elasticity and its...

Elasticity and Its

Application

Sakib Bin Amin, Ph.D.

Assistant Professor

School of Business and Economics

North South University

What is an Elasticity?

Measurement of the percentage change in

one variable that results from a 1%

change in another variable.

When the price rises by 1%, quantity

demanded might fall by 5%.

The price elasticity of demand is -5 in this

example.

Types of Elasticity

1.Elasticity of Demand

i) Price Elasticity of Demand

ii) Income Elasticity of Demand

iii) Cross Price Elasticity of Demand

2.Elasticity of Supply

Price Elasticity of Demand

Price elasticity of demand is the

percentage change in quantity demanded

given a percent change in the price.

It is a measure of how much the quantity

demanded of a good responds to a change

in the price of that good.

Price Elasticity of Demand

Q

P

P

Q

PP

QQ

/

/

•The price elasticity of demand is always negative.

•Economists usually refer to the price elasticity of

demand by its absolute value (ignore the negative

sign).

Computing the Price Elasticity

of Demand

price inchange Percentage

demandedquatity inchange Percentagedemand of elasticityPrice

Example: If the price of an ice cream cone increases

from $2.00 to $2.20 and the amount you buy falls from

10 to 8 cones then your elasticity of demand would be

calculated as:

2percent10

percent20

100002

002202

10010

810

.

)..(

)(

Example:

P0 = 8 P1 = 7

Q0 = 40 Q1 = 48

Step 1: Q = 48 - 40 = 8

P = 7 - 8 = -1

Step 2: Use the formula for Ed.

Example:

Step 3:

Ed = (Qd / P) * P0 / Q0

= (8 /-1) * (8/40) = - 1.6

Step 4:

This means that for every 1 % change in price that

there is a 1.6 % change in quantity demanded in the

opposite direction.

0 1 2 3 4 5 6

Inelastic

Unit elastic

Elastic

Price elasticity of demand

Demand is said to be: elastic when Ed > 1,

unit elastic when Ed = 1, and

inelastic when Ed < 1.

Inelastic Demand

Inelastic demand

The percentage change in quantity is less

than the percentage change in price.

Price elasticity of demand < 1

Inelastic Demand

- Elasticity is less than 1

Quantity

Price

4

$5 1. A 25% increase in price...

Demand

100 90 2. ...leads to a 10% decrease in quantity.

Elastic Demand

Elastic demand

The percentage change in quantity is greater

than the percentage change in price.

Price elasticity of demand > 1

Elastic Demand

- Elasticity is greater than 1

Quantity

Price

4

$5 1. A 25% increase in price...

Demand

100 50 2. ...leads to a 50% decrease in quantity.

Unit Elastic Demand

Unit elasticity

The percentage change in quantity equals the percentage change in price.

Price elasticity of demand = 1

Unit Elastic Demand

- Elasticity equals 1

Quantity

Price

4

$5 1. A 25% increase in price...

Demand

100 75 2. ...leads to a 25% decrease in quantity.

The flatter the demand curve, the more price elastic is the

demand.

P

Qd

P

Qd

flatter steeper

The flatter the demand

curve, the more room

there is for the quantity

to adjustment.

Hence, the flatter the

demand curve, the more

responsive is the quantity

to a price change.

Perfectly Elastic Demand

- Elasticity equals infinity

Quantity

Price

Demand $4

1. At any price above $4, quantity demanded is zero.

2. At exactly $4, consumers will buy any quantity.

3. At a price below $4, quantity demanded is infinite.

Perfectly Inelastic Demand

- Elasticity equals 0

Quantity

Price

4

$5

Demand

100 2. ...leaves the quantity demanded unchanged.

1. An increase in price...

Examples of Demand Elasticity

When the price of gasoline rises by 1% the

quantity demanded falls by 0.2%, so gasoline

demand is not very price sensitive.

Price elasticity of demand is -0.2 .

When the price of gold jewelry rises by 1% the

quantity demanded falls by 2.6%, so jewelry

demand is very price sensitive.

Price elasticity of demand is -2.6 .

Determinants of

Price Elasticity of Demand

Necessities versus Luxuries

Availability of Close Substitutes

Time Horizon

Factors That Influence

Elasticity

The Closeness of Substitutes.

The closer the substitutes, the more elastic the

demand – more elastic means a higher price elasticity (but not necessarily > 1)

Factors That Influence

Elasticity Proportion of Income Spent on the Good

The greater the proportion of income spent on food, the more elastic the demand

• Because of Income Effect of a price change

Factors That Influence

Elasticity

Time Elapsed Since Price Change

The longer the time, the more elastic the demand

• Short-run demand

• Long-run demand

Determinants of

Price Elasticity of Demand

Demand tends to be more elastic :

if the good is a luxury.

the longer the time period.

the larger the number of close

substitutes.

Determinants of Price

Elasticity of Demand

Demand tends to be more inelastic

If the good is a necessity.

If the time period is shorter.

The smaller the number of close substitutes.

