Elasticity of Demand - Concept and Measurements

INTRODUCTION TO ECONOMICS
Course Code: MBA 045
ASSIGNMENT
TOPIC: ELASTICITY OF DEMAND - CONCEPTS AND MEASUREMENT
Date: 10th August, 2016
SUBMITTED TO:
Professor Shiba Prasad Sen
Pro-Vice Chancellor
Metropolitan University
SUBMITTED BY:
Sadia Tasnim
Batch: MBA 38 (A)
ID: 162-126-004

TABLE OF CONTENTS
1. Elasticity of Demand
 Definition 1
 Types of Elasticity of Demand 1
2. Price Elasticity of Demand
 Definition 2
 Formula 2
 Numerical Measurement 3
 Categories 5
 Diagram 5
 Geometric Measurement 6
 Price Elasticity of Demand at different
points of straight line demand curve
7
3. Income Elasticity of Demand
 Definition 8
 Formula 8
 Measurement 9
 Relationship with nature of commodity 10
4. Cross Elasticity of Demand
 Definition 11
 Formula 11
 Measurement 12
 Relation between original commodity
& other commodity
14
References 15

ELASTICITY OF DEMAND - CONCEPTS AND MEASUREMENT
Page 1 of 15
ELASTICITY OF DEMAND
Elasticity measures how one variable responds to a change in another variable, namely the
percentage change in one variable resulting a one percentage change in another variable (the
percentage change is independent of units). In economics, the quantitative relationship
between price and quantity purchased is analyzed using the concept of elasticity. The
elasticity can be an aspect to analyze the elasticity of demand, elasticity of supply or other
theories.
Elasticity of demand is an important variation on the concept of demand. It
refers to the rate at which demand changes due to change of price or increase of consumers or
price of other commodity while the other influencing factors are constant. It is a technical
term which helps in determining the magnitude of change in quantity demand for a rise or fall
in the price of the product. It‘s a concept devised to indicate the degree of responsive of
quantity demand of a product to the changes in the market price of the product. It depends
primarily on the percentage changes and is independent of the units used to measure the
quantity and price.
TYPES OF ELASTICITY OF DEMAND
Elasticity of demand is classified into three types. They are as follows:
1. Price Elasticity of Demand
2. Income Elasticity of Demand
3. Cross Elasticity of Demand

Page 2 of 15
PRICE ELASTICITY OF DEMAND
The price elasticity of demand (sometimes called price elasticity) measures how much the
quantity demanded of a good changes when its price changes. The precise definition of price
elasticity is the percentage change in quantity demanded divided by the percentage change in
price. It the responsiveness of quantity demanded to changes in the price of the product.
FORMULA OF PRICE ELASTICITY OF DEMAND
The price elasticity of demand is found by the following formula:
𝐸𝑝 =
Δ𝑞
q
÷
Δ𝑝
p
=
Δ𝑞
q
×
𝑝
Δ𝑝
=
Δ𝑞
Δ𝑝
×
𝑝
q
Here,
𝐸𝑝 = Price elasticity of demand
q = Original demand
Δ𝑞 = Change in demand
p = Original price
Δ𝑝 = Change in price
We know,
Δ𝑞
q
= % of relative change in demand, &,
Δ𝑝
p
= % of relative change in price
So, 𝐸𝑝 =
% of relative change in demand
% of relative change in price
Or, 𝐸𝑝 =
% of change in demand
% of change in price
[Derivation of original formula]
MEASUREMENT OF ELASTICITY OF DEMAND
The elasticity of demand can be calculated in two different ways:
1. Numerical measurement of price elasticity of demand
2. Geometric measurement of price elasticity of demand

Page 3 of 15
It should be noted here that, since price and quantity are inversely related, the price elasticity
of demand will always be negative. Thus the change in quality will in the opposite direction
to the change in price. The negative sign is usually ignored and consider absolute values for
price elasticity.
1. NUMERICAL MEASUREMENT OF PRICE ELASTICITY OF DEMAND
Numerical measurement of price elasticity of demand is calculated by the
original formula. In order to measure price elasticity of demand
numerically, the value of original demand (q), change in demand (Δ𝑞),
original price (p), and change in price (Δ𝑝) is needed. In order to assume
the value of above information, some case studies are done as follows.
Case Study – 1
Here, 𝐸𝑝 =
Δq
Δp
×
p
q
=
0
1
×
5
10
= 0
So, 𝐸𝑝 = 0 [Perfectly inelastic demand]
Case Study – 2
Here, 𝐸𝑝 =
Δq
Δp
×
p
q
=
1
1
×
5
10
= 0.5
So, 𝐸𝑝 = 0.5 [Inelastic demand]
Price Demand
5 10
4 10
-1 0
Price Demand
5 10
4 11
-1 0
Original
Price
Change
in price
Original
demand
Change in
demand
Original
Price
Change
in price
Original
demand
Change in
demand

