Colander-ch06-Elasticities

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Describing Supply and Demand:
Elasticities
Chapter 6
Classifying Demand and Supply as
to their relative responsiveness to
price changes: Elasticity
• It is helpful to describe the relative
responsiveness of consumers and suppliers
to price changes.
• For example, after a large price increase
there may be a large or small drop in the
quantity demanded.
• We call this relative responsiveness to price
changes the elasticity of demand or supply.
Responsiveness of Demand
Here we have two different demand curves. Let’s pretend that they possibly
represent the demand behavior of consumers in the antacid market. The
problem is that we don’t which curve is the real demand curve. If the real
curve is DA then raising the price from P1 to P2 will cause quantity demanded
to drop from QA,1 to QA,2. However, if the real curve is DB then demand falls
from QB,1 to QB,2
P
Price
P2
P1
DA
DB
QB,2
QA,2 QB,1
Quantity Demanded
QA,1
Q
Responsiveness of Supply
Here we have two different supply curves. Let’s pretend that they possibly
represent the supply curves of your firm in the antacid market. The problem
is that you don’t which curve is the real supply curve. If the real curve is SA
then raising the price from P1 to P2 will cause quantity supplied to rise from
QA,1 to QA,2. However, if the real curve is SB then demand falls from QB,1 to
QB,2. Think what happens to profits if you get it wrong. Either your costs
rise faster than your revenues or your revenues do not expand due to
P
increased opportunity.
SA
SB
Price
P2
P1
QB,1
QA,2 QA,1
Quantity Demanded
QA,2
Q
Elasticity: Definition
• Elasticity is defined as the percentage
change in Quantity Demanded or Supplied
relative to a percentage change in Price.
• We usually “normalize” the change in price
to a 1% increase.
• The change in Quantity Demanded or
Supplied as being less than 1%, 1% also, or
more than 1%.
Price Elasticity: Formula
• The formula for computing an elasticity
is to divide the percentage change in
price by the percentage change in
quantity demanded or supplied:
% Q
E
% P
Elastic Demand and Supply
• For elastic points on curves, the
percentage change in quantity is
greater than the percentage change in
price.
E > 1
Elastic Demand and Supply
• Common sense tells us that an elastic
supply means that quantity changes by
a greater percentage than the
percentage change in price.
• The same holds true for demand.
Inelastic Demand and Supply
• For inelastic points on curves, the
percentage change in quantity is less
than the percentage change in price.
E < 1
Inelastic Demand and Supply
• Common sense tells us that an inelastic
supply means that quantity doesn't
change much with a change in price.
• The same holds true for demand.
What Information Price Elasticity
Provides
• Price elasticity gives of demand and
supply gives information about the
exact quantity response to a price
change.
• As elasticity increases, responsiveness
of quantity to price also increases.
Elasticity Is Independent of Units
• Percentages allow us to have a
measure of responsiveness that is
independent of units.
Elasticity Is Independent of Units
• Having a measure of responsiveness
that is independent of units makes
comparisons of responsiveness of
different goods easier.
Calculating Elasticities
• To determine elasticity divide the
percentage change in quantity by the
percentage change in price.
The End-Point Problem
• The end-point problem is that the
percentage change differs depending
on whether you view the change as a
rise or a decline in price.
The Arc Convention
• Economists use the arc convention to
get around the end-point problem.
• The arc elasticity method entails the
calculating the percentage change at
the midpoint of the range.
The Arc Convention
• Using the arc convention, the average
of the two end points are used as the
starting point when calculating
percentage change.
(Q2 - Q1)
Elasticity = (P
2
- P1)
½Q2  Q1 
½P1 + P2 
Graphs of Elasticities
B
$26
24
22
20
18
16
14
0
C (midpoint)
A
D
10
12
14
Quantity of software (in hundred thousands)
Elasticity of demand = 1.3
Graphs of Elasticities
$6.00
5.50
5.00
4.50
4.00
3.50
3.00
0
A
B
C (midpoint)
470 480 490
Quantity of workers
Elasticity of supply = 0.18
Graphs of Elasticities
$10
9
8
7
6
5
4
3
2
1
B
A
C
E = 0.54
F
E
5
(c)
E=4
E = 0.67
D
1015 20 25 30 35 40 45 55
50
60
Quantity
Somexamples
e
Calculating Elasticity at a Point
• Let us now turn to a method of
calculating the elasticity at a specific
point, rather than over a range or an
arc.
Calculating Elasticity at a Point
• To calculate elasticity at a point,
determine a range around that point
and calculate the arc elasticity.
