Measurement of Elasticity of Demand
There are three methods for measuring elasticity of demand. •
Outlay method
•
Point method
•
Arc method
Outlay Method
Prof. Prof. Marsha Marshall ll develop developed ed outlay outlay method method to measur measuree the degree degree of elasti elasticit city y of demand. demand. According to this method, we examine whether the total outlay of the consumer or revenue of the seller has changed after the price change. Total outlay of total revenue = Price X Quantity purchased or sold. If the total outlay remains unchanged, after the change in price, the demand is said to be unit elastic (e p = 1). When with a rise in price, if total outlay falls or with a fall in price if total outlay rises, elasticity of demand is greater than unity (e p > 1). The price and total outlay moves in the opposite direction.
When with a rise in price, if total outlay rises and with a fall in price if total outlay falls, elasticity of demand is said to be less than unity (e p < 1). In this case we notice that price and total outlay move in the same direction.
Table 1.Total outlay Method Price Increase
Total outlay Constant
Type of demand (e = 1)
Decrease Increase
Constant Decreases
Unitary elastic (e >1)
Decrease Increase
Increases Increases
Relatively elastic (e<1)
Decrease
Decreases
Relatively inelastic
e p
=
Percentage Change in Quantity Demanded Percentage Change in Price
e p
=
ΔQ/ Q ΔP/ P
=
(ΔQ/ Q) X (P/ΔP)
Where Q is the original quantity ΔQ is the quantity after the price change P is the original price ΔP is the new price ΔQ
= (Q2 – Q1)
ΔP
= (P2 – P1)
Illustration
Find the price elasticity of demand from the following data. Price of sugar :
10
Quantity Purchased: 100
20
40
10
20
40
10
20
40
75
65
100
50
25
100
45
15
Solution
Price of Sugar
I
II
III
Quantity Demanded
Total Outlay
(in Rs.)
(in Kg.)
10
100
1000
20
75
1500
40
65
2600
10
100
1000
20
50
1000
40
25
1000
10
100
1000
20
45
900
40
15
600
e <1
e =1
e >1
When price change from 10 to Rs.20 in the Ist case Q1
= 100
Q2
= 75
P1
= 10
P2
=20
ΔQ
= (Q2 – Q1)
=
75-100 = 25
ΔP
= (P2 – P1)
=
20 – 10 = 10
e p
=
ΔQ/ Q ΔP/ P
e p
=
(ΔQ/ Q) X (P/ΔP)
=
(25/100) X (10/10)
=
0.25
When price change from 20 to Rs.40 in the Ist case Q1
= 75
Q2
= 65
P1
= 20
P2
=40
ΔQ
= (Q2 – Q1)
=
65-75 = 10
ΔP
= (P2 – P1)
=
40 – 20 = 20
e p
=
ΔQ/ Q ΔP/ P
e p
=
(ΔQ/ Q) X (P/ΔP)
=
(10/75) X (20/20)
=
0.13
When price change from 10 to Rs.20 in the IInd case Q1
= 100
Q2
= 50
P1
= 10
P2
=20
ΔQ
= (Q2 – Q1)
=
50-100
= 50
ΔP
= (P2 – P1)
=
20 – 10
= 10
e p
=
ΔQ/ Q ΔP/ P
e p
=
(ΔQ/ Q) X (P/ΔP)
=
(50/100) X (10/10)
=
0.5
When price change from 20 to Rs.40 in the IInd case
Q1
= 50
Q2
= 25
P1
= 20
P2
=40
ΔQ
= (Q2 – Q1)
=
25-50
= 25
ΔP
= (P2 – P1)
=
40 – 20
= 20
e p
=
ΔQ/ Q ΔP/ P
e p
=
(ΔQ/ Q) X (P/ΔP)
=
(25/50) X (20/20)
=
0.5
When price change from 10 to Rs.20 in the IIIrd case Q1
= 100
Q2
= 45
P1
= 10
P2
=20
ΔQ
= (Q2 – Q1)
=
45-100
= 55
ΔP
= (P2 – P1)
=
20-10
= 10
e p
=
ΔQ/ Q ΔP/ P
e p
=
(ΔQ/ Q) X (P/ΔP)
=
(55/100) X (10/10)
=
0.55
When price change from 20 to Rs.40 in the IIIrd case Q1
= 45
Q2
= 15
P1
= 20
P2
=40
ΔQ
= (Q2 – Q1)
=
15-45
= 30
ΔP
= (P2 – P1)
=
40 – 20
= 20
e p
=
ΔQ/ Q ΔP/ P
e p
=
(ΔQ/ Q) X (P/ΔP)
=
(30/45) X (20/20)
=
0.66
Point Elasticity Method
Point elasticity measures price elasticity at various points on the demand curve. When a point is plotted on the demand curve, it divides the curve into two segments. The point elasticity is measured by the ratio of the lower segment of the curve below the given point to the upper segment of the curve above the point. Point elasticity
=
lower segment of the demand curve below the given point
Upper segment of the demand curve above the given point e
=
L U
Where e stands for elasticity, L stands for lower segment, and U stands for upper segment.
