Download Chapter 3: Supply and Demand - Vancouver Island University

Learning Objectives
• Define and measure elasticity
• Apply concepts of price elasticity,
cross-elasticity, and income elasticity
• Understand determinants of
elasticity
• Show how elasticity affects revenue
Elasticity of Demand
Measures responsiveness of demand to
changes in an underlying factor such
as the price of the product, income,
prices of related products or
advertising expenditures.
There is an elasticity corresponding to
every factor that affects demand
Own Price Elasticity of Demand (E)
• Measures responsiveness or sensitivity of
consumers to changes in the price of a good
•
%Q
E
%P
• P & Q are inversely related by the law of
demand so E is always negative
– The larger the absolute value of E, the more
sensitive buyers are to a change in price
Calculating Price Elasticity of
Demand
• Price elasticity can be measured at
an interval (or arc) along demand, or
at a specific point on the demand
curve
– If the price change is relatively small, a
point calculation is suitable
– If the price change spans a sizable arc
along the demand curve, the interval
calculation provides a better measure
Computation of Elasticity Over
an Interval
• arc elasticity formula
Q Average P
E

P Average Q
E = dQ/dP * (average P / average Q)
Elasticity at a Point
• When calculating price elasticity at a point
on demand,
E = dQ/dP * (p/Q)
multiply the slope of demand (Q/P),
computed at the point of measure, times
the ratio P/Q, using the values of P and Q
at the point of measure
• Qx = 408 – 2Px
What is own price elasticity at Px = 154?
What is the arc elasticity if Px increases
from 154 to 179?
The Price Elasticity of
Demand
• Elasticity differs
along a linear
demand curve.
A report reveals that sales of new
houses increased by 12% after a 10%
drop in the price of new houses. In a
meeting, a manager says, “based on
this information, we can conclude
that the price elasticity for new
houses is -1.2. What would you say to
the manager?
Price Elasticity of
Demand (E)
Elasticity
Responsiveness
E
Elastic
%Q%P E 1
Unitary Elastic
%Q%P E 1
Inelastic
%Q%P
Perfect elasticity: E = ∞
Perfect inelasticity: E = 0
E 1
Steep curve = inelastic
‘Flat’ curve = elastic
Horizontal curve = infinite elasticity
Vertical curve = zero elasticity
Factors Affecting Price
Elasticity of Demand
• Availability of substitutes
– The better & more numerous the substitutes
for a good, the more elastic is demand
• Percentage of consumer’s budget
– The greater the percentage of the consumer’s
budget spent on the good, the more elastic is
demand
• Time period of adjustment
– The longer the time period consumers have to
adjust to price changes, the more elastic is
demand
Factors Affecting Price
Elasticity of Demand
• Definition of product (broad or narrow)
•
•
•
•
•
– Demand for cigarettes compared to demand
for a particular brand.
Buyer’s loyalty
Sunk costs
Information and education
Frequency of purchases
Customer storage costs
• You manage your country’s agricultural exports
which includes two products: Bitter Leaf and
ordinary butter. Bitter Leaf has very few
substitutes. The supply of your products to the
world market depends on the exchange rate
between your local currency and other world
currencies. If your local currency appreciates
and becomes more expensive, you increase the
supply of your products to the world market.
Suppose your local currency appreciates and
becomes 10% more expensive, how would these
affect the prices of your Bitter Leaf and butter
on world markets?
Elasticity and incidence
of tax
If demand is inelastic then consumer
bear more of the incidence of tax.
As demand becomes more elastic,
then, ceteris paribus, the incidence is
shifted to the suppliers.
• According to empirical study on cigarette sales,
when the price of cigarettes increased by 1%,
consumption of cigarettes would be lowered by
0.4% in the short run and 0.75% in the long run.
a. What is the SR and LR own price elasticities of
demand cigarettes?
b. Explain the difference between the 2 numbers
c. What would be the implications of imposing a tax
on cigarettes based on your answers in (a) and (b)
above?
Price Elasticity of Demand & TR
– Because a demand curve is downward sloping, a
decrease in price will increase the quantity
demanded
– If elasticity is greater than 1, the quantity
effect is stronger than the price effect, and
total revenue will increase
Price Elasticity & Total
Revenue
Elastic
Unitary elastic
Inelastic
Quantity-effect
dominates
No dominant
effect
Price-effect
dominates
Price
rises
TR falls
No change in TR
TR rises
Price
falls
TR rises
No change in TR
TR falls
• You have 2 bottles of old wine in the
cellar and decided to drink one of the
two bottles with your friends.
By drinking one of the two bottles,
can you simultaneously enjoy the wine
and increase the value of the
remaining wine?
• As price decreases
– Revenue rises when
demand is elastic.
– Revenue falls when
it is inelastic.
– Revenue reaches its
peak when
elasticity of
demand equals 1.
MR, TR, & Price
Elasticity
Marginal
Total revenue
revenue
MR > 0 TR increases as
Q increases
MR = 0
MR < 0
(P decreases)
Price elasticity
of demand
Elastic
Elastic
(E> 1)
(E> 1)
Unit
Unitelastic
elastic
TR is maximized (E= 1)
(E= 1)
TR decreases as Inelastic
Inelastic
(E<
1)
Q increases
(P decreases)
(E< 1)
Marginal Revenue & Price
Elasticity
• For all demand & marginal revenue
curves, the relation between marginal
revenue, price, & elasticity can be
expressed as
1

