### Explain any ‘two methods’ of measuring price elasticity of demand.

Explain any ‘two methods’ of measuring price elasticity of demand.

Measurement of Price Elasticity of Demand
Price elasticity of demand is measured with the help of the following three methods.
1)      Ratio or Proportional Method
This ratio method of measuring elasticity of demand is also known as Arithmetic or Percentage method also. This method is developed by Dr. Marshall. In this method we consider percentage change in quantity demanded and divide it by percentage change in the price of the commodity.
Thus
Numerical Illustration­
Table No.3.4
Ratio or Proportional Method
 Price of X Demand (Units) 200 1000 100 1500

Price of commodity X falls from Rs. 200/- to Rs. 100/- and quantity demanded increases from 1000 units to 1500 units. Here percentage change in demand is 50, whereas percentage change in price is also 50. Therefore, 50%, / 50% = 1, which, means Ed is unitary or one, in this example.
2)      Total Expenditure Method
The name of Dr. Marshall is associated with this method. This method is also known as Total Expenditure Method Total Revenue Method. In this method, statistics of total expenditure is used to find out elasticity of demand. Total expenditure at the original price and total expenditure at the new price is compared with each other, and we come to know the elasticity of demand.
When price falls or rises, total expenditure does not change or remains constant, demand is unitary elastic.
When price falls, total expenditure increases or price rises and total expenditure decreases, demand is elastic or elasticity of demand is greater than one.
When price falls and total expenditure decreases or price rises and total expenditure increases, demand is inelastic or elasticity of demand is less than one. Measurement of elasticity of demand with the help of total, expenditure method can be better understood with the help of the following example.
Table No. 3.5 - Total Expenditure Method
 Price (Rs.) Demand (Units) Total Outlay (Rs.) Elasticity of Demand A 10 8 12 15 120 120 Unitary or 1 B 10 8 12 20 120 160 Elastic or > 1 C 10 8 12 14 120 112 Inelastic or < 2

In example A, original price is Rs. 10 per unit and demand is 12 units. Therefore total expenditure incurred is Rs. 120/-. Price falls to the level of Rs. 8/- and demand rises up to15 units. But total expenditure is still Rs. 120/-. In this case, total outlay does not change even though there is change in price. Therefore, demand is unitary elastic.
In example B, at the price Rs. 10/-, 12 units are demanded. So total original expenditure is Rs. 120/-. Price falls to Rs. 8/- per unit and demand rises to the level of 20 units. Therefore, total expenditure incurred on commodity rises to Rs. 160/-. Total expenditure under this new condition of change in price, is greater than original expenditure. Hence, in this example, demand is elastic or elasticity of demand is greater than one.
In example C, original total outlay is Rs. 120/- with a change in price to Rs. 8/- per unit, demand expands to the extent of 14 units. Nevertheless, total expenditure Rs. 112/-, which is less than original expenditure. Therefore, in this example demand tends to be inelastic or elasticity of demand is less than one.
3)      Point Elasticity Method or Geometric Method
The proportional method and total outlay method enable us to measure elasticity of demand at a given point on the demand curve. Therefore, Dr. Marshall has developed yet another method to measure elasticity of demand, which is known as Point or Geometric method. At any point on demand curve elasticity of demand is measured with the use of the following formula.

With the help of the following example, we can understand how to measure elasticity of demand at a point on, linear demand curve.
Linear Demand Curve

Fig. No. 3.10
In the above figure DD is, demand curve and we assume that its length is 6 cm. At Point P, demand is infinite elastic, whereas at point P4 elasticity of demand is zero. Therefore, we have to measure elasticity of demand on points, P1, P2 and P3
At point P1, elasticity of demand = lower segment of the demand curve below the given point P2 P4 ÷ Upper segment of the demand curve above the point is P1 P. Therefore, Ed = P1 P4 ÷ P1P. Ed>1. It means demand is elastic or elasticity of demand is greater than one at point.
Similarly, by using the above given formula, we can measure elasticity of demand at point P2 and P3. At point P2 , demand is unitary elastic. It means elasticity of demand is equal to one whereas at point P3 demand is less than one.

Non-Linear Demand Curve

Fig. No 3.11

If the demand curve is non-linear, then a tangent is, drawn to the demand curve at the given point. The tangent should touch both the axes - OX axis and OY axis. The price elasticity is measured by the ratio of lower segment to the upper segment.