Calculating Elasticity at a Point
$10
9
8
7
6
5
4
3
2
1
(28 - 20)
E=
C
½28  20 
 0.66
(5 - 3)
½5 + 3 
A
B
20 24 28
40
Quantity
Calculating Elasticity at a Point
$10
9
8
7
6
5
4
3
2
1
Demand
A
Supply
EA = 2.33
D
C E = 0.75
C
6
ED = 0.86
EB = 0.11
B
12 18 24 30 36 42 48 54 60
Quantity
Elasticity and Supply and Demand
Curves
• Two important points to consider:
– Elasticity is related (but is not the same
as) slope.
– Elasticity changes along straight-line
demand and supply curves.
Elasticity Is Not the Same as
Slope
• The relationship between elasticity
and slope means that the steeper the
curve begins at a given point, the less
elastic is supply or demand.
Elasticity Is Not the Same as
Slope
• There are two limiting examples of
this.
Elasticity Is Not the Same as
Slope
• When the curves are flat, we call the
curves perfectly elastic.
• Perfectly elastic curves are flat
curves in which quantity changes
enormously in response to a
proportional change in price (E = ).
Elasticity Is Not the Same as
Slope
• When the curves are vertical, we call
the curves perfectly inelastic.
• Perfectly inelastic curves are vertical
curves in which quantity does not
change at all in response to an
enormous proportional change in price
(E = 0).
Perfectly Inelastic Demand Curve
Perfectly inelastic
demand curve
0
Quantity
Perfectly Elastic Demand Curve
Perfectly inelastic
demand curve
0
Quantity
Elasticity Changes Along StraightLine Curves
• Elasticity is not the same as slope.
• Elasticity changes along the straight
line supply and demand curves—slope
does not.
Elasticity Changes Along StraightLine Curves
• On a demand curve, elasticity is
perfectly elastic (E = ) at the price
intercept.
• It becomes smaller as you move down
the demand curve until it becomes
zero at the quantity intercept.
Elasticity Changes Along StraightLine Curves
• Elasticity is perfectly elastic (E = )
where a straight line supply curve
intercepts the price axis.
• Points become less elastic as you
move out along the supply curve.
Elasticity Along a Demand Curve
Ed = 
Elasticity declines along demand
curve as one moves toward
the quantity axis
Ed > 1
Price
$10
9
8
7
6
5
4
3
2
1
0
Ed = 1
Ed < 1
Ed = 0
1
2
3
4 5 6
Quantity
7
8
9 10
Elasticity Along a Supply Curve
S0
Price
$10
9
8
7
6
5
4
3
2
1
0
S1
Es declines
Es rises
Es = 
Es = 0
1
2
3
4 5 6
Quantity
7
8
9 10
Elasticity Review
• Perfectly elastic – quantity responds
enormously to price changes (E = ).
• Elastic – the percentage change in
quantity exceeds the percentage
change in price (E >1).
Elasticity Review
• Unit elastic – the percentage change
in quantity is the same as the
percentage change in price (E = 1).
Elasticity Review
• Inelastic – the percentage change in
quantity is less than the percentage
change in price (E <1).
• Perfectly inelastic – quantity does
not respond at all to price changes (E
= 0).
Substitution and Elasticity
• As a general rule, the more
substitutes a good has, the more
elastic is its supply and demand.
Substitution and Elasticity
• Factors that affect a good’s
substitutability of demand differ
from factors that affect a good’s
substitutability of supply.
Substitution and Demand
• The larger the time interval
considered, or the longer the run, the
more elastic is the good’s demand
curve.
– There are more substitutes in the long
run than in the short run.
– The long run provides more options for
change.
Substitution and Demand
• The less a good is a necessity, the
more elastic its demand curve.
• Necessities tend to have fewer
substitutes than do luxuries.
Substitution and Demand
• As the definition of a good becomes
more specific, demand becomes more
elastic.
– If the good is broadly defined—say,
transportation—there are not many
substitutes and demand will be inelastic.
Substitution and Demand
• As the definition of a good becomes
more specific, demand becomes more
elastic.
– If the definition of a good is narrowed—
say to transportation by bus—there are
more substitutes.
Substitution and Demand
• Demand for goods that represent a
large proportion of one's budget are
more elastic than demand for goods
that represent a small proportion of
one's budget.
Substitution and Demand
• Goods that cost very little relative to
your total expenditures are not worth
spending a lot of time figuring out if
there is a good substitute.
• It is worth spending a lot of time
looking for substitutes for goods that
take a large portion of one’s income.
Substitution and Supply
• The longer the time period considered,
the more elastic the supply.
Substitution and Supply
• The reasoning is the same as for
demand.
– In the long run there are more options
for change so it is easier (less costly)
for suppliers to change into the
production of another good.
Substitution and Supply
• Economists distinguish three time
periods relevant to supply:
– The instantaneous period.
– The short run.
– The long run.
Substitution and Supply
• In the instantaneous period, quantity
supplied is fixed so the elasticity of
supply is perfectly inelastic.
• This supply is sometimes called the
momentary supply.
