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


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


Δp×

p

q =

2

1 ×

5

10 = 1

So, 𝐸𝑝 = 1 [Unitary elastic demand]

Case Study – 4


Δp×

p

q =

3

1 ×

5

10 = 1.5

So, 𝐸𝑝 = 1.5 [Elastic demand]

Case Study – 5


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 = FD 1

FD , FD1 < FD

So, at point F, Ep is less than 1, which is inelastic demand.

At point E, price elasticity of demand, Ep = ED 1

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 = DD 1

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.

𝑬𝑰 > 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

𝑬𝑰 = 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

𝑬𝑰 < 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:

𝐸𝐶 =Δ𝑞𝑥

𝑞𝑥 ÷

Δ𝑝𝑦

𝑝𝑦=

Δ𝑞𝑥

𝑞𝑥 ×

𝑝𝑦

Δ𝑝𝑦=

Δ𝑞𝑥

Δ𝑃𝑦×

𝑝𝑦

𝑞𝑥

Here,

𝐸𝐶 = Cross elasticity of demand

𝑞𝑥 = Original demand for commodity X

Δ𝑞𝑥 = Change in demand for commodity X

𝑝𝑦 = Original price of commodity Y

Δ𝑝𝑦 = Change in price of commodity Y

We know,

Δ𝑞𝑥

𝑞𝑥= % of relative change in demand for commodity X

Δ𝑝𝑦

𝑝𝑦 = % of relative change in price of commodity Y


Page 12 of 15

∴ 𝐸𝐶 =% of relative change in demand for commodity X

% of relative change in price of commodity Y

𝑜𝑟, 𝐸𝐶 =% 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.

𝑬𝑪 > 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 = Δ𝑞𝑥

Δ𝑃𝑦×

𝑝𝑦

𝑞𝑥=

50

50×

100

50= 2, so 𝐸𝐶 > 0

𝑬𝑪 = 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).

𝑝𝑦 𝑞𝑥

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 =Δ𝑞𝑥

Δ𝑃𝑦×

𝑝𝑦

𝑞𝑥=

0

50×

100

50= 0, so 𝐸𝐶 = 0

𝑬𝑪 < 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).

∴ 𝐸𝐶 =Δ𝑞𝑥

Δ𝑃𝑦×

𝑝𝑦

𝑞𝑥=

−25

50×

100

50= −1, so 𝐸𝐶 < 0

𝑝𝑦 𝑞𝑥

100 50

150 50

50 00

𝑝𝑦 𝑞𝑥

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, 𝐸𝐶 is positive (𝐸𝐶 > 0), commodities are

substitute for each other.

𝐸𝐶 > 0 Commodities are substitute

Independent Commodities

When cross elasticity of demand, 𝐸𝐶 is equal to zero (0) (𝐸𝐶 = 0)

commodities are independent for each other.

𝐸𝐶 = 0 Commodities are independent

Complementary Commodities

When cross elasticity of demand, 𝐸𝐶 is negative (𝐸𝐶< 0) commodities are

complementary commodity.

𝐸𝐶 < 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

Economy & Finance