## Difference between “Arc Price Elasticity” and “Point Price Elasticity” of Demand

Illustration 2.2

(i) Quantity demanded, QD, of a product is given as a function of price as below

QD = 150,000 – 3P

Calculate price elasticity of demand at price P = 10,000

(ii) Quantity demanded, QD, of a product is given as

QD = 100,000/vP

Calculate price elasticity of demand at price P = 10,000

(iii) Given the demand curve and given a point on it, obtain an expression for the elasticity of demand.

(iii) Point price elasticity at a given point on a given demand curve is derived below:

In Figure 2.14, AB is a linear demand curve on which point T(Q, P) is given. We have to determine price elasticity of demand at this point. Take point S (Q R) close to point T(Q, P) so that PP’ = TR = AP and QQ’ = RS = AQ. In Figure 2.15, DD is a non-linear demand curve and T(Q, P) is a point given on it.

Draw AB tangential to DD at point T. Take point S (Q’, P’) close to point T(Q, P) on AB as shown. As soon as AB, tangential to DD at point T, is drawn, we can forget the non-linear demand curve DD for all practical purposes hence onwards.

Geometrical treatment, from this point onwards, refers to both the figures

[We have used the Basic Proportionality Theorem (BPT) of similar triangles.]

Thus, price elasticity of demand at a point on the demand curve is given as