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2.4 Elasticity of Demand and Supply
(A) Price Elasticity
i) Elasticity of Demand: Elasticity of demand
can be classified into two major divisions: one the highly elastic,
unitary elastic and the highly inelastic type and two, the extreme cases
of the perfectly elastic and the perfectly inelastic type.
a) Highly elastic, Unitary elastic and highly inelastic:
The laws of demand and supply are no doubt an important part of economic
analysis. But the knowledge about demand and supply relations serves only
a limited purpose. This is in view of the fact that both demand and supply
laws are applicable to all kinds of goods. However, an actual rise or
fall in the quantity demanded or supplied with a small variation in the
price may considerably differ for different goods such as food,
automobiles, film shows, garments, hardware materials, machines, land
etc. In other words it is important to know the extent of rise
or fall in the demand with a given change in the price for each individual
good. This is exactly the purpose served by the concept of price elasticity
of demand; this concept is advanced and subtle in nature. It was first
developed by Alfred Marshall; he has defined elasticity as follows:
Elasticity of demand is the degree of responsiveness
with which quantity demanded changes for a given change in price.
In other words it is a proportional change in the
quantity demanded to a proportional change in price.
Price Elasticity
of demand is then the ratio of the proportional change in the quantity
demanded to the proportional change in price.
Proportional change in quantity can be expressed as  where
q1 is the initial and q2 is the new quantity demanded. Proportional change in price is similarly  where P1 is initial and P2 is the
new price.
Elasticity ratio e is therefore, 
If symbols q and P are used for small variations in quantity and price respectively
then,
Note that Dq / Dp
is in the limit derivative or marginal change and p/q is the reciprocal
of average change, therefore
Let’s illustrate
this. In our demand schedule example above, when price changes from 2
to 3 units, the quantity demanded changes from 4 to 1 units. Substituting
these values we have:
Note that the elasticity ratio 3/2 is more than one and
has a negative sign. Both these are important features. Numerical values
explain the extent or degree of change in demand while the sign
of the ratio explains the direction of change. Since the law of
demand is based on the inverse relation between price and quantity, the
elasticity of demand is always stated with a negative sign.
The numerical value of elasticity can be equal to 1 (that
is called ‘unit’) more than one or less than one. In case of unit elastic
demand (e = 1) both price and quantity (demanded) changes occur in the
same proportion. If the value of elasticity exceeds one (e >
1) then the percentage or proportional change in quantity demanded is
greater than that in price and the good is said to be price elastic
or highly responsive to a change in price. If the value of elasticity
is less than one (e < 1) then the proportional change in quantity is
smaller than that in price and the demand for the good is said to be price
inelastic or not very responsive to a change in price. The information
about the value of elasticity therefore serves an important purpose in
classification of various goods as elastic or inelastic
in demand. This helps in several practical and policy applications such
as taxation, foreign trade, monopoly, price determination etc.
There are four methods of measurement of elasticity of
demand. These are percentage, proportion, outlay and
geometric or point elasticity methods. The one mentioned
last (point elasticity method) is the most accurate and can be explained
conveniently with a given demand curve:
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