Measurement of

Elasticity

This Presentation on Measurement of elasticity

was preparedBy

Mr.Prem Raj Bhatta

Nepal Western AcademyDhagadhi-2 , Kailali, Nepal

This Topic Contains:#Meaning of Elasticity of Demand,#Types of Elasticity of Demand,

1. Meaning of Elasticity of DemandElasticity of demand refers to the responsiveness of

dependent variable to the change in independent variable. It is a measure of how much the quantity demanded of a commodity responds to a change in the price of the commodity, income of the consumer, prices of related goods etc.

In other words, elasticity of demand refers to the ratio of percentage change in quantity demanded of a commodity to the percentage change in any determinant of demand.

Elasticity of demand can also be expressed as follows;

= -

It’s a sensitivity or responsiveness of demand to the change in an independent variable, or…

It is the result calculated as the percentage change in demand divided by percentage change in an independent variable

2-Types of Elasticity of Demand

Elasticity of demand is of three types.• Price Elasticity of Demand • Income Elasticity of Demand• Cross elasticity of Demand

2.1. Price Elasticity of Demand• Price elasticity of demand is a measure of how much the quantity

demanded of a commodity responds to a change in the price of that commodity. In other words, it is the radio of the percentage change in quantity demanded of a commodity to the percentage change in its price, other things being equal.

• It is expressed as follows;

= -

It is the percentage change in quantity divided by percentage change in price, or

Responsiveness of demand to changes in price.

Mathematically, price elasticity of demand is expressed as follows;

X

Where;

∆Q = Change in Quantity∆P = Change in priceP1 = Initial PriceP2 = New priceQ1 = Initial quantityQ2 = New quantity

5

For example, Suppose the quantity demanded of sugar was 200 kg at Rs,50 per kg. when price rose up to Rs. 60 per kg, demand for sugar decreased to 180 kg.

Solution, Initial quantityQ1=200kg,

New quantityQ2=180 kgInitial price P1=50 New price P2 = 60

∆Q= 180 – 200 = - 20

∆P = 60 – 50 = 10Here,

= - x Substitute the values in the above formula.

=- x

= 0.5 ans.

Note:- or the coefficient of price elasticity of demand is always negative because when price changes, demand moves in opposite direction. But the negative sign (- ) is ignored while using the coefficient.

Price elasticity of demand is generally divided under the following sub headings;

1. Perfectly Elastic Demand2. Relatively Elastic Demand, or More than unity (one)3. Unitary Elastic Demand, or Equal to unity (one)4. Relatively Inelastic Demand, or Less that Unity (one)5. Perfectly Inelastic Demand All these types of price elasticity demand have been explained as under.

* 2.1.1-Types of Price Elasticity of Demand

1- Perfectly elastic Demand = ∞)Price elasticity of demand is said to be perfectly elastic when a small reduction in prices causes the buyers to increase the quantity demanded from zero to all they wanted and a small rise in price makes them cut in demand completely.The demand in such a case hyper-sensitive and elasticity of demand is infinite. Such a price elasticity of demand is rare in actual life. The following figure shows the nature of perfectly elastic demand. In the figure, at per unit price Rs.11 demand is zero unit and a fall in price by Rs. 1 has caused an increase in demand by 100 units.Here, P1=11, P2=10 ,Q1=0 & Q2=100

∆Q = 100 & ∆P=1

= - 𝑒𝑝 X

= 𝑒𝑝 X = 𝑒𝑝 = ∞ ans.𝑒𝑝

D D

Y

X100

1011

0

pric

e

Quantity

Fig-1

2-Rlatively Elastic Demand ()Price elasticity of demand said to be

relatively elastic or greater than one when the percentage change in quantity demanded is greater than the percentage change in price.

Relatively elastic demand is shown in figure-2 . In the figure, quantity demanded is 5 unit at Rs. 10, when per unit price falls to Rs.5, demand will rise to 15 units.

The percentage change in price is 50% and percentage change in quantity demanded is 200%. Elasticity of demand is 4, which is greater that one (4>1).Here, given Q1=5, Q2=15

P1=10, P2=5∆Q= Q2-Q1, 15-5, 10∆P= P2-P1, 5-10, -5

= -

= - ans.

Or, = 𝒆𝒑= 4 ans.

0 5 10 15

10

5

A

B50%

200%

P

Q

Quantity

Pri

ce

Fig - 2

Fig -3

= - X

= - x = 1 Ans.

