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### Explain Ratio method and Geometric method of measuring price elasticity of demand.

Price elasticity of demand is measured with the help of the following two 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.

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.