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The responsiveness of one variable to
changes in another
When price rises, what happens
to demand?
Demand falls
BUT!
How much does demand fall?
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If price rises by 10% - what happens to
demand?
We know demand will fall
By more than 10%?
By less than 10%?
Elasticity measures the extent to which
demand will change
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4 basic types used:
Price elasticity of demand
Price elasticity of supply
Income elasticity of demand
Cross elasticity

Price Elasticity of Demand
◦ The responsiveness of demand
to changes in price
◦ Where % change in demand
is greater than % change in price – elastic
◦ Where % change in demand is less than % change in
price - inelastic
The Formula:
Ped =
% Change in Quantity Demanded
___________________________
% Change in Price
If answer is between 0 and -1: the relationship is inelastic
If the answer is between -1 and infinity: the relationship is elastic
Note: PED has – sign in front of it; because as price rises
demand falls and vice-versa (inverse relationship between
price and demand)
Price (£)
The demand curve can be a
range of shapes each of which
is associated with a different
relationship between price and
the quantity demanded.
Quantity Demanded
Price
Total
revenue is of
price
x
The importance
elasticity
quantity sold. In this
is the information it
example,
TRthe
= £5
x 100,000
provides on
effect
on
=
£500,000.
total revenue of changes in
price.
This value is represented by
the grey shaded rectangle.
£5
Total Revenue
D
100
Quantity Demanded (000s)
Elasticity
Price
If the firm decides to
decrease price to (say) £3,
the degree of price
elasticity of the demand
curve would determine the
extent of the increase in
demand and the change
therefore in total revenue.
£5
£3
Total Revenue
D
100
140
Quantity Demanded (000s)
Price (£)
Producer decides to lower price to attract sales
% Δ Price = -50%
10
% Δ Quantity Demanded = +20%
Ped = -0.4 (Inelastic)
Total Revenue would fall
5
Not a good move!
D
5 6
Quantity Demanded
Price (£)
10
Producer decides to reduce price to increase sales
% Δ in Price = - 30%
% Δ in Demand = + 300%
Ped = - 10 (Elastic)
Total Revenue rises
Good Move!
7
D
5
Quantity Demanded
20
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

If demand is price
elastic:
Increasing price
would reduce TR
(%Δ Qd > % Δ P)
Reducing price
would increase TR
(%Δ Qd > % Δ P)



If demand is price
inelastic:
Increasing price
would increase TR
(%Δ Qd < % Δ P)
Reducing price
would reduce TR
(%Δ Qd < % Δ P)

Income Elasticity of Demand:
◦ The responsiveness of demand
to changes in incomes


Normal Good – demand rises
as income rises and vice versa
Inferior Good – demand falls
as income rises and vice versa
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Income Elasticity of Demand:
A positive sign denotes a normal good
A negative sign denotes an inferior good


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

For example:
Yed = - 0.6: Good is an inferior good but inelastic – a rise in
income of 3% would lead to demand falling
by 1.8%
Yed = + 0.4: Good is a normal good but inelastic –
a rise in incomes of 3% would lead to demand rising
by 1.2%
Yed = + 1.6: Good is a normal good and elastic –
a rise in incomes of 3% would lead to demand rising
by 4.8%
Yed = - 2.1: Good is an inferior good and elastic –
a rise in incomes of 3% would lead to a fall in demand of 6.3%


Cross Elasticity:
The responsiveness of demand
of one good to changes in the price of a
related good – either
a substitute or a complement
% Δ Qd of good t
__________________
Xed =
% Δ Price of good y

Goods which are complements:
◦ Cross Elasticity will have negative sign (inverse
relationship between the two)

Goods which are substitutes:
◦ Cross Elasticity will have a positive sign (positive
relationship between the two)