Or, =

= 1

3- Unitary Elastic Demand (=1)

• Price elasticity of demand is said to be unitary or equal to one when the percentage change in quantity demanded equals to the percentage change in its price. It is shown in the figure-3.

• The figure shows that the initial price is Rs. 10 and at this price quantity demanded is 10 units. When the price falls to Rs, 5, quantity demanded extents to 15 units. It means the change in quantity demanded(50%) is equal to the change in price(50%).

Given, Q1=10, Q2=15, P1=10, P2=5• %change in price=(P2-P1)/P1 X 100

• =(5-10)10 X 100• = 50%

• %change in demand=(Q2-Q1)Q1X100• = (15-10)10X100• = 50%

P

Q

A

B

D

D

10 15

5

10

0

50%

50%

Pri

ce

Quantity

Note :- ∆Q=Q2-Q1 & ∆P=P2-P1

Fig -4

= - X

= - x = 0.83 ans.

Here, < 1𝑒𝑝

4- Relatively Inelastic Demand (< 1)Price elasticity of demand is said to be

relatively inelastic or less than unity, when the percentage change in quantity demanded is less than that of the percentage change in price. It is shown in the figure – 4.

The figure shows that quantity demanded of the commodity is 10 units at the initial price Rs.10 and a fall in the price from Rs. 10 to 4 causes an increase in demand from 10 to 15 units. The quantity demanded has changed by 50% whereas the price has changed by 60%. The percentage change in demand is less that that of the percentage change in price.Given, QI=10, Q2=15, P1=10 & P2= 4 % change in demand ∆Q= (Q2-Q1)/Q1 x100 = (15-10)/10 x100 = 50%%change in price ∆P=(P2-P1)/P1x 100 = (4-10)/10 x 100 = - 60% 0r 60%

Q

PD

D

A

B

0

4

10

5 10 15

Pri

ce

Quantity

60%

50%

Note:- ∆Q =Q2-Q1 & ∆P=P2-P1

Fig-5

= - X

= - X= 0 ans.

5- Perfectly Inelastic demand (= 0)• Price elasticity of demand is said to be perfectly

inelastic when quantity demanded of a commodity remains unchanged or unresponsive even if there is any change in price. The nature perfectly inelastic demand has been shown in the figure- 5.The figure shows that initial quantity demanded of a commodity is 10 units at initial price Rs. 4 but there is no change or zero percent change in quantity demanded even if the price falls from Rs. 4 to 2 by 50%. Hence, quantity demanded is perfectly inelastic or equal to zero.

• Given, Q1=10, Q2=10, P1=4 & P2=2% change in demand ∆Q=(Q2-Q1)/Q1X100• =(10-10)/10X100• = 0%

%change in price ∆P=(P2-P1)/P1X100• =(2-4)/4X100• =-50% or 50%

Q

PD

D

0

4

2

10

A

B

Quantity

Pri

ce 50%

=

Table showing elasticity of various goods

*Let’s summarize the slope of demand curves

1- perfectly elastic (horizontal)2- relatively elastic (flatter)3- unitary elastic (steeper)4- relatively inelastic (more steeper)5- perfectly inelastic (vertical)

Types of price elasticity of demand

Variety of goods

1-Perfectly elastic No, practical importance, rare use2- Relatively elastic Luxurious goods and goods having close substitutes 3- Unitary elastic No specific goods 4- relatively elastic Goods of daily uses and goods having no close substitutes5- perfectly inelastic most necessary goods and services, like medicine, drugs

Fig- 6

A

BD

D

P

Q0 80 120

46

3- Midpoint Method of Calculating Price PlasticityIf we try to calculate the price elasticity of demand between two points on a demand curve, we will face an annoying problem; that is, the elasticity from point A to point B seems different from the elasticity from point B to point A. For example, consider the figure-5 and following calculations.From point A to B ∆P=(6-4)/4x100=50%

∆Q=(80-120)/120x100=33.33%From point B to A ∆P=(4-6)/6x100=33.33%

∆Q=(120-80)/80x100=50%From point A to B = 33.33% / 50%

= 0.66From point B to A = 50% / 33.33%

= 1.5It is seen in the above calculations that when we move from point A to B and from point B to A on the same demand curve, the coefficient of price elasticity of demand differs. This problem is avoided by using midpoint or average method of calculating elasticity.

To calculate elasticity by midpoint or average or midway method, the following formula is applied.

= -

= - x Now, from point A to B ∆Q=80-120, =-40∆P=