Page 4 of 15
Case Study – 3
Here, 𝐸𝑝 =
Δq
Δp
×
p
q
=
2
1
×
5
10
= 1
So, 𝐸𝑝 = 1 [Unitary elastic demand]
Case Study – 4
Here, 𝐸𝑝 =
Δq
Δp
×
p
q
=
3
1
×
5
10
= 1.5
So, 𝐸𝑝 = 1.5 [Elastic demand]
Case Study – 5
Here, 𝐸𝑝 =
Δq
Δp
×
p
q
=
4
0
×
5
10
= ∞
So, 𝐸𝑝 = ∞ [Perfectly Elastic demand]
Price Demand
5 10
4 12
-1 2
Price Demand
5 10
4 13
-1 3
Price Demand
5 10
5 14
0 4
Original
Price
Change
in price
Original
demand
Change in
demand
Original
Price
Change
in price
Original
demand
Change in
demand
Original
Price
Change
in price
Original
demand
Change in
demand

Page 5 of 15
From the above case studies, it can be seen that the value of price elasticity of demand varies
between 0 and ∞, i.e. 0< 𝐸𝑝<∞. Based on the value, price elasticity of demand has different
categories.
CATEGORIES OF PRICE ELASTICITY OF DEMAND
i. With the change of price if demand remains constant, in that case demand
will be perfectly inelastic demand ( 𝐸𝑝 = 0)
ii. If rate of change of demand is less than the rate of change of price, in that
case demand is called inelastic demand ( 𝐸𝑝 < 1)
iii. If rate of change of demand is equal to the rate of change of price, in that
case demand is called inelastic demand ( 𝐸𝑝 = 1)
iv. If rate of change of demand is greater than the rate of change of price, in that
case demand is called elastic demand ( 𝐸𝑝 > 1)
v. If at the same price any amount is demanded, in that case it will be perfectly
elastic demand (𝐸𝑝 = ∞)
PRICE ELASTICITY IN DIAGRAMS

Page 6 of 15
2. GEOMETRIC MEASUREMENT OF PRICE ELASTICITY OF DEMAND
Geometric measurement is used for measuring elasticity of demand on
different points on a straight line demand curve.
FORMULA OF GEOMETRIC MEASUREMENT
The price elasticity of demand at a point on a straight line is equal to the
lower segment of the demand curve divided by upper segment of the demand curve.
That is,
𝐸𝑝 =
𝐿𝑜𝑤𝑒𝑟 𝑠𝑒𝑔𝑚𝑒𝑛𝑡 𝑜𝑓 𝑑𝑒𝑚𝑎𝑛𝑑 𝑐𝑢𝑟𝑣𝑒 𝑓𝑟𝑜𝑚 𝑝𝑎𝑟𝑡𝑖𝑐𝑢𝑙𝑎𝑟 𝑝𝑜𝑖𝑛𝑡
𝑈𝑝𝑝𝑒𝑟 𝑠𝑒𝑔𝑚𝑒𝑛𝑡 𝑜𝑓 𝑑𝑒𝑚𝑎𝑛𝑑 𝑐𝑢𝑟𝑣𝑒 𝑓𝑟𝑜𝑚 𝑡𝑕𝑎𝑡 𝑝𝑜𝑖𝑛𝑡
EXAMPLE
At Point L, 𝐸𝑝 =
𝐿𝐷1
𝐿𝐷
As, 𝐿𝐷1 <𝐿𝐷, so 𝐸𝑝 is less than 1 (𝐸𝑝 < 1)
At Point K, 𝐸𝑝 =
𝐾𝐷1
𝐾𝐷
As, 𝐾𝐷1 >𝐾𝐷, so 𝐸𝑝 is greater than 1 (𝐸𝑝 > 1)

Page 7 of 15
PRICE ELASTICITY OF DEMAND AT DIFFERENT POINTS OF STRAIGHT LINE DEMAND
CURVE
Here, OY axis represents price (p) and OX axis represents demand (q). DD1 is a straight line
demand curve. A spectrum OL is drawn at 45° which intersect the demand curve at point E.
Other two different points are placed as G and F.
At point D1, price elasticity of demand, Ep =
0
D1D
= 0
So, at point D1, Ep is zero (0), which is perfectly inelastic demand.
At point F, price elasticity of demand, Ep =
FD1
FD
, FD1 < FD
So, at point F, Ep is less than 1, which is inelastic demand.
At point E, price elasticity of demand, Ep =
ED1
ED
, ED1= ED
So, at point E, Ep is equal to 1, which is unitary elastic demand.
At point G, price elasticity of demand, Ep =
GD 1
GD
, GD1 > GD
So, at point E, Ep is greater than 1, which is elastic demand.
At point D, price elasticity of demand, Ep =
DD1
0
= ∞
So, at point D, Ep is equal to ∞, which is perfectly elastic demand.
From the above discussion, it can be said that price elasticity of demand at different points of
a straight line demand curve is not same.
At middle point of straight line demand curve, Ep = 1
Any point below the middle point, Ep >1
Point at which demand curve cuts X- Axis, Ep = 0
Point at which demand curve cuts Y- Axis, Ep = ∞