Price Elasticity of Supply:
◦ The responsiveness of supply to changes
in price
◦ If Pes is inelastic - it will be difficult for
suppliers to react swiftly to changes in price
◦ If Pes is elastic – supply can react quickly to
changes in price
%
Δ Quantity Supplied
____________________
Pes =
% Δ Price
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Time period – the longer the time under
consideration the more elastic a good is likely to be
Number and closeness of substitutes –
the greater the number of substitutes,
the more elastic
The proportion of income taken up by the product
– the smaller the proportion the more inelastic
Luxury or Necessity - for example,
addictive drugs
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Relationship between changes
in price and total revenue
Importance in determining
what goods to tax (tax revenue)
Importance in analysing time lags in
production
Influences the behaviour of a firm
The focus of this lecture is the elasticity. Students will learn about
the price elasticity of demand, price elasticity of supply, cross
elasticity and income elasticity.
OBJECTIVES
1. Understand the definition of elasticity.
2. Be able to compute the elasticity coefficients.
3. Analyze the elasticity characteristics.
4. Illustrate the determinants of the elasticity.
5. Explain the total revenue test and understand the relationship
between total revenue and price elasticity of demand.
TOPICS
Please read all the following topics.
PRICE ELASTICITY OF DEMAND
Definition:
Law of demand tells us that consumers will respond to a price drop by buying more, but it does not tell us how much
more. The degree of sensitivity of consumers to a change in price is measured by the concept of price elasticity of
demand.
Price elasticity formula: Ed = percentage change in Qd / percentage change in Price.
If the percentage change is not given in a problem, it can be computed using the following formula:
Ed = Q2-Q1) /P2-P1)X (P1 + P2)/(Q1+Q2)
Because of the inverse relationship between Qd and Price, the Ed coefficient will always be a negative number. But,
we focus on the magnitude of the change by neglecting the minus sign and use absolute value
Examples:
1. If the price of Product A increased by 10%, the quantity demanded decreased by 20%. Then the coefficient
for price elasticity of the demand of Product A is:
Ed = percentage change in Qd / percentage change in Price = (20%) / (10%) = 2
2. If the quantity demanded of Product B has decreased from 1000 units to 900 units as price increased from $2 to $4
per unit, the coefficient for Ed is:
Ed = (Q2-Q1) /P2-P1)X (P1 + P2)/(Q1+Q2)= - 0.16
Take the absolute value of - 0.16, Ed = 0.16
Ed approaches infinity, demand is perfectly elastic. Consumers are
very sensitive to price change.
Ed > 1, demand is elastic. Consumers are relatively responsive to
price changes.
Ed = 1, demand is unit elastic. Consumers’ response and price
change are in same proportion.
Ed < 1, demand is inelastic. Consumers are relatively unresponsive
to price changes.
Ed approaches 0, demand is perfectly inelastic. Consumers are
very insensitive to price change.
DEMAND FUNCTION FOR PRODUCT X: P = 2.50.01Q
P = PRICE; Q = QUANTITY, TR = TOTAL
REVENUE
Ed = PRICE ELASTICITY OF DEMAND
I
Q:
00
P:
0.5
Ed:
2
A
B
C
D
E
F
G
H
J
0 50 100 150 200 250 300 350 4
450
4.5 4
3.5
3
2.5
2
1.5
1
0
17 5
2.6 1.57
1
0.64 0.38 0.
0.06
ELASTICITY OF DEMAND;
FROM A TO E Ed >1
FROM E TO F Ed =1
Various factors influence the price elasticity of
demand. Here are some of them:
1. # of Substitutes: If a product can be easily
substituted, its demand is elastic, like Gap's jeans. If
a product cannot be substituted easily, its demand is
inelastic, like gasoline.
2. Luxury Vs Necessity: Necessity's demand is usually
inelastic because there are usually very few
substitutes for necessities. Luxury product, such as
leisure sail boats, are not needed in a daily bases.
There are usually many substitutes for these
products. So their demand is more elastic.
3. Price/Income Ratio: The larger the percentage of
Total revenue (TR) is calculated by multiplying price (P) per
unit and quantity (Q) of the good sold.
TR = P x Q
The total revenue test is a method of estimating the price
elasticity of demand. As Ed will impact the total revenue,
we can estimate the Ed by looking at the movement of the
total revenue.
Total Revenue Test
Ed > 1, total revenue will decrease as price increases. P
and TR moves in opposite directions. Producers can
increase total revenue ( TR = Price x Quantity) by lowering
the price. Therefore, most department stores will have
sales to attract customers. Apparel's demand is elastic.
DEMAND FUNCTION FOR PRODUCT X: P = 2.50.01Q
P = PRICE; Q = QUANTITY, TR = TOTAL REVENUE
Ed = PRICE ELASTICITY OF DEMAND
A
I
B
C
D
E
F
G
H
J
Q:
0 50 100
400 450
P:
4.5 4
3.5
0.5 0
TR: 0 200 350
0 200 0
150
200 250 300 350
3
2.5
450
500 500 450 35
2
1.5
1
Definition:
Law of supply tells us that producers will respond to a price drop by producing less, but it
