Elasticity as a measure of responsiveness
This presentation is the property of its rightful owner.
Sponsored Links
1 / 34

Elasticity as a measure of responsiveness PowerPoint PPT Presentation


  • 68 Views
  • Uploaded on
  • Presentation posted in: General

Elasticity as a measure of responsiveness. Y = Effect variable X = Cause variable Y = ƒ ( X ) Y = α – β X Where α & β are the coefficients. Summing UP. Introductory Economic Lecture 6. Elasticity. Definitions Computations. Recap. Y = α – β X in Y-X space. Y.

Download Presentation

Elasticity as a measure of responsiveness

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Elasticity as a measure of responsiveness

Elasticity as a measure of responsiveness

Y = Effect variable

X = Cause variable

Y = ƒ ( X )

Y = α – β X

Where α & β are the coefficients


Elasticity as a measure of responsiveness

Summing UP


Elasticity as a measure of responsiveness

Introductory

Economic

Lecture 6


Elasticity

Elasticity

Definitions

Computations


Elasticity as a measure of responsiveness

Recap


Y x in y x space

Y = α – βX in Y-X space

Y

E (elastic)

C

P

R

Q

IE (inelastic)

B

A

O

X

β = slope = ∆Y / ∆X

CA / AB > PQ / QR


Real world example

Real world example

Qd

E ( elastic )

C

P

R

Q

IE ( inelastic )

B

A

P


Conventional representation

Conventional representation

P

IE ( inelastic )

R

B

C

A

E ( elastic )

P

Q

Qd


Slope of a demand curve

Slope of a demand curve

Slope of a demand curve = β

Higher slope = Inelastic demand curve (Steep)

Lower slope = Elastic demand curve

(Flat)


Price elasticity of other variables

Price elasticity of other variables

Y = ƒ ( X )

  • Y = Qd & X = Price Price elasticity of demand.

  • Y = Qs & X = Price Price elasticity of supply.

  • Y = Qd & X = Income Income elasticity of demand.

  • Y = Qda & X = PricebCross price elasticity of demand.


Formal definition of the four combinations

Formal definition of the four combinations

1. Price elasticity of demand

can be defined as

PЄd = Percentage change in Quantity Demanded

Percentage change in Price

Where Є = Epsilon; universal notation for elasticity.


P d percentage change in quantity demanded percentage change in price

PЄd = Percentage change in Quantity DemandedPercentage change in Price

Example

If, for example, a 20% increase in the price of a product causes a 10% fall in the Quantity demanded , the price elasticity of demand will be:

PЄd = - 10% = - 0.5

20%


Elasticity as a measure of responsiveness

Formal definition of the four combinations

2. Price elasticity of supply

can be defined as

PЄs = Percentage change in Quantity Supplied

Percentage change in Price


P s percentage change in quantity supplied percentage change in price

PЄs = Percentage change in Quantity Supplied Percentage change in Price

Example

If a 15% rise in the price of a product causes a 15% rise in the quantity supplied, the price elasticity of supply will be:

PЄs = 15 % = 1

15 %


Formal definition of the four combinations1

Formal definition of the four combinations

3. Income elasticity of demand

can be defined as

YЄd = Percentage change in Quantity Demanded

Percentage change in Income


Y d percentage change in quantity demanded percentage change in income

YЄd = Percentage change in Quantity Demanded Percentage change in Income

Example

If a 2% rise in the consumer’s incomes causes an 8% rise in product’s demand, then the income elasticity of demand for the product will be :

YЄd = 8% = 4

2%


Elasticity as a measure of responsiveness

Formal definition of the four combinations

4. Cross price elasticity of demand

can be defined as

PbЄda= Percentage change in Demand for good a

Percentage change in Price of good b


P b d a percentage change in demand for good a percentage change in price of good b

PbЄda= Percentage change in Demand for good a Percentage change in Price of good b

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.

PbЄda= 2% = 0.25

8%


P b d a percentage change in demand for good a percentage change in price of good b1

PbЄda= Percentage change in Demand for good a Percentage change in Price of good b

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 butter with respect to bread would be :

PbЄda= - 3% = - 0.75

4%


Elasticity as a measure of responsiveness

8

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

Є = 0

P

Є < 1

P

Qd

P

Є = 1

Qd

Є >1

P

Qd

P

Є = α

Qd

Elastic

Inelastic

Qd

Perfectly Elastic

Perfectly Inelastic

Unit Elastic


Elasticity as a measure of responsiveness

Total revenue and elasticity

Firm B

Firm A

O

O

* Not perfect competition


Elasticity as a measure of responsiveness

Firm A

P

OAFD > OBTC

TR as P

Inelastic demand Curve

D

F

10

C

T

6

A

B

Qd

O

90

100


Elasticity as a measure of responsiveness

Firm B

OVZU > OYUR

TR as P

Elastic demand curve

P

R

U

7

Z

U

6

Y

V

O

100

Qd

40


Elasticity as a measure of responsiveness

Numerical calculation of elasticity for firm A

Є = percentage change in Qd

percentage change in P

= 90 – 10010 – 6

100 6

= - 0.15

P

D

F

10

C

T

6

A

B

O

90

100

Qd


Elasticity as a measure of responsiveness

Numerical calculation of elasticity for Firm B

Є = percentage change in Qd

percentage change in P

= 40 – 1007 – 6

100 6

= - 3 . 6

P

R

U

7

Z

U

6

Y

V

O

100

Qd

40


Elastic demand between 2 points

Elastic demand between 2 points

P

ЄKL = percentage change in Qd

percentage change in P

= 16– 8÷6 – 8

8 8

= - 4

8

K

L

6

Qd

O

8

16

TR as the P


Inelastic demand between 2 points

Inelastic demand between 2 points

ЄGH = percentage change in Qd

percentage change in P

= 36– 28 ÷ 1 – 3

28 3

= - 3

7

P

G

3

H

1

Qd

O

28

36

TR as the P


Elasticity as a measure of responsiveness

Overview of previous example

ЄKL = percentage change in Qd

percentage change in P

= 16– 8 ÷ 6 – 8

8 8

= - 4

ЄLK = percentage change in Qd

percentage change in P

= 8 – 16 ÷ 8 – 6

16 6

= - 3

2


Concept of arc elasticity

Concept of arc elasticity

As Є = ∆ Q÷∆ P

Q P

To measure arc elasticity we take average values for Q and P respectively.

ЄKL = 16– 8 ÷ 6 – 8 = - 7

12 7 3

ЄLK = 8 – 16 ÷ 8 – 6 = - 7 12 7 3

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


Q p q p

Є = ∆ Q÷∆ P Q P

Point elasticity

Є = ∆ Q x P ∆ P Q

d = infinitely small change in price

Є = d Q x P d P Q

A straight line demand curve will have a different Є at each point on it except Є = 0 or Є = α .


Elasticity as a measure of responsiveness

Previous example

P

dP = -1

dQ 4

8

K

L

P at K = 8 = 1

Q 8

Є = - 4 x 1 = -4

6

Qd

P at L = 6 = -3

Q 16 8

Є = - 4 x 3 = - 3

8 2

8

O

16


Elasticity as a measure of responsiveness

Qd = 60 – 15P + P2


Elasticity as a measure of responsiveness

Qd (000s)

Price

Quantity demanded


P d d q x p d p q

PЄd = 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 of 3 for example, dQ/dP = -15 + ( 2 x 3 ) = -9 Thus price Elasticity of demand at Price 3 is - 9 x P/Q

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


  • Login