Download Q d

Elasticity as a measure of
responsiveness
Y = Effect variable
X = Cause variable
Y=ƒ(X)
Y=α–βX
Where α & β are the coefficients
Summing UP
Introductory
Economic
Lecture 6
Elasticity
Definitions
Computations
Recap
Y = α – βX in Y-X space
Y
E (elastic)
C
P
R
Q
A
O
B
IE (inelastic)
X
β = slope = ∆Y / ∆X
CA / AB > PQ / QR
Real world example
Qd
E ( elastic )
C
P
R
Q
A
B
IE ( inelastic )
P
Conventional representation
P
IE ( inelastic )
R
B
C
A
Q
P
E ( elastic )
Qd
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
Y=ƒ(X)
1. Y = Qd & X = Price
Price elasticity of demand.
2. Y = Qs & X = Price
Price elasticity of supply.
3. Y = Qd & X = Income
Income elasticity of demand.
4. Y = Qda & X = Priceb
Cross price elasticity of
demand.
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.
PЄd = Percentage change in Quantity Demanded
Percentage 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%
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
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
combinations
3. Income elasticity of demand
can be defined as
YЄd = 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%
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
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%
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%
P
8
0 < |Є|<
(for absolute values of elasticity)
Є=0
P
Є<1
Qd
P
Є=1
Qd
P
Є >1
Qd
P
Є=α
Qd
Elastic
Inelastic
Perfectly Inelastic
Unit Elastic
Qd
Perfectly Elastic
Total revenue and elasticity
Firm B
Firm A
O
O
* Not perfect competition
Firm A
P
10 D
OAFD > OBTC
F
TR as P
Inelastic demand Curve
6C
O
T
A B
90 100
Qd
Firm B
OVZU > OYUR
TR as P
Elastic demand curve
P
7
6
O
R
U
Z
U
Y
40
V
100
Qd
Numerical calculation of elasticity for
firm A
Є = percentage change in Qd
percentage change in P
P
10 D
6C
O
F
= 90 – 100
100
T
A B
90 100
= - 0.15
Qd
10 – 6
6
Numerical calculation of elasticity for
Firm B
Є = percentage change in Qd
percentage change in P
P
7
6
O
=
R
40 – 100
100
U
Z
U
Y
40
V
100 Qd
=-3.6
7–6
6
Elastic demand between 2 points
P
8
ЄKL = percentage change in Qd
percentage change in P
K
L
6
=
16– 8
8
= -4
O
8
TR as the P
16
Qd
÷
6–8
8
Inelastic demand between 2 points
P
3
G
1
O
TR
as the P
28
ЄGH = percentage change in Qd
percentage change in P
= 36– 28
÷ 1–3
28
3
=-3
H
7
36
Qd
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
As Є = ∆ Q
Q
÷ ∆P
P
To measure arc elasticity we take average values for Q and
P respectively.
ЄKL = 16– 8
12
÷
ЄLK = 8 – 16 ÷
12
6–8
7
=-7
3
8– 6
7
=-7
3
average elasticity along arc KL or LK is - 7/ 3
Point elasticity
Є=∆Q
Q
Є= ∆Q
∆P
÷
x
∆P
P
P
Q
d = infinitely small change in price
Є=dQ
dP
x
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
8
dQ
K
4
P at K = 8 = 1
L
6
Q
8
Є = - 4 x 1 = -4
O
8
16
Qd
P at L = 6 = -3
Q
16 8
Є=-4x3 =-3
8
2
Qd = 60 – 15P + P2
P
60
- 15 P
P2
Qd (000s)
0
1
2
3
4
5
6
60
60
60
60
60
60
60
0
-15
-30
-45
-60
-75
-90
0
1
4
9
16
25
36
60
46
34
24
16
10
6
Price
Qd (000s)
7
6
5
4
3
2
1
0
0
20
40
Quantity demanded
60
80
PЄd = d Q x P
dP
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