Y
Percentage change in quantity
demanded of good X
Cross price elasticity of demand =
Percentage change in the
price of good Y
Cross elasticity is positive if X and Y are substitutes, and it is negative if X and Y are
complements. (Why?)
7
06.03.2012
Price elasticity of supply
Price elasticity of supply: an example
 The price elasticity of supply is a measure of how much the quantity
supplied of a good responds to a change in the price of that good.
 The price elasticity of supply is computed as the percentage
change in the quantity supplied divided by the percentage change
in price.
 Ability of sellers to change the amount of the good they produce.
 Beach-front land is inelastic.
 Books, cars, or manufactured goods are elastic.
 Supply is more elastic in the long run.
Price elasticity of supply =
•
 … using the midpoint method, we calculate the percent change in the price as
(2.10 - 1.90) / 2.00 x 100 = 10%
 Similarly, we calculate the percent change in the quantity supplied as
(11,000 – 9,000) / 10,000 x 100 = 20%
20%
Price elasticity of supply =
10%
=
2.0
Percentage change
in quantity supplied
Percentage change in price
Inelastic Supply
Perfectly Inelastic Supply
Price
Suppose an increase in the price of milk from $1.90 to $2.10 per liter raises
the amount that dairy farmers produce from 9000 to 11 000 liters (per
month)
Supply
E=0
$5.00
Price
Supply
E<0
$5.00
$4.00
$4.00
1. An increase in
price…
1. A 22% increase
in price…
0
100
2. …leaves the quantity supplied unchanged.
Quantity
0
100
110
Quantity
2. …leads to a 10% increase in quantity supplied.
8
06.03.2012
Unit Elastic Supply
Elastic Supply
E=1
Price
E>1
Price
Supply
Supply
$5.00
$5.00
$4.00
$4.00
1. A 22% increase
in price…
1. A 22% increase
in price…
0
100
125
0
Quantity
100
200
Quantity
2. …leads to a 67% increase in quantity supplied.
2. …leads to a 22% increase in quantity supplied.
How the price elasticity of supply can vary?
Perfectly Elastic Supply
E=
Price
Price
$15
Elasticity is less
than 1
$12
1. At any price above $4, quantity supplied is
infinite.
Elasticity is greater
than 1
Supply
$4.00
2. At exactly $4, producers will supply any quantity.
$4
$3
3. At any price below $4, quantity supplied is zero.
0
0
Quantity
100
200
500
525
Quantity
9
06.03.2012
Three applications of supply, demand, and
elasticity
Elasticity of supply: examples
 When the price of DaVinci paintings increases by 1% the
quantity supplied doesn't change at all, so the quantity
supplied of DaVinci paintings is completely insensitive to the
price.
 Price elasticity of supply is 0.
 Good news vs bad news for farmers
 OPEC
 Drugs and crime
 Teen smokers
 Gasoline tax decreases accidents.
 When the price of beef increases by 1% the quantity supplied
increases by 5%, so beef supply is very price sensitive.
 Price elasticity of supply is 5.
Application 1: Good news vs bad news for the
farmers
Price of
Wheat
Increase in Supply
1. When demand is inelastic, an increase
in supply…
Application 2: OECD
(a) Oil Market in the Short Run
Price
of Oil
(b) Oil Market in the Long Run
Price
of Oil
1. In the short run, when supply and
demand are inelastic, a shift in supply…
S2
S2
1. In the long run, when supply and
demand are elastic, a shift in supply…
S2
$3
P2
P2
P1
$2
P1
2. … leads to
a fall in
price…
2. … leads to
a large increase
in price…
Demand
Demand
100
110
3. …and a proportionately smaller increase in quantity sold. As a result revenue falls from $300 to
$220.
2. … leads to
a small
increase in
price…
Demand
Quantity of Wheat
Quantity of Oil
Quantity of Oil
10
06.03.2012
Application 3: Drugs and Crime
(a) Drug Interdiction
Price of
Drugs
Application 3: Drugs and Crime
(b) Drug Education
Price of
Drugs
1. Drug interdiction reduces the supply
of drugs…
S2
How elasticity affects the market for illegal goods
1. Drug education reduces the demand
for drugs…
In an important new study, world-renowned economists argue that when demand for a
good is inelastic, the cost of making consumption illegal exceeds the gain. Their
forthcoming paper in the Journal of Political Economy is a definitive explanation of the
economics of illegal goods and a thoughtful explication of the costs of enforcement.
P2
P1
P2
P1
D1
2. … which
reduces the
price…
2. … which
raises the
price…
D2
Demand
Q2
Q1
Quantity of Drugs
3. … and reduces the
quantity sold.
Q2
Q1
Quantity of Drugs
The authors demonstrate how the elasticity of demand is crucial to understanding the
effects of punishment on suppliers. Enforcement raises costs for suppliers, who must
respond to the risk of imprisonment and other punishments. This cost is passed on to the
consumer, which induces lower consumption when demand is relatively elastic.
However, in the case of illegal goods like drugs--where demand seems inelastic--higher
prices lead not to less use, but to an increase in total spending. In the case of drugs,
then, the authors argue that excise taxes and persuasive techniques –such as advertising-are far more effective uses of enforcement expenditures. "This analysis…helps us
understand why the War on Drugs has been so difficult to win…why efforts to reduce
the supply of drugs leads to violence and greater power to street gangs and drug
cartels," conclude the authors. "The answer lies in the basic theory of enforcement
developed in this paper."
3. … and reduces the quantity sold.
Application 4: Teen smokers
Application 5: Gasoline tax decreases
accidents