Substitution and Supply
• In the short run, some substitution is
possible, so the short-run supply curve
is somewhat elastic.
Substitution and Supply
• In the long run, significant
substitution is possible; the supply
curve becomes very elastic.
Substitution and Supply
• An additional factor to consider:
– Many goods are produced, so we must
take into account how easy it is to
substitute for existing goods by
producing more of those same goods.
How Substitution Factors Affect
Specific Decisions
• Suppose you’ve been asked to evaluate
the potential impact of a 10¢ gas tax
increase in Washington, D.C. and in the
nation.
Impact of a 10¢ Gas Tax Increase
• In the short run the demand curve for
gasoline would be less elastic than in
the long run.
• In the long run, motorists would
switch to fuel efficient cars.
Impact of a 10¢ Gas Tax Increase
• Although gasoline is considered a
necessity, it is only a small part of
what it costs to drive, demand would
probably be inelastic.
Impact of a 10¢ Gas Tax Increase
• For the entire U.S., demand would be
inelastic, but for Washington, it would
be very elastic since there are many
alternative choices of transportation.
Impact of a 10¢ Gas Tax Increase
• Some may switch to an alternative
form of transportation.
• Others would go to neighboring
states to buy gasoline.
Impact of a 10¢ Gas Tax Increase
• Smaller geographic areas have more
elastic demands.
• This limits how highly state and local
governments can tax goods relative to
their neighboring localities or states.
Empirical Estimates of Elasticities
• The following table provides shortand long-term estimates of elasticities
for a number of goods.
Empirical Estimates of Elasticities
• These demand estimates are for the
entire U.S.
• If they were for specific regions or
cities, the examples would show
greater elasticity.
Empirical Estimates of Elasticities
Product
Tobacco products
Electicity (household)
Health Services
Nodurable toys
Movies/motion pictures
Beer
Wine
University tuition
Price elasticity
Short Run Long Run
0.46
1.89
0.13
1.89
0.20
0.92
0.30
1.02
0.87
3.67
0.56
1.39
0.68
0.84
0.52
—
Empirical Estimates of Elasticities
• There are many fewer empirical
measurements of elasticity of supply
than there are of demand.
Empirical Estimates of Elasticities
• One does find empirical measurements
of elasticity of supply in factor
markets, such as the market for labor
services.
Empirical Estimates of Elasticities
• Other areas in which elasticities of
supply are estimated are agricultural
and raw materials markets.
– In these markets, economists have
generally found that the short-run
supplies are highly inelastic, and that the
long-run supplies are highly elastic.
Elasticity, Total Revenue, and
Demand
• Knowing the elasticity of demand tells
suppliers how their total revenue will
change if their price changes.
• Total revenue equals total quantity
sold multiplied by price of good.
Elasticity, Total Revenue, and
Demand
• If ED is elastic (ED > 1), a rise in price
lowers total revenue.
• Price and total revenue move in
opposite directions.
Elasticity, Total Revenue, and
Demand
• If ED is unit elastic (ED = 1), a rise in
price leaves total revenue unchanged.
Elasticity, Total Revenue, and
Demand
• If ED is inelastic (ED < 1), a rise in
price increases total revenue.
• Price and total revenue move in the
same direction.
Elasticity and Total Revenue
(a) Unit Elastic Demand
E=1
$10
TR constant
Price
8
F
6
Gained revenue
C
E
4
A
2
0
1
2
Lost
revenue
B
3
4
5
6
7
8
9
Quantity
Elasticity and Total Revenue
(b) Inelastic Demand
E<1
$10
TR rises
Price
8
6
4
Gained
revenue
Lost
revenue
H
2
0
G
C
A
1
2
B
3
4
5
6
7
8
9
Quantity
Elasticity and Total Revenue
$10
Price
8
6
(c) Elastic Demand
E=1
K
J
C
A
Gained
revenue
B
4
Lost
revenue
2
0
TR falls
1
2
3
4
5
6
7
8
9
Quantity
Total Revenue Along a Demand
Curve
• ED is elastic at prices above the point
where demand is unit elastic – a rise in
price lowers total revenue.
• If ED is inelastic at prices below the
point where demand is unit elastic – a
rise in price increases total revenue.
Elastic range ED > 1
ED = 1
Inelastic range
Total revenue
How Total Revenue Changes Along
a Demand Curve
ED < 1
0
(a)
Q0
0
Quantity
(b)
Q0
Quantity
Elasticity of Individual and Market
Demand
• Market demand elasticity is influenced
both by:
– Many people drop out totally when price
increases.
– How much an existing consumer marginally
changes his or her quantity demanded.
Elasticity of Individual and Market
Demand
• Price discrimination occurs when a
firm separates the people with less
elastic demand from those with more
elastic demand.
