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Elasticity as a measure of responsiveness

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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

Definitions

Computations

Recap

Y

E (elastic)

C

P

R

Q

IE (inelastic)

B

A

O

X

β = slope = ∆Y / ∆X

CA / AB > PQ / QR

Qd

E ( elastic )

C

P

R

Q

IE ( inelastic )

B

A

P

P

IE ( inelastic )

R

B

C

A

E ( elastic )

P

Q

Qd

Slope of a demand curve = β

Higher slope = Inelastic demand curve (Steep)

Lower slope = Elastic demand curve

(Flat)

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.

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.

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%

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

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 %

3. Income elasticity of demand

can be defined as

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%

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

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%

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%

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

Total revenue and elasticity

Firm B

Firm A

O

O

* Not perfect competition

Firm A

P

OAFD > OBTC

TR as P

Inelastic demand Curve

D

F

10

C

T

6

A

B

Qd

O

90

100

Firm B

OVZU > OYUR

TR as P

Elastic demand curve

P

R

U

7

Z

U

6

Y

V

O

100

Qd

40

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

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

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

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

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

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

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 .

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

Qd = 60 – 15P + P2

Qd (000s)

Price

Quantity demanded

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