# Elasticities by nikeborome

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```									        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
B       IE (inelastic)
A

O                               X
β = slope = ∆Y / ∆X
CA / AB > PQ / QR
Real world example
Qd
E ( elastic )

C
P
R
Q
B        IE ( inelastic )
A

P
Conventional representation
P
IE ( inelastic )
R
B
C
A
P           E ( elastic )
Q

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%
8
0 < |Є|<     (for absolute values of elasticity)
Є=0
P

P     Є<1

Qd                  P   Є=1
Qd
P   Є >1
Qd                  P   Є=α
Qd

Inelastic                   Elastic              Qd

Perfectly Inelastic         Unit Elastic          Perfectly Elastic
Total revenue and elasticity

Firm A                     Firm B

O                               O

* Not perfect competition
Firm A

P                      OAFD > OBTC
10 D     F             TR as P
Inelastic demand Curve
6C           T

A B
O      90 100     Qd
Firm B

P                       OVZU > OYUR
TR as P
Elastic demand curve
R    U
7
U              Z
6

Y      V
O       40       100    Qd
Numerical calculation of elasticity for
firm A
Є = percentage change in Qd
P                      percentage change in P

10 D      F             = 90 – 100       10 – 6
100             6

6C           T               = - 0.15

A B
O      90 100    Qd
Numerical calculation of elasticity for
Firm B
Є = percentage change in Qd
percentage change in P
P
=   40 – 100    7–6
100        6
R           U
7                                   =-3.6
U                  Z
6

Y         V
O             40     100 Qd
Elastic demand between 2 points

P

8              ЄKL = percentage change in Qd
K
percentage change in P
6          L
= 16– 8   ÷   6–8
8         8
= -4

O     8   16    Qd

TR as the P
Inelastic demand between 2 points

ЄGH = percentage change in Qd
P
percentage change in P
G        = 36– 28 ÷ 1 – 3
3                           28           3
=-3
H
1                          7

O          28   36      Qd

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
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
Point elasticity

Є=∆Q          ÷     ∆P
Q                  P

Є= ∆Q         x    P
∆P              Q

d = infinitely small change in price

Є=dQ          x     P
dP                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       K             dQ   4
L                   P at K = 8 = 1
6                               Q         8
Є = - 4 x 1 = -4
Qd
O   8       16                  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   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
7             Qd (000s)
6
5
Price

4
3
2
1
0
0   20          40           60   80
Quantity demanded
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

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