does not tell us how much less. The degree of sensitivity of producers to a change in price
is measured by the concept of price elasticity of supply.
Price elasticity formula: Es = percentage change in Qs / percentage change in Price.
If the percentage change is not given in a problem, it can be computed using the
following formula:
Q2-Q1) /P2-P1)X (P1 + P2)/(Q1+Q2)=
Because of the direct relationship between Qs and Price, the Es coefficient will always be a
positive number.
Examples:
1. If the price of Product A increased by 10%, the quantity supplied increases by 5%.
Then the coefficient for price elasticity of the supply of Product A is:
Es = percentage change in Qs / percentage change in Price = (5%) / (10%) = 0.5
2. If the quantity supplied of Product B has decreased from 1000 units to 200 units as
price decreases from $4 to $2 per unit, the coefficient for Es is:
Es Q2-Q1) /P2-P1)X (P1 + P2)/(Q1+Q2)= = 2
Characteristics:
Es approaches infinity, supply is perfectly elastic. Producers are very
sensitive to price change.
Es > 1, supply is elastic. Producers are relatively responsive to price
changes.
Es = 1, supply is unit elastic. Producers’ response and price change are
in same proportion.
Es < 1, supply is inelastic. Producers are relatively unresponsive to price
changes.
Es approaches 0, supply is perfectly inelastic. Producers are very
insensitive to price change.
It is impossible to judge elasticity of a supply curve by its flatness or
steepness. Along a linear supply curve, its elasticity changes.
Determinants:
Definition:
Cross elasticity (Exy) tells us the relationship between two products. it measures the
sensitivity of quantity demand change of product X to a change in the price of product Y.
Formula: Exy = percentage change in Quantity demanded of X / percentage change in
Price of Y.
Characteristics:
Exy > 0, Qd of X and Price of Y are directly related. X and Y are substitutes.
Exy approaches 0, Qd of X stays the same as the Price of Y changes. X and Y are not
related.
Exy < 0, Qd of X and Price of Y are inversely related. X and Y are complements.
Examples:
1. If the price of Product A increased by 10%, the quantity demanded of B increases by
15 %. Then the coefficient for the cross elasticity of the A and B is :
Exy = percentage change in Qx / percentage change in Py = (15%) / (10%) = 1.5 > 0,
indicating A and B are substitutes.
2. If the price of Product A increased by 10%, the quantity demanded of B decreases by
15 %. Then the coefficient for the cross elasticity of the A and B is :
Exy = percentage change in Qx / percentage change in Py = (- 15%) / (10%) = - 1.5 < 0,
indicating A and B are complements.
Definition:
Income elasticity of demand (Ey, here y stands for income) tells us the relationship a
product's quantity demanded and income. It measures the sensitivity of quantity
demand change of product X to a change in income.
Price elasticity formula: Ey = percentage change in Quantity demanded / percentage
change in Income
If the percentage change is not given in a problem, it can be computed using the
following formula:
Percentage change in Qx where Q1 = initial Qd, and Q2 = new Qd.
Percentage change in Y where Y1 = initial Income, and Y2 = New income.
Putting the two above equations together:
Ey = {(Q1-Q2) / (Y1-Y2) X (Y1 + Y2/Q1+Q2)]
Characteristics:
Ey > 1, Qd and income are directly related. This is a normal good and it is income
elastic.
0< Ey<1, Qd and income are directly related. This is a normal good and it is income
inelastic.
Ey < 0, Qd and income are inversely related. This is an inferior good.
Ey approaches 0, Qd stays the same as income changes, indicating a necessity.
Example:
If income increased by 10%, the quantity demanded of a product increases by 5 %.
2.4
● elasticity Percentage change in one variable
resulting from a 1-percent increase in another.
Price Elasticity of Demand
● price elasticity of demand Percentage change
in quantity demanded of a good resulting from a
1-percent increase in its price.
(2.
2.4
Linear Demand Curve
● linear demand curve
straight line.
Figure 2.11
Linear Demand Curve
The price elasticity of demand
depends not only on the slope of
the demand curve but also on the
price and quantity.
The elasticity, therefore, varies
along the curve as price and
quantity change. Slope is
constant for this linear demand
curve.
Near the top, because price is
high and quantity is small, the
elasticity is large in magnitude.
The elasticity becomes smaller as
we move down the curve.
Demand curve that is a
2.4
Linear Demand Curve
Figure 2.12
(a) Infinitely Elastic Demand
For a horizontal demand curve,
ΔQ/ΔP is infinite. Because a tiny
change in price leads to an
enormous change in demand, the
elasticity of demand is infinite.
● infinitely elastic demand Principle that
consumers will buy as much of a good as they can
get at a single price, but for any higher price the
quantity demanded drops to zero, while for any
2.4
Linear Demand Curve
Figure 2.12
(b) Completely Inelastic Demand
For a vertical demand curve,
ΔQ/ΔP is zero. Because the