Page 8 of 15
INCOME ELASTICITY OF DEMAND
Income elasticity of demand measures the responsiveness of sales to change in income.
Income elasticity of demand can be defined as the rate at which demand changes due to
change of income of consumers holding other influencing factors same is called income
elasticity of demand. This term denotes the percentage change in quantity demanded
divided by the percentage change in income.
FORMULA OF INCOME ELASTICITY OF DEMAND
The income elasticity of demand is found by the following formula:
𝐸𝐼 =
Δ𝑞
q
÷
Δ𝐼
I
=
Δ𝑞
q
×
𝐼
Δ𝐼
=
Δ𝑞
Δ𝐼
×
𝐼
q
Here,
𝐸𝐼 = Income elasticity of demand
q = Original demand
Δ𝑞 = Change in demand
𝐼 = Original income
Δ𝐼 = Change in income
We know,
Δ𝑞
q
= % of relative change in demand
Δ𝐼
I
= % of relative change in income
So, 𝐸𝐼 =
% of relative change in demand
% of relative change in price
Or, 𝐸𝐼 =
% of change in demand
% of change in price
[Derivation from original formula]

Page 9 of 15
MEASUREMENT OF INCOME ELASTICITY OF DEMAND
Income elasticity of demand 𝐸𝐼 could be greater than zero (0), which is
positive, equal to zero (0) or less than zero (0), which is negative.
 𝑬 𝑰 > 0 (Positive): With the rise of income if demand rises, in that case
income elasticity of demand will be positive ( 𝐸𝐼 > 0)
∴ 𝐸𝐼 =
25
50
×
100
50
= 1, so 𝐸𝐼 > 0
 𝑬 𝑰 = 0 (Zero): With the rise of income if demand remains constant, in
that case income elasticity of demand will be zero ( 𝐸𝐼 = 0)
∴ 𝐸𝐼 =
0
50
×
100
50
= 0, so 𝐸𝐼 = 0
 𝑬 𝑰 < 0 (Negative): With the rise of income if demand falls, in that case
income elasticity of demand will be negative ( 𝐸𝐼 < 0)
∴ 𝐸𝐼 =
25
50
×
100
50
= -1, so 𝐸𝐼 < 0
Income Demand
100 50
150 75
50 25
Income Demand
100 50
150 50
50 0
Income Demand
100 50
150 25
50 25
Original
Income
Change
in income
Original
demand
Change in
demand
Original
Income
Change
in income
Original
demand
Change in
demand
Original
Income
Change
in income
Original
demand
Change in
demand

Page 10 of 15
RELATIONSHIP WITH NATURE OF COMMODITY
The nature of the commodity can be determined from measurement of
income elasticity of demand.
Normal Commodity
When 𝐸𝐼 is positive (𝐸𝐼 > 0) for particular commodity, that commodity is
called normal commodity.
𝐸𝐼 > 0 Commodity is normal commodity
Highly Essential Commodity for Life
When 𝐸𝐼 is equal to zero (0) (𝐸𝐼 = 0) for particular commodity, that
commodity is called highly essential commodity for life.
𝐸𝐼 = 0 Commodity is highly essential for life
Inferior Commodity
When 𝐸𝐼 is negative (𝐸𝐼 < 0) for particular commodity, that commodity is
called inferior commodity
𝐸𝐼 < 0 Commodity is inferior commodity

Page 11 of 15
CROSS ELASTICITY OF DEMAND
The quantity demanded of a particular good varies according to the price of other goods. For
example, a rise in price of a good such as tennis racket would lead to a fall in quantity
demanded of a complement such as tennis ball.
Cross elasticity of demand is a measure of how much the quantity demanded of
one good responds to a change in the price of another good. In other words, the rate at which
demand changes due to change of price of other commodities while the other factors
remaining same, is called cross elasticity of demand. Cross elasticity of demand allows a
business to gauge how demand for its product will react if the price of rival’s products or
complementary goods changes.
FORMULA OF CROSS ELASTICITY OF DEMAND
Suppose,
X is original commodity
Y is other commodity
So, it can be said that cross elasticity of demand is other factors remaining same, the rate at
which demand for commodity X changes due to particular change of commodity Y.
Cross elasticity of demand for the commodity X and commodity Y can be calculated using
the following formula:
𝐸 𝐶 =
Δ𝑞 𝑥
𝑞 𝑥
÷
Δ𝑝 𝑦
𝑝 𝑦
=
Δ𝑞 𝑥
𝑞 𝑥
×
𝑝 𝑦
Δ𝑝 𝑦
=
Δ𝑞 𝑥
Δ𝑃𝑦
×
𝑝 𝑦
𝑞 𝑥
Here,
𝐸𝐶 = Cross elasticity of demand
𝑞 𝑥 = Original demand for commodity X
Δ𝑞 𝑥 = Change in demand for commodity X
𝑝 𝑦 = Original price of commodity Y
Δ𝑝 𝑦 = Change in price of commodity Y
We know,
Δ𝑞 𝑥
𝑞 𝑥
= % of relative change in demand for commodity X
Δ𝑝 𝑦
𝑝 𝑦
= % of relative change in price of commodity Y