Elasticity along a linear

demand curve

Computing the Price Elasticity of

Demand Using the Midpoint

Formula

The midpoint formula is preferable when

calculating the price elasticity of demand

because it gives the same answer regardless

of the direction of the change.

)/2]P)/[(PP(P

)/2]Q)/[(QQ(Q=Demand of Elasticity Price

1212

1212

Computing the Price Elasticity

of Demand

Example: If the price of an ice cream cone increases

from $2.00 to $2.20 and the amount you buy falls from

10 to 8 cones the your elasticity of demand, using the

midpoint formula, would be calculated as:

32.25.9

22

2/)20.200.2(

)00.220.2(

2/)810(

)810(

percent

percent

)/2]P)/[(PP(P

)/2]Q)/[(QQ(Q=Demand of Elasticity Price

1212

1212

Arc elasticity measure

where:

Example

Suppose that quantity demanded falls from 60 to 40 when the price rises from $3 to $5. The arc elasticity measure is given by:

In this interval, demand is inelastic (since elasticity < 1).

Slope Compared to Elasticity

The slope measures the rate of change of one variable (P, say) in terms of another (Q, say).

The elasticity measures the percentage change of one variable (Q, say) in terms of another (P, say).

Because the price elasticity of demand measures how much quantity demanded responds to the price, it is closely related to the slope of the demand curve.

Elasticity: Mathematical Definition

slopeP

Q

1

slope

Q

P

elasticityP

Q slope

1

Exercise -- Linear Demand

Quantity Price

10 40

11 38

12 36

13 34

14 32

15 30

16 28

17 26

18 24

19 22

20 20

Compute the elasticity at the

point indicated in red on the

table (Q=18,P=24).

Slope = -2

1/Slope = -1/2

P/Q = 24/18 = 4/3

Elasticity = -2/3

Elasticity and Total Revenue

Total revenue is the amount paid by

buyers and received by sellers of a good.

Computed as the price of the good times

the quantity sold.

TR = P x Q

$4

Demand

Quantity

P

0

Price

P x Q = $400

(total revenue)

100 Q

Elasticity and Total Revenue

Elasticity and Total Revenue

If demand is elastic in the relevant range of prices, price and total revenue vary inversely.

That is, a price increase will decrease total revenue.

An elastic demand means that the percentage change in quantity demanded is greater than the percentage change in price.

Hence, an increase in price will result in a more than offsetting percentage decrease in quantity taken.

Elastic: p q TR

Elasticity and Total Revenue

If demand is inelastic in the relevant range of prices, price and total revenue vary directly.

That is, a price increase will increase total revenue.

An inelastic demand means that the percentage change in quantity demanded is less than the percentage change in price.

Hence, an increase in price will result in a less than offsetting percentage decrease in quantity taken.

Inelastic:

p q TR

Elasticity and Total Revenue

If demand is unitary in the relevant range of prices, total revenue does not change in response to price changes. A unitary own-price elasticity of demand means that the

percentage change in quantity demanded is equal to the percentage change in price.

Hence, an increase in price will result in an offsetting percentage decrease in quantity taken.

Unitary:

p q TR

STAYS

The Total Revenue Test for

Elasticity

INELASTIC

DEMAND

ELASTIC

DEMAND

Decrease in

Price

ELASTIC

DEMAND

INELASTIC

DEMAND

Increase in

Price

Decrease in

Total Revenue

Increase in

Total Revenue

Price

Quantity

D

P2

Q2

P1

Q1

P1 x Q1 = A + B

P2 x Q2 = A + C

(P2 x Q2) - (P1 x Q1) =

(A + C) - (A + B) =

C - B

C

A B

Expenditure = Price x Quantity

Price

Quantity

D

P 2

Q1

Inelastic Demand: Area C > Area B

P1

Q2

C

A B

Price

Quantity

D

P

Q

2

2

P1

Elastic Demand: Area B > Area C

Q1

C

A B

Income Elasticity of Demand

Income elasticity of demand measures

how much the quantity demanded of a

good responds to a change in consumers’

income.

It is computed as the percentage change

in the quantity demanded divided by the

percentage change in income.

Computing Income Elasticity

Income Elasticity of Demand

Percentage Change in Quantity Demanded

Percentage Change in Income

=

Income Elasticity - Types of Goods -

Normal Goods

Income Elasticity is positive.

Inferior Goods

Income Elasticity is negative.

Higher income raises the quantity demanded for normal goods but lowers the quantity demanded for inferior goods.

Income elasticity of demand

A good is a luxury good if income elasticity > 1.

A good is a necessity good if income elasticity < 1.

A good is a normal good if income elasticity > 0.

A good is an inferior good if income elasticity < 0.

Cross Price Elasticity of

Demand

Elasticity measure that looks at the

impact a change in the price of one good

has on the demand of another good.

% change in demand Q1/% change in

price of Q2.

Positive-Substitutes

Negative-Complements.

Cross-Price elasticity of demand

The cross-price elasticity of demand

between two goods j and k is defined as:

Cross-Price elasticity (cont.)

Cross-price elasticity is positive if and only if the goods

are substitutes

Cross-price elasticity is negative if and only if the

goods are complements.