MR  P 1  
E

• Drugs that are not covered by patent can be
freely manufactured by anyone. The advertising
elasticity of the demand for all drugs is around
0.26, and 0.24 for those covered by patents. For
all drugs, the own price elasticity is about -2
without advertising and about -1.6, in the long run
with advertising.
a. By how much would the demand for patented
drug rise if there is a 5% increase in advertising
expenditure?
b. Suppose the drug manufacturer were to increase
advertising. Explain why it should also raise the
price of its drug
MORE EXAMPLES
T/F and why?
• If the price elasticity is less than one than an
increase in the price reduces revenue?
• A product with perfect substitutes has a price
elasticity of zero
• A farmer is happy because a bumper crop is
expected. Will the farmer increase his profits
when all farmers have record crops?
The Cross-Elasticity of
Demand
• Cross-elasticity of demand: The
percentage change in quantity
consumed of one product as a result
of a 1 percent change in the price of
a related product.
%Qx
EX 
%Py
The Cross-Elasticity of
Demand
• Arc Elasticity
dQx AveragePy
Ex 
.
dPy AverageQx
The Cross-Elasticity of
Demand
• The sign of cross-elasticity for
substitutes is positive.
• The sign of cross-elasticity for
complements is negative.
• Two products are considered good
substitutes or complements when the
coefficient is larger than 0.5.
The own price elasticity of SUVs is -2.5 while the cross elasticity of
demand for SUVs with respect to gasoline prices is -0.25. Recently, the
price of gasoline rose by 66% while at the same time SUV manufactures
offer their customers rebates totaling $500 (1.4% of the average price
of a large SUV).
a.
What does this imply for SUV sales. Explain fully
Income Elasticity
• Income Elasticity of Demand: The
percentage change in quantity
demanded caused by a 1 percent
change in income.
%Q
EY 
%Income
Income Elasticity
• Categories of income
elasticity
– Superior goods: EY > 1
– Normal goods: 0 >EY >1
– Inferior goods –
demand decreases as
income increases: EY < 0
Other Elasticity
Measures
• Elasticity is encountered every time a
change in some variable affects
quantities.
– Advertising expenditure
– Interest rates
– Population size
T/F and why?
1. Demand volatility will be higher, the
higher the income elasticity of demand
2. Demand facing the (more popular)
“Greasy Spoon” restaurant will fall if the
income elasticity for the (more upscale)
“Golden Fork” is positive and income falls
Uses of Elasticities
• Pricing.
• Managing cash flows.
• Impact of changes in competitors’
prices.
• Impact of economic booms and
recessions.
• Impact of advertising campaigns.
• And lots more!
Elasticity of Supply
• Price Elasticity of Supply: The
percentage change in quantity supplied
as a result of a 1 percent change in
price.
% Quantity Supplied
ES 
% Price
• If the supply curve slopes upward and
to the right, the coefficient of supply
elasticity is a positive number.
Elasticity of Supply
• Arc elasticity
Q2  Q1
P2  P1
Es 

