Point Elasticity Method

Measuring Elasticity Of Demand on a Linear demand Curve
Let a straight line demand curve DD’ be given and we have to measure price elasticity of demand at the point R on this demand curve.

The measure of price elasticity of demand is given by: Ep =(∆ q/∆ p) (p/q) The first term in this formula, (∆ q/∆ p) is the reciprocal of the slope of the demand curve DD’(slope of the demand curve is equal to Change in price divided by change in quantity demanded and will be the same all along the straight line demand curve). The second term is the original price divided by the Original Quantity. Thus
Ep =(1/slope)(p/q)
Now at point R in the diagram, Original price p = OP and Original quantity q = OQ. Further, slope of the demand curve DD’ is ∆ p/∆ q = PD/PR
Substituting these in the above formula we have
Ep =[ 1/(PD/PR)](OP/OQ) = (PR/PD)(OP/OQ)
However PR =OQ and they will get cancelled and therefore
Ep = OP/PD
This represents the ratio of the distances on the vertical axis.
In a right angled triangle ODD’, PR is parallel to OD’.
Therefore
Ep = OP/PD =RD’/RD
RD’ is the lower segment of the demand curve DD’ at point R and RD is its upper segment.
Therefore,
Ep = RD’/RD =Lower segment/Upper segment.

Measuring Price elasticity on a non –linear demand curve.

In order to measure elasticity in case of a non linear curve we draw a tangent at the given point R on the demand curve DD’ and then measure price elasticity by finding out the value of RT’/RT.

On a Linear Demand curve price elasticity varies from Zero to infinity. This can be represented diagrammatically as follows.In this diagram elasticity is being calculated at five points D, S, R, Land D'.

From the changes in the total expenditure made as a result of changes in its price, we can know the price elasticity of demand for the good. However it should be taken note that it is possible to identify whether price elasticity of demand will be greater than one, less than one or equal to one only. The exact or accurate price elasticity of demand cannot be found. Let us under the relationship precisely. Unit Elasticity: With a change in the price of the good, quantity demanded increases, the total expenditure remaining the same, elasticity of demand is equal to one. The reason for this is, if total outlay has to be the same then the percentage change in price has to be equal to percentage change in quantity demanded. Elasticity greater than one: With a decline in the price of the good, quantity demanded increases, the total expenditure also increases, elasticity of demand is greater than one. The reason for this is, if total outlay has to increase then the percentage change in quantity demand has to be greater than percentage change in price. Similarly due to an increase in the price of a good if there is a fall in the demand and as a result there is a decline in the total expenditure then also the elasticity of demand is greater than one. Elasticity Less than one: With a decline in the price of the good, quantity demanded decrease, the total expenditure also decreases, elasticity of demand is less than one. The reason for this is, if total outlay has to decreases then the percentage change in quantity demand has to be less than percentage change in price. Similarly due to an increase in the price of a good if there is an increase in the demand and as a result there is a increase in the total expenditure then also the elasticity of demand is less than one. Let us understand this method with the help of an illustration. The table given below gives data on the price per unit of pen, the quantity demanded at different price levels, the resultant expenditure and the elasticity of demand under different situations.

Arc Elasticity of demand When price changes are large or we have to measure elasticity over an arc of the demand curve rather than at a specific point on the demand curve, the point elasticity method does not provide a true or correct measure of price elasticity of demand. Further, in such cases, the elasticity would be different depending on whether we choose original price and original demand or the subsequent price and quantity demanded as the basis for measurement of elasticity of demand. The outcome would be different under the two situation. Hence, when the change in price is quite large then accurate measure of price elasticity can be obtained by taking the average of original price and new price as well as average of the old quantity and new quantity as the basis of measurement of percentage changes in price and quantity. Thus if the price of a good declines from p1 to p2 and as a result the quantity demanded increases from q1 to q2 the average of the two prices is given by (p1+p2)/2 and Average of the two quantities is given by (q1+q2)/2. Thus the formula for measuring Arc elasticity Is given by
E p = {∆ q/(p1+p2)/2} /{∆ p/(q1+q2)/2}
= { ∆ q/(q1+q2)} {∆ p/(p1+p2)}
= (∆ q/∆ p) {(p1+p2)/(q1+q2)}