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Elasticity as a measure of

responsiveness

Y = Effect variable

X = Cause variable

Y = ( X )

Y = X

Where & are the coefficients

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Summing UP

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Introductory

Economic

Lecture 6

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Elasticity

DefinitionsComputations

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Recap

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Y = X in Y-X space

E (elastic)Y

X

= slope = Y / X

C

A B

P

Q

R

IE (inelastic)

CA / AB > PQ / QR

O

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Real world example

E ( elastic )Qd

P

C

A B

P

Q

R

IE ( inelastic )

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Conventional representation

IE ( inelastic )P

R

Q P

B

A

C

E ( elastic )

Qd

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Slope of a demand curve

Slope of a demand curve =

Higher slope = Inelastic demand curve(Steep)

Lower slope = Elastic demand curve

(Flat)

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Price elasticity of other variables

Y = ( X )

1. Y = Qd & X = PricePrice elasticity of demand.

2. Y = Qs & X = PricePrice elasticity of supply.

3. Y = Qd & X = IncomeIncome elasticity of demand.

4. Y = Qda & X = PricebCross price elasticity of

demand.

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Formal definition of the four

combinations

1. Price elasticity of demand

can be defined as

Pd = Percentage change in Quantity Demanded

Percentage change in Price

Where = Epsilon; universal notation forelasticity.

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Pd = Percentage change in Quantity Demanded


Example

If, for example, a 20% increase in the price of aproduct causes a 10% fall in the Quantity

demanded , the price elasticity of demand will be:

Pd = - 10% = - 0.5

20%

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2. Price elasticity of supply

can be defined as

Ps = Percentage change in Quantity Supplied



combinations

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Ps = Percentage change in Quantity Supplied


Example

If a 15%

rise in the price of a product causes a15% rise in the quantity supplied, the price

elasticity of supply will be:

Ps = 15 % = 1

15 %

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3. Income elasticity of demand

can be defined as

Yd = Percentage change in Quantity Demanded

Percentage change in Income


combinations

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Yd = Percentage change in Quantity Demanded

Percentage change in Income

Example

If a 2% rise in the consumers incomes causes an8% rise in products demand, then the income

elasticity of demand for the product will be :

Yd = 8% = 4

2%

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4. Cross price elasticity of demand

can be defined as

Pbda = Percentage change in Demand for good a

Percentage change in Price of good b


combinations

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Example

If, for example, the demand for butter rose by

2% when the price of margarine rose by 8%,

then the cross price elasticity of demand of

butter with respect to the price of margarine will

be.

Pbda = 2% = 0.25

8%

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Example

If, on the other hand, the price of bread (a compliment)

rose, the demand for butter would fall. If a 4% rise in

the price of bread led to a 3% fall in the demand for

butter, the cross-price elasticity of demand for butterwith respect to bread would be :

Pbda = - 3% = - 0.75

4%

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0 < ||< (for absolute values of elasticity)

Unit ElasticUnit ElasticPerfectly InelasticPerfectly Inelastic Perfectly ElasticPerfectly Elastic

ElasticElasticInelasticInelastic

= 1= 1

= 0= 0

< 1< 1

>1>1

==

P

Qd

Qd

Qd

Qd

Qd

P

P

P

P

8

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Total revenue and elasticity

Firm A Firm B

O O

* Not perfect competition

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Firm A

O

6

100

10

90B

F

TC

D

AQd

P OAFD > OBTC

TR as P

Inelastic demand Curve

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Firm B

P

QdO

R

U

Y V

U

Z6

40 100

7

OVZU > OYUR

TR as P

Elastic demand curve

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O

6

10090

B

F

TC

D

A

P

Numerical calculation of elasticity for

firm A = percentage change in Qd

percentage change in P

= 90

100

10

6100 6

= - 0.15

Qd

10

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Numerical calculation of elasticity for

Firm B = percentage change in Qd


= 40

100

7 6100 6

= - 3 . 6

Qd

P

O

R

U

Y V

U

Z

6

40 100

7

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Elastic demand between 2 points

O

6

168

K

P

8

TR as the P

L

KL = percentage change in Qd


= 16 8 6 8

8 8

= - 4

Qd

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Inelastic demand between 2 points

O

1

3628

G

P

3

TR as the P

H

GH = percentage change in Qd


= 3628 1 328 3

= - 3

7

Qd

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LK = percentage change in Qd


= 8 16 8 616 6

= - 3

2

KL = percentage change in Qd


= 16 8 6 8

8 8= - 4

Overview of previous example

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Concept of arc elasticity

As = Q PQ P

To measure arc elasticity we take average values for Q and

P respectively.

KL = 16 8 6 8 = - 7

12 7 3

LK = 8 16 8 6 = - 7

12 7 3

average elasticity along arc KL or LK is - 7/3

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= Q P

Q P

= Q x P

P Q

d = infinitely small change in price

= d Q x Pd P Q

A straight line demand curve will have a different at

each point on it except = 0 or = .

Point elasticity

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O

6

168

K

P

8

L

dP = -1

dQ 4

P at K= 8 = 1Q 8

= - 4 x 1 = -4

P at L = 6 = -3

Q 16 8

= - 4 x 3 = - 3

8 2

Previous example

Qd

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P 60 - 15 P P2 Qd (000s)

0 60 0 0 60

1 60 -15 1 46

2 60 -30 4 34

3 60 -45 9 24

4 60 -60 16 16

5 60 -75 25 10

6 60 -90 36 6

Qd = 60 15P + P2

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0

1

2

3

4

5

6

7

0 20 40 60 80

Qd (000s)

Quantity demanded

Pr

ice

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Pd = d Q x P

d P Q

Differentiating the demand Equation

Given Qd = 60 15P + P2

then dQ/dP = -15 + 2P

Thus at a price of3 for example,

dQ/dP = -15 + ( 2 x 3 ) = -9 Thus price Elasticity ofdemand at Price 3 is - 9 x P/Q

= - 9 x 3/24 = - 9/8

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