(Q1  Q2 ) / 2 ( P1  P2 ) / 2
Elasticity of Supply
• When the supply curve is more
elastic, the effect of a change in
demand will be greater on quantity
than on the price of the product.
• With a supply curve of low elasticity,
a change in demand will have a
greater effect on price than on
quantity.
• You are the owner of a novelty shop that
sells greeting cards and flowers. You are
aware that as Valentine’s Day approaches,
demand for greeting cards and roses will
jump up. Your knowledge of demand-supply
analysis leads you to expect the prices of
both products to rise. You have noticed
that the price of roses, however, always
increases much more sharply than the
price of greeting cards. Why is that?
• When does an increase in income
reduce the amount spent on a
product but keep the price
unchanged
• T/F and why?
Increases and decreases in demand will
lead to larger increases and
decreases in price the lower the
responsiveness of quantity supplied
to price
Examples: Pricing and Cash
Flows
• According to an FTC Report by
Michael Ward, AT&T’s own price
elasticity of demand for long distance
services is -8.64.
• AT&T needs to boost revenues in
order to meet it’s marketing goals.
• To accomplish this goal, should AT&T
raise or lower it’s price?
Answer: Lower price!
• Since demand is elastic, a reduction
in price will increase quantity
demanded by a greater percentage
than the price decline, resulting in
more revenues for AT&T.
Example 2: Quantifying the
Change
• If AT&T lowered price by 3 percent,
what would happen to the volume of
long distance telephone calls routed
through AT&T?
Answer
• Calls would increase by 25.92 percent!
EQX , PX
% Q X
 8.64 
% PX
d
% Q X
 8.64 
 3%
d
 3%   8.64   % QX
d
% Q X  25.92%
d
Example 3: Impact of a
change in a competitor’s
price
• According to an FTC Report by
Michael Ward, AT&T’s cross price
elasticity of demand for long
distance services is 9.06.
• If competitors reduced their prices
by 4 percent, what would happen to
the demand for AT&T services?
Answer
• AT&T’s demand would fall by 36.24 percent!
EQX , PY
%QX
 9.06 
%PY
%QX
9.06 
 4%
d
 4%  9.06  %QX
d
%QX  36.24%
d
d
Interpreting Demand Functions
• Mathematical representations of demand
curves.
• Example: d
QX  10  2 PX  3PY  2M
• X and Y are substitutes (coefficient of PY
is positive).
• X is an inferior good (coefficient of M is
negative).
Linear Demand Functions
• General Linear Demand Function:
QX  0   X PX  Y PY   M M   H H
d
P
EQX , PX   X X
QX
Own Price
Elasticity
EQ X , PY
PY
 Y
QX
Cross Price
Elasticity
M
EQX , M   M
QX
Income
Elasticity
Example of Linear
Demand
•
•
•
•
Qd = 10 - 2P.
Own-Price Elasticity: (-2)P/Q.
If P=1, Q=8 (since 10 - 2 = 8).
Own price elasticity at P=1, Q=8:
(-2)(1)/8= - 0.25.
Log-Linear Demand
• General Log-Linear Demand Function:
ln QX d   0   X ln PX  Y ln PY   M ln M   H ln H
X
Cross Price Elasticity :  Y
Income Elasticity :
M
Own Price Elasticity :
Example of Log-Linear
Demand
• ln(Qd) = 10 - 2 ln(P).
• Own Price Elasticity: -2.