quantity demanded is the same no
matter what the price, the elasticity
of demand is zero.
● completely inelastic demand Principle that
consumers will buy a fixed quantity of a good
regardless of its price.
2.4
Other Demand Elasticities
● income elasticity of demand Percentage change
in the quantity demanded resulting from a 1-percent
increase in income.
(2.2)
● cross-price elasticity of demand Percentage
change in the quantity demanded of one good
resulting from a 1-percent increase in the price of
(2.3)
another.
Elasticities of Supply
● price elasticity of supply Percentage change in
quantity supplied resulting from a 1-percent
increase in price.
2.4
Point versus Arc Elasticities
● point elasticity of demand Price elasticity at a
particular point on the demand curve.
Arc Elasticity of Demand
● arc elasticity of demand Price elasticity
calculated over a range of prices.
(2.4)
2.4
For a few decades, changes in the wheat market
had major implications for both American
farmers and U.S. agricultural policy.
To understand what happened, let’s examine the
behavior of supply and demand beginning in 1981.
By setting the quantity supplied equal to the quantity
demanded, we can determine the market-clearing price of
wheat for 1981:
2.4
Substituting into the supply curve equation, we get
We use the demand curve to find the price elasticity of demand:
Thus demand is inelastic.
We can likewise calculate the price elasticity of
supply:
Because these supply and demand curves are
linear, the price elasticities will vary as we move
along the curves.
2.5
Demand
Demand
Figure 2.13
(b) Automobiles: Short-Run and Long-Run
Demand Curves
. If price increases, consumers initially
defer buying new cars; thus annual
quantity demanded falls sharply.
In the longer run, however, old cars wear
out and must be replaced; thus annual
quantity demanded picks up. Demand,
therefore, is less elastic in the long run
than in the short run.
2.5
Demand
Income Elasticities
Income elasticities also differ from the short run to
the long run.
For most goods and services—foods, beverages,
fuel, entertainment, etc.— the income elasticity of
demand is larger in the long run than in the short run.
For a durable good, the opposite is true. The shortrun income elasticity of demand will be much larger
than the long-run elasticity.
2.5
Demand
Cyclical Industries
● cyclical industries Industries in which sales tend
to magnify cyclical changes in gross domestic
Figure 2.14
product and national income.
GDP and Investment in Durable
Equipment
Annual growth rates are
compared for GDP and
investment in durable
equipment.
Because the short-run GDP
elasticity of demand is larger
than the long-run elasticity for
long-lived capital equipment,
changes in investment in
equipment magnify changes in
GDP. Thus capital goods
industries are considered
“cyclical.”
2.5
Demand
Cyclical Industries
Figure 2.15
Consumption of Durables versus
Nondurables
Annual growth rates are compared for
GDP, consumer expenditures on
durable goods (automobiles,
appliances, furniture, etc.), and
consumer expenditures on nondurable
goods (food, clothing, services, etc.).
Because the stock of durables is large
compared with annual demand, shortrun demand elasticities are larger than
long-run elasticities. Like capital
equipment, industries that produce
consumer durables are “cyclical” (i.e.,
changes in GDP are magnified). This
is not true for producers of
nondurables.
2.5
Demand
TABLE 2.1
Elasticity
10
Price
Income
TABLE 2.2
Elasticity
10
Price
−0.4
Income
Demand for Gasoline
Number of Years Allowed to Pass Following
a Price or Income Change
1
2
3
5
−0.2
−0.3
−0.4
−0.5
−0.8
1.0
0.2
0.4
0.5
0.6
Demand for Automobiles
Number of Years Allowed to Pass Following
a Price or Income Change
1
2
3
5
−1.2
−0.9
−0.8
−0.6
1.9
3.0
1.4
2.3
1.0
2.5
Supply
Supply
Figure 2.16
Copper: Short-Run and Long-Run
Supply Curves
Like that of most goods, the
supply of primary copper, shown
in part (a), is more elastic in the
long run.
If price increases, firms would like
to produce more but are limited by
capacity constraints in the short
run.
In the longer run, they can add to
capacity and produce more.
2.5
Figure 2.17
Price of Brazilian Coffee
When droughts or
freezes damage Brazil’s
coffee trees, the price of
coffee can soar.
The price usually falls
again after a few years,
as demand and supply
adjust.
2.5
Figure 2.18
Supply and Demand for Coffee
(c) In the long run, supply is
extremely elastic; because
new coffee trees will have had
time to mature, the effect of
the freeze will have
disappeared. Price returns to
P0.
2.6
Figure 2.19
Fitting Linear Supply and Demand
Curves to Data
Linear supply and demand curves
provide a convenient tool for
analysis.
Given data for the equilibrium
price and quantity P* and Q*, as
well as estimates of the elasticities
of demand and supply ED and ES,
we can calculate the parameters c
and d for the supply curve and a
and b for the demand curve. (In
the case drawn here, c < 0.) The
curves can then be used to analyze
the behavior of the market
quantitatively.