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Elasticity of Demand

Introduction

– There is relationship between demand and price –

Law of Demand

– It indicates the direction of change of quantity demanded to change in price.

– But it does not give the answer to how much or to what extent?

– This information is given by Elasticity of Demand.

Elasticity of Demand

– It is defined as degree of responsiveness of quantity demanded of a good to changes in one of the variables .

» Price» Consumers Income» Prices of related goods

Price Elasticity of Demand

• It is defined as ratio of the percentage change in quantity demanded of a commodity to percentage change in price.

ep = % change in QD

% change in Price

• The price elasticity are expressed with a +ve sign even if they are inversely related as we want to measure the “magnitude of responsiveness”.

Price Elasticity of Demand

ep = % change in QD % change in Price

ep = Change in Quantity * 100 Original Quantity

Change in Price * 100 Original Price

ep = ∆q * p q ∆p

• It has a negative sign• The price elasticity are expressed with a positive sign even if

they are inversely related as we want to measure the magnitude of responsiveness.

Numerical

Q 1. The price of a Chocolate Bar in the local newsagent rises from 25p to 30p. As a result, the newsagent finds that the demand for this product falls from 80 bars a day to 40

bars a day. Find the price elasticity of demand.

(-2.5)

Q2. The price of a litre of unleaded petrol rises from Rs 80 to Rs 84 . As a result, the quantity demanded at a local station falls from 4000 to 3880 litres a day. What is the price elasticity of demand?

(-0.6)

Notice: The answer is negative. This is because the price rose (+ve) causing the quantity demanded to fall (-ve). The demand curve is nearly always downward sloping showing a negative relationship between price and quantity demanded

Q A company decides to increase the price of Brand X drink from Rs2 a bottle to Rs2.10 a bottle. The price elasticity of demand for Brand X is 0.8. He currently sells 300 bottles a day. What will the new demand be (ceteris paribus)?

Ans 288

Three Concept of Demand Elasticity

1. Price Elasticity:

Degree of responsiveness to change in its price

2. Income Elasticity:

Sensitiveness of quantity demanded to change in income.

3. Cross Elasticity:

Degree of responsiveness to change in the price of a

related good (Substitute /Complement).

Types of Price Elasticity

The value of ep varies from Zero (0) to Infinity ( ∞ )

Elastic Demand:

When the percentage change in quantity demanded is greater than percentage change in price.

Inelastic Demand:

When the percentage change in quantity demanded is less than percentage change in price.

O M M’

P’

P

D

D

O M M’

P’

P

D

D

Types of Price Elasticity

• There are 5 types of price elasticity

• The main reason for differences in elasticity is the possibility of substitution i.e

presence or absence of competing products.

1) Perfectly Elastic or ep = ∞

When demand is infinite or

unlimited at given price.

A reduction in price causes the

quantity to increase from

zero to infinite.

Types of Price Elasticity

2) Perfectly Inelastic or ep = 0

When change in prices have

a zero impact on the

quantity demanded

3) Unitary Elastic Demand or ep = 1When change in quantitydemanded is equal to the change in price.

Types of Price Elasticity

4) Relatively Elastic or ep > 1

When change in quantity

demanded is greater

than change in prices

5) Relatively Inelastic or ep < 1When change in quantity

demanded is less than the change in price.

To Summarise………

Determinants of Price Elasticity

• The Availability of Substitutes

– The number and kind of substitute makes the consumer sensitive to change in prices.

– If close substitute are available, its demand is elastic.– If no close substitute are not available, even with rise in

price the demand is inelastic.

• The proportion of Consumer Income spent– Greater the proportion of income spent o the commodity,

greater the elasticity of demand.

• The number of uses of a commodity– The greater the number of uses to which a commodity

can be put, the greater will be its price elasticity of demand.

Determinants of Price Elasticity

• Complementarity between Goods

– Complementarily or joint demand for goods effects the elasticity

– Consumers are less sensitive to change in prices of goods that are complementary with each other.

• Time and Elasticity– Demand is more elastic if the time involved is long, as

consumers can substitute goods in the long run.– Demand is inelastic in the short run.