Elasticity of Individual and Market
Demand
• Firms that price discriminate can
charge more to the individuals with
inelastic demand and less to individuals
with elastic demands.
Elasticity of Individual and Market
Demand
• Examples of price discrimination
include:
– Airlines’ Saturday stay-over specials.
– The phenomenon of selling new cars.
– The almost-continual-sale phenomenon.
Other Elasticity Concepts
• Other elasticities can be useful in
specifying the effects of a shift
factor of demand:
– Income elasticity of demand.
– Cross-price elasticity of demand.
Income Elasticity of Demand
• Income elasticity of demand is
defined as the percentage change in
demand divided by the percentage
change in income.
EIncome
Percentage change in demand
=
Percentage change in income
Income Elasticity of Demand
• Income elasticity of demand tells us
the responsiveness of demand to
changes in income.
Income Elasticity of Demand
• An increase in income generally
increases one’s consumption of almost
all goods, although the increase may
be greater for some goods than for
others.
Income Elasticity of Demand
• Normal goods are those whose
consumption increases with an
increase in income.
• They have income elasticities greater
than zero.
Income Elasticity of Demand
• Normal goods are divided into luxuries
and necessities.
Income Elasticity of Demand
• Luxuries are goods that have an
income elasticity greater than one.
• Their percentage increase in demand
is greater than the percentage
increase in income.
Income Elasticity of Demand
• Shoes are a necessity—a good that
has an income elasticity less than 1.
• The consumption of a necessity rises
by a smaller proportion than the rise
in income.
Income Elasticity of Demand
• Inferior goods are those whose
consumption decreases when income
increases.
• Inferior goods have income
elasticities less than zero.
• Dried milk is an example of an
inferior good.
Income Elasticities of Selected
Goods
Income elasticity
Product
Short Run Long Run
Motion pictures
0.81
3.41
Foreign travel
0.24
3.09
Tobacco products
0.21
0.86
Furniture
2.60
0.53
Jewelry and watches
1.00
1.64
Hard liquor
—
2.50
Private university tuition
—
1.10
Cross-Price Elasticity of Demand
• Cross-price elasticity of demand is
defined as the percentage change in
demand divided by the percentage
change in the price of another good.
ECross-Price
Percentage change in demand
=
Percentage change in price
of another good
Cross-Price Elasticity of Demand
• Cross-price elasticity of demand tells
us the responsiveness of demand to
changes in prices of other goods.
Complements and Substitutes
• Substitutes are goods that can be
used in place of another.
• When the price of a good goes up, the
demand for the substitute good also
goes up.
Complements and Substitutes
• Complements are goods that are used
in conjunction with other goods.
• A fall in the price of a good will
increase the demand for its
complement.
• The cross-price elasticity of
complements is negative.
Cross-Price Elasticities
Commodities
Beef in response to price change in pork
Beef in response to price change in chicken
U.S. automobiles in response to price changes
in European and Asian automobiles
European automobiles in response to price
changes in U.S. and Asian automobiles
Beer in response to changes in wine
Hard liquor in response to price changes in
beer
Cross-Price
Elasticity
0.11
0.02
0.28
0.61
0.23
- 0.11
Some Examples
(26 - 20)
E=
26
=
= 1.3
20
P0
½ 26  20 
20
P0
Shift due to 20%
rise in income
D0 D1
20
26
Quantity
Some Examples
(104 - 108)
½ 104  108 
– 33
– 3.8
=
= 1.3
– 33
S0
E=
P0
S1
P0
Shift due to 33%
rise in price
of pork
104
108 Quantity
The Power of Supply and Demand
Analysis
• A number of questions may be
answered by combining supply and
demand analysis with elasticity.
When Should a Supplier Raise
Price?
• The supplier should raise his price
when it faces an inelastic demand.
– Total revenue increases with a price
increase because quantity drops
proportionally less than price goes up.
– Since costs also fall, profit rise.
When Should a Supplier Raise
Price?
• When you have an elastic demand, you
should hesitate to increase price.
Elasticity and Shifting Supply and
Demand
• Elasticity can tell us more exactly the
effect of shifting supply and demand.
Elasticity and Shifting Supply and
Demand
• The more elastic the demand, the
greater the effect of a supply shift on
quantity, and the smaller effect on
price.
Elasticity and Shifting Supply and
Demand
• The more elastic the supply, the
greater the effect of a demand shift
on quantity, and the smaller the
effect on price.
Effects of Shifts in Supply on
Price and Quantity
Inelastic Supply and Inelastic Demand
Price
Demand
S0
S1
P0
P1
Q0 Q1
Quantity
Effects of Shifts in Supply on
Price and Quantity
Inelastic Supply and Elastic Demand
Price
Demand
S0
S1
P0
P1
Q0 Q1
Quantity
Describing Supply and Demand:
Elasticities
End of Chapter 6
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