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6.1 DEFINITION^ OF^ PRICE^ ELASTICITY^ OF^ DEMAND
The law of demand states that when price of a good falls, consumers demand more units of the good. But how much more? It is important and useful to have
magnitude of change in quantity demanded to a change in price. This magnitude
of change is measured by price elasticity of demand.
Price elasticity of demand measures responsiveness of demand of a good to a change in its price. Alfred Marshall was the first economist to formulate the concept of price elasticity of demand as the ratio of a relative change in quantity demanded to a relative change in price. A relative measure is needed so that changes in different measures can be compared. These relative changes in demand and price are measured by percentage changes. Percentage changes are^ independent^ of^ units^ of^ measurement.^ Numerically,^ price^ elasticity^ of demand e is^ calculated^ as percentage change in quantity demanded percentage change in price
AQ -Q)/Q_ (-P)IP AP P
AQ P AP O
ep
where
AQ = Change in (^) quantity demanded
Q (^) Original (^) quantity (^) demanded AP = Change in (^) price P Original price e (^) or (^) e, = Coefficient (^) of elasticity of^ demand. (^) e, is (^) negative. Thehe^ ratio^ isa negative number^ because (^) price and (^) quantity demanded are^ inve
rsely
related. In numerical sums, minus
sign is^ dropped from the (^) nu
mbers and (^) all (^) percentage (^) changes are (^) treated as (^) positive.
Elasticity of (^) demand (^) (e,)
Percentage (or proportionate) change in quantity demanded
percentage (or^ proportionate) (^) change in^ price
Change in^ quantity (^) demanded. x 100 Original quantity Change in^ price (^100)
Orginal price
x 100
Aq4P AgPAg 9 Ap Ap
Here,
Aqis change in quantity.
Apis change in price.
pis original price.
q is original quantity.
Table 8.3: Effect of (^) Change in Price on Total (^) Outlay (T.O.) and^ Elasticity of Demand
Change in Price (^) Value (^) ofElasticity (^) ofDemand
<1 >
Fall in Price (^) T. O. remains (^) T. O. fallIs T. O. rises constant
Rise in Price (^) T. O. remains (^) T. O. rises (^) T. O. falls
Constant
Y D
Y
R R
D Pi RI
P2 (^) R
R
P R
Pa
R D
D X Quantity
X (^) O
Quantity Q1^ Q2 Quantity^ Q1Q
Fig. 8.3 Fig.^ 8.4 Fig.^ 8.
F
P
P
P
d
Quantity
Fig. 6.3^ :Perfectly Inelastic Demand^ Curve
Table 6.4: Perfectly Inelastic Demand Schedule
Price () Demand (Units)
15 10
(^10 )
20 10
Price
d
P
P
\D
Q Q Quantity
Fig. 6.4:^ Inelastic^ Demand^ Curve
Price d (^) Price d
|
P
P C 4C Q Q (^) Quantity (^) Quantity
Fig. 6.5 Unitary Elastic Demand Curves
Table 6.6: Unitary Elastic Demand Schedule
Price () Demand (Units)
(^10 )
5 30
Price
d P
P
B
O (^) Q Quantity
Fig. 6.6: Elastic Demand Curve
Table 6.7 Elastic Demand Schedule
Price ( Demand (Units)
10 20
9 40
Price d (^) -A
B
D F
Quantity
Fig. 6.2:^ Different^ Types^
of Price (^) Elasticity of Demand
Table 6.3 : Different Values of Elasticity of Demand
S.No.Coefficient of ep
Type (^) of Good^ Shape^
of Demand
Curve
Type of e (^) Discription
(See Fig. 6.2)
- (^) Perfectly This Vetical^ (dF) when to a per- life saving dugs
centage change in price there is no change in quantity manded.
e0 occurs^ Essentials^ like inelastic demand
de-
Inslastic (or This less than
unitary elastic
0<e<
occurs Necessities like Sleeper (dD) when to a per- food, fuel, etc. centage change in price there is less than propor- tionate change in quantity de- manded.
demand)
6.5 (^) ELASTICITY (^) ALONG A (^) LINEAR (^) DEMAND CURVE
In the (^) Geometric (^) Method, the (^) elasticity of (^) demand is (^) measured (^) by using the
formula:
Lower (^) segment on demand curve Elasticity of^ demand^
= Upper segment on demand curve
Price
A
(e>1) E (e= 1)
D
e 0 o B Quantity
Fig. 6.10:^ e,^ on^ a^ Linear Demand^ Curve
Lower Segment BC
e at^ Point^ C^ = Upper Segement AC e^ '.e^
...(since (^) BC<AC)
BD ep at^ mid-point^ D^
= (^) ep 1 ..(as BD =AD)
AD
BE ep at^ pojnt^ E^
= , e> AE
..(as BE > AE)
0 ep at^ point^ B^
= - AB
Be=0 (^) ...(Since numerator is zero)
AB ..(since denominator is zero) ep at^ point^ A^
= (^) -, p
=
6.10 CROSS-PRICE ELASTICITY OF DEMAND
- The Concept
The cross-price elasticity of demand (ev) is a
quantitative measure^ of^ the
effect on the quantity demanded of good x due to change in
price of^ good
z. That^ is, it is^ a^ measure of the responsiveness of the quantity demanded ofx to
a percentage change in the price of z. The cross-price
elasticity between^ two
goods x and z is calculated as
% change in quantity demanded of x exz % change in price ofz
A8x
A
A8x
e,4 AP
Qx
where Pz
P Initial^ price^ of good z
,-Initial quantity demanded ofgoodx
AQ. = Change in^ quantity demanded^ of^ good^ x
AP= Change in^ price of good z
Coefficient of cross-elasticity of demand.
Table 6.11 : Different Values of Cross-price Elasticity of Demand
Value of exz (^) Relationship between two^ goods X^ and^ Z
e +oo Perfect substitutes
Substitutes
e 0 Unrelated
e 0 Complements
e
Perfect complements