• Durability of the commodity

Measurement of Price Elasticity

Methods

• Percentage Method

• Midpoint Method

• Total Outlay Method

1) Percentage Method:

It is defined as ratio of the percentage change in quantity demanded of a commodity to percentage change in price.

ep = % change in QD % change in Price

ep = Change in Quantity * 100 Original Quantity

Change in Price * 100 Original Price

ep = ∆q * p ∆p q

Numerical

Q. If the price of the commodity falls from Rs 6 to Rs 4 per unit and due to it QD increases from 80 units to 120 units.

Find out the price elasticity of demand?Ans: 1.5

Q. If the price of the commodity rises from Rs 4 to Rs 6 per unit , the QD falls from 120 to 80 units.What is the price elasticity of demand?Ans: 0.60

2) Midpoint / ARC Method:

– Which price and quantity to use while calculating the % change.

– When the changes in price and quantity are substantially large.

– In this method we take the midpoint of the initial and final values of price and quantity as a base.

( q2-q1) p2 - p1

ep = q1 + q2 ÷ p1 + p2

2 2

ep = ∆q * p1 + p2

∆p q1 + q2

• What is the point, after all, of a firm knowing the elasticity of demand for the product he sells?

If he can assess what the change in his sales will be for a given change in the price of his product, and then he can work out the change in his revenue.

P* Q = TR

P

Q

D

3) Total Revenue Method

– Total revenue is the amount received by the seller from the sale of the quantity of the good sold in the market.

– Total Revenue: P * Q

Numerical

Q. Suppose a seller of a textile cloth wants to lower the price of its cloth from Rs 150 per metre to Rs 142.5 per metre. If its present sales are 2000 metres per month and

further estimated that its elasticity of demand for the product equals -0.7. show

a) Whether or not total revenue will increase as a result of his decision to lower the price.

Ans: 2070

b) Calculate the exact magnitude of its new total revenue.Ans: Rs 2,94,975(With reduction in price his total revenue has decreased)

1. Demand is elastic ( ep >1)

The % increase in quantity demanded of the commodity will be greater than the % fall in price.

Total Revenue will increase.

Conversely a rise in price reduces Total revenue.

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P

Q Q’

R

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For Example:A vegetable seller decides to cut the price of his potatoes from Rs 40/Kg to Rs 32p/Kg. The ep for this product is 2. He currently sells 80 Kg of potatoes a day. How many will he sell after the price cut?

But what will happen to his revenue?

Revenue before the price cut: Rs 40 × 80Kg = Rs3200 Revenue after the price cut: Rs32 × 112Kg = Rs3584

The price cut causes revenue to increase. The rise in demand as a result of the price cut was proportionately higher than the fall in price

'gain' box is larger than the 'loss' box,so the seller's total revenue has increased

b) What will happen if he increase the price to Rs 44 / kg

Revenue before the price increase:= 40p × 80 = Rs3200 Revenue after the price increase: = 44 × 64 = Rs 2816

2. Demand is Inelastic (ep<1)

A fall in price reduces total revenue

A rise in price raises total revenue

A rise in price will lead to a percentage decline in quantity demanded that is proportionately less than the rise in price.

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For example:Petrol has a relatively inelastic demand. If value of the elasticity is 0.5, the initial price is 80p per litre and sales of 4000 litres per day.

a) What happens when the price is cut to Rs 72 per litre. The cut in the price will lead to an increase in less demand. The new demand will be 4200 litres.

Revenue before the price cut:= 80 × 4000 litres = 3200

Revenue after the price cut: = 72 × 4200 litres = 3024

• There is a fall in total revenue where the 'loss' box is much

bigger than the 'gain' box.

• For example:

b) Increase in the price to 88p per litre. This 10% rise in the price will lead to a fall in demand, but by only 5%. The new demand will be 3800 litres.

Revenue before the price cut: = 80 × 4000 litres = Rs 3200

Revenue after the price rise: = 88p × 3800 litres = Rs 3344 • This rise in total revenue , where the 'gain' box is much

bigger than the 'loss' box.