Page 12 of 15
∴ 𝐸 𝐶 =
% of relative change in demand for commodity X
% of relative change in price of commodity Y
𝑜𝑟, 𝐸 𝐶 =
% of relative change in demand for commodity X
% of relative change in price of commodity Y
[Derived from formula]
MEASUREMENT OF CROSS ELASTICITY OF DEMAND
Cross elasticity of demand 𝐸𝑐 could be greater than zero (0), which is
positive, equal to zero (0) or less than zero (0), which is negative.
 𝑬 𝑪 > 0 (Positive): If with the rise of price of other commodity, demand for
original commodity rises, in that case cross elasticity of demand will be positive
( 𝐸𝐶 > 0).
Suppose, X is original commodity, Y is other commodity. With the rise
of price of other commodity Y, if demand for original commodity X
rises, in that case cross elasticity of demand will be positive ( 𝐸𝐼 > 0).
∴ 𝐸𝑐 =
Δ𝑞 𝑥
Δ𝑃𝑦
×
𝑝 𝑦
𝑞 𝑥
=
50
50
×
100
50
= 2, so 𝐸 𝐶 > 0
 𝑬 𝑪 = 0 (Zero): If with the rise of price of other commodity, demand for original
commodity remain constant, in that case cross elasticity of demand will be zero
( 𝐸𝐶 = 0).
of price of other commodity Y, if demand for original commodity X remains
constant, then cross elasticity of demand will be zero ( 𝐸𝐼 = 0).
𝑝 𝑦 𝑞 𝑥
100 50
150 150
50 50
Original price of
other commodity Y
Change in price of
other commodity
Y
Original demand for
commodity X
Change in demand for
commodity X

Page 13 of 15
∴ 𝐸𝐶 =
Δ𝑞 𝑥
Δ𝑃𝑦
×
𝑝 𝑦
𝑞 𝑥
=
0
50
×
100
50
= 0, so 𝐸 𝐶 = 0
 𝑬 𝑪 < 0 (Negative): If with the rise of price of other commodity, demand for
original commodity falls, in that case cross elasticity of demand will be less than
zero ( 𝐸𝐶 < 0).
of price of other commodity Y, if demand for commodity X falls, in that case
cross elasticity of demand will be less than zero ( 𝐸𝐼 < 0).
∴ 𝐸 𝐶 =
Δ𝑞 𝑥
Δ𝑃𝑦
×
𝑝 𝑦
𝑞 𝑥
=
−25
50
×
100
50
= −1, so 𝐸 𝐶 < 0
𝑝 𝑦 𝑞 𝑥
100 50
150 50
50 00
𝑝 𝑦 𝑞 𝑥
100 50
150 25
50 -25
Original price of
other commodity Y
Change in price of
other commodity
Y
Original demand for
commodity X
commodity X
Original price of
other commodity Y
Change in price of
other commodity
Y
Original demand for
commodity X
commodity X

Page 14 of 15
RELATION BETWEEN ORIGINAL COMMODITY AND OTHER COMMODITY
Cross elasticity of demand enables us to know the relationship between
original commodity and other commodity.
Substitute Commodities
When cross elasticity of demand, 𝐸 𝐶 is positive (𝐸 𝐶 > 0), commodities are
substitute for each other.
𝐸 𝐶 > 0 Commodities are substitute
Independent Commodities
When cross elasticity of demand, 𝐸 𝐶 is equal to zero (0) (𝐸 𝐶 = 0)
commodities are independent for each other.
𝐸 𝐶 = 0 Commodities are independent
Complementary Commodities
When cross elasticity of demand, 𝐸 𝐶 is negative (𝐸 𝐶< 0) commodities are
complementary commodity.
𝐸 𝐶 < 0 Commodities are complementary

Page 15 of 15
REFERENCES
o Samuelson, Paul and Nordhaus, William. Economics. 19th
ed. McGraw-Hill/Irwin,
2010.
o Class lecture
o Notes and handouts on economics by several universities

Elasticity of Demand - Concept and Measurements

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