At point c, price elasticity e p = CB/AC = 1; note that the line segment CB and AC are of equal length. At point A,
e p = AB / 0;
e p = §.
At point B,
e p = 0 / AB;
e p = 0.
At point D,
e p = db / ad;
e p > 1 because db>ad. Note that the length of line segment DB is
more than AD. At point E,
e p = EB / AE; e p < 1 because eb
less than AE.
Arc Elasticity of Demand
Arc method is used to measure the elasticity of demand for big change in price. The formula for measuring price elasticity f demand through arc method is
ep=
Original quantity- quantity after change/ Original quantity + quantity after change
---------------------------------------------------------------------------------------------Original price – price after change/ Original price + price after change e p=
( Q - Q1)/ (Q + Q1) (P - P1) / ( P +P1)
Illustration
Measure arc elasticity of demand for the following data.
e p=
Original price of a commodity
=
Rs. 10/-
Quantity purchased at this price
= 100 units
Price after change
= Rs. 5/-
Quantity purchased at new price
= 300 units
( Q - Q1)/ (Q + Q1) (P - P1) / ( P +P1) ( 100 -3001)/ (100 + 300) (10- 5) / (10 +5) (- 200/400) (5/15) (- 200/400) X (15/5) = - 1.5
Arc method is the most popular method of measuring elasticity of demand.
Factors Determining Price Elasticity of Demand
The price elasticity of demand depends on several factors. They are as follows:-
1. The Nature of Commodity: Demand for necessary goods do not change with changes in their
price, and therefore their demand is inelastic. e.g., demand for salt or medicine. On the other hand, demand for luxury goods is elastic. When their prices increase, consumers would postpone their purchase and when their price falls, consumers are induced to purchase them e.g., demand for air conditioners, electric chimneys etc.
2. Substitutes: Demand for those goods, which have several substitutes, is usually elastic;
because a slight reduction in the price of substitute goods leads to substitution effect and attracts consumers to goods whose price has fallen. On the other hand, a slight increase in its price drives away consumers to purchase other substitutes e.g., demand for toilet soaps.
3. Extent of Use: Demand for commodities, which have a variety of use is elastic. When their
price rises, their consumption will be restricted to most important use. Commodities, which have limited use, are of inelastic demand.
4.Proportion of Income Spent: If the proportion of income spent on a particular commodity is
very small, its demand will be inelastic e.g., demand for salt, matches etc.
5.Possibility of postponement of use : If consumers can postpone the use of a commodity, its
demand will be elastic. Urgent wants create inelastic demand.
6. Durability of Goods: Durable goods are elastic because consumers replace them when their
price falls and postpone their purchase when price increase e.g., a consumer thinks of replacing a car when its price falls.
7. Ranges of Prices: At very high level of prices and low ranges of prices, demand is inelastic.