3. Demand is Unit elastic ( ep = 1)

The percentage increase in quantity demanded of the commodity will be equal to the percentage fall in price.

Total Revenue will be same.

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P’

P

Q

R

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Elasticity and Revenue

P Qd TR

P *Q

(ep)

5.00 30 150 -

4.75 40 190 e >1

4.50 50 225 e >1

4.25 60 255 e >1

4.00 75 300 e >1

3.75 80 300 e =1

3.50 84 294 e <1

3.25 87 282.75 e <1

To Summarise…………..

Numerical

Q1. Price of the good falls from Rs 10 to Rs 8 per unit. As a

result, its quantity demanded increases from Rs 80 units

to 100 units. Find out the elasticity of the goods.

Ans: ep=1

Q2. If the price of commodity rises from Rs 15 to Rs 16 per

unit. As a result the QD falls from Rs 100 to 80 units.

Find out ep is more than one or less than one?

Ans: ep> 1

Q3. The ep for petrol is equal to unity and at Rs 15/litre an individual demand 80 litre of petrol in a week. How much price of petrol should be fixed so that he demands 60 litres of petrol?

Ans: 60 Litre

Importance for Business Decision Making

• Pricing of Public Utilities:

Charging higher prices for high end consumers/ lower prices

to the low end consumers.

• International Trade:

Charge a higher export prices if the demand for exports is

inelastic, charge lower prices and earn higher revenue.

• Product differentiation and Differential pricing:

Company to produce different products and charge different

prices depending on the elastic or inelastic demand.

• Shifting the Taxation:

Shifting the taxation depends upon the elasticity of demand.

Cross Elasticity of Demand

• The degree of responsiveness of demand for one good in response to the change in prices of another good.

• Good X and Good Y are substitute of each other

P1

P2

Q1 Q2Good Y

P

M1

M2Good X

What would have happen if Good X & Y were complement Goods?

Cross Elasticity of Demand

ec = Percentage change in Qd of X

Percentage change in the price of good Y

ec = Qx2 – Qx1 ÷ Py2 – Py1

Qx2 + Qx1 Py2 + Py1

2 2

Substitute and Complementary Goods

• Positive Cross Elasticity:– Rise in price of good X leads to rise in demand of

good Y– They are substitute goods

• Negative Cross Elasticity:– Rise in price of good X leads to fall in demand of good Y– They are Complementary goods

• Zero Cross Elasticity:– Rise in price of good X will have no effect on good Y– They are unrelated goods

Importance for Business Decision Making

• It helps in formulating pricing strategy for multi-product firms.

• It defines the boundaries of an Industry

( Anyone company cannot raise the price of the product without losing sales to the other firm)

Numerical

Q.

Colgate sells its standard size toothpaste for Rs 25. Its sales

have been on an average 8000 units per month over the

past year. Recently, its close competitor Binaca reduced the

price of its same standard size toothpaste from Rs 35 to

Rs30. As a result colgate sales declined by 1500 per units per month.

1) Calculate the cross elasticity between the two products.

2) What does it indicate about the relationship between the two.

Income Elasticity

• It shows the degree of responsiveness of quantity demanded of a good to a small change in the income of consumers.

• Income Elasticity = % change in purchase of a good

% change Income

ei = q2 – q1 ÷ y2 – y1

q2 + q1 y2 + y1

2 2

Income Elasticity and Goods

Zero Income Elasticity : Rise in Income does not lead to increase in quantity demanded(Unresponsive to change)

Positive Income Elasticity: Rise in Income leads to rise in quantity demanded ( Luxury / Normal goods)

Negative Income Elasticity:Rise in income leads to fall in quantity demanded ( Necessity /Inferior Goods)

Income Elasticity is Unity: Proportion of income spent on the good remain the same aconsumers income increases.

Importance for Business Firms

• The firms which are producing goods which have high

income elasticity have a great potential for growth.– The firms will be located in those areas which are

growing– The marketing strategies will be targeted to those

segment whose income is increasing.

• Demand for products which have low income elasticity will be not be greatly effected by economic fluctuations.

( Recession proof)