Difference between “Arc Price Elasticity” and “Point Price Elasticity” of Demand are as follows:
(i) Arc price elasticity:
It is slightly different from the price elasticity as defined above. We have seen that price elasticity is given as
Here, changes in demand and price are taken to be proportionate changes to their original levels, Q1 and P1 respectively. If the points are separated by a larger distance on the demand curve, it is customary to express the change in demand and price as a proportion of their average values rather than of their original values.
(ii) Point price elasticity:
Point price elasticity refers to the price elasticity at a point on the demand curve. In other words, it accounts for the price elasticity of demand in the close proximity of the point, that is, proportionate change in demand in response to an infinitesimally small change in price at the point.
The point price elasticity, thus, has its relevance to the situations in which either the equation of the demand curve is given, or the demand curve itself is given. To understand, let us refer to the following illustrations.
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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
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(ii) Quantity demanded, QD, of a product is given as
QD = 100,000/√P
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