In a 1996 article in the Energy Journal, authors Jonathan Haughton and Soumodip Sarkar attempt
to answer the question of what impact a $1 gasoline tax increase would have on driving and
accidents.They submit that with a gas tax of $1, miles driven would decrease by up to 12% and
fatalities by up to 18%.

How do they get to these results? By estimating and using the own-price elasticity of gasoline to
calculate the impact on gasoline consumption.
The retail price of gasoline in 1991 was $1.13, of which 28% or $0.32 was tax. Assuming that the
entire tax increase is applied to the price, this means a price increase of $0.68, or 46%. The long
run own-price elasticity of demand for gasoline over a ten-year period was calculated to be in the
range -0.23 to -0.35. Using this knowledge we can calculate the change in consumption:
 Price Elasticity of cigarettes
U.S. has increased taxes on cigarettes dramatically in the past 5 years. A
majority of adult smokers have sucked it up and continued smoking. Dr. Thomas
R. Frieden, the commissioner of the city Department of Health and Mental
Hygiene in New York has conducted several surveys among young adult and
teen smokers. City and state tobacco taxes, which have been gradually rising in
recent years and now add $3 to the price of each pack of cigarettes, for a total
of $5.50 or more. “Kids are most susceptible to price because they don’t have a
whole lot of disposable income,” Dr. Frieden said. “So when you increase the
price of cigarettes, you drive smoking down generally among adults but
especially for teens.” Raising the taxes will have a much more noticeable effect
short term users. The older (faithful users) they are less sensitive to price
changes.
Source: A. RAMIREZ, New York Times, Published: January 3, 2008 Teenagers
in the City Smoke Less, Report Finds
%ΔQ/46% = -0.23
%ΔQ = -0.23 * 46% = -10.6%
%ΔQ/46% = -0.35
 %ΔQ = -0.35 * 46% = -16.1%




Without going into the effect on accidents, we can still determine that a gas tax of $1 would
decrease gas consumption by between 10.6% and 16.1%.
Source: Haughton, J. & Sarkar, S. (1996) Gasoline Tax as a Corrective Tax: Estimates for the United
States, 1970-1991, Energy Journal vol 17 no 2 p103-26.
11
06.03.2012
Why do economists use elasticity?
 Economists want to compare apples and oranges all the time.
 Is oil market demand more price sensitive than wheat demand?




(no)
Is the labor supply of women more wage sensitive than the labor
supply of men? (yes)
An elasticity is a unit-free measure.
By comparing markets using elasticities, it does not matter how
we measure the price or the quantity in the two markets.
Elasticities allow economists to quantify the differences among
markets without standardizing the units of measurement.
Summary
 Price elasticity of demand measures how much the quantity
demanded responds to changes in the price.
 Price elasticity of demand is calculated as the percentage change in
quantity demanded divided by the percentage change in price.
 If a demand curve is elastic, total revenue falls when the price
rises.
 If it is inelastic, total revenue rises as the price rises.
Examples of unit-free comparisons
 Gasoline and jewelry
 It doesn't matter that gas is sold by the gallon for about $1.09 and
gold is sold by the ounce for about $290.
 We compare the demand elasticities of -0.2 (gas) and -2.6 (gold
jewelry).
 Gold jewelry demand is more price sensitive.
 Paintings and meat
 It doesn't matter that classical paintings are sold by the canvas for
millions of dollars each while beef is sold by the pound for about
$1.50.
 We compare the supply elasticities of 0 (classical paintings)
and 5 (beef).
 Beef supply is more price sensitive.
Summary
 The income elasticity of demand measures how much the quantity
demanded responds to changes in consumers’ income.
 The cross-price elasticity of demand measures how much the
quantity demanded of one good responds to the price of another
good.
 The price elasticity of supply measures how much the quantity
supplied responds to changes in the price.
12
06.03.2012
Summary
 In most markets, supply is more elastic in the long run than in the
short run.
 The price elasticity of supply is calculated as the percentage
change in quantity supplied divided by the percentage change in
price.
 The tools of supply and demand can be applied in many different
types of markets.
13