Methods of measuring price elasticity of demand

• Percentage method or proportional method or Formula Method.
• Point elasticity method or Geometric Method.
• Arc elasticity method.
• Total outlay method or Expenditure method.

Percentage change or proportional or formula method:

This is measured as the relative change in demand divided by relative change in price (or) percentage change in demand divided by percentage change in price. Example

The price of rice rises by 10% and the demand for rice falls by 15%.

Ep = % ∆ quantity / % ∆ price

= 15/10

= 1.5

Point elasticity method:

It measures elasticity of demand at a particular point on the demand curve. We can calculate the price elasticity of demand at a point on the linear demand curve. This method is usually used when the percentage change is extremely small. Formula to find out Ep through point method is Ep = Lower segment of the demand curve/Upper segment of the demand curve. If a demand curve is drawn in such a manner, as it is tangent to both the axis, then at the mid point of the demand curve, the elasticity of demand is equal to one, any point above then this, elasticity goes of increasing and reaches infinity and any point below this, elasticity goes of decreasing and reaches zero. In the above figure, the length of the demand curve AB has 4 equal parts, AB, BC, CD, DE.

 S. No. Ep at different Point on the demand curve as seen in the figure above Ep = lower segment / upper segment Price elasticity 1 Ep at point C (exactly at the middle point of AB demand curve) CE/CA = 2/2 = 1 therefore Ep = 1 2 Ep at point D (middle point of CE portion of demand curve) DE/DA = 1/3 = 0.33 therefore Ep < 1 3 Ep at point B (middle point of AC portion of demand curve) BE/AB = 3/1 = 3 therefore Ep > 1 4 Ep at point E (bottom of the demand curve) O/AE= 0/4 = 0 (zero by anything is zero, a mathematical principle) therefore Ep = 0 5 Ep at point A (top of the demand curve) AE/O = 4/0 = ∞ (Anything by zero becomes infinity, a mathematical principle) therefore Ep = ∞

Arc elasticity of demand:

A segment of a demand curve between two points is called an arc. It measures elasticity when there are large changes in price or when elasticity is to be measured between two points on the demand curve. Since point elasticity differs at various points on the demand curve, arc elasticity takes the average of two points to measure elasticity. Arc elasticity is calculated from the following formula: Where,
q1 = original quantity
q2 = new quantity
p1 = original price
p2 = new price

Note: If the problem is silent about the method to calculate price elasticity, then Arc method should be used.

Example

P1 = 50, Q1 = 10

P2 = 30 , Q2 = 17

So, by using the formula, Ep = 10-17/10+17 x 50 + 30/50 – 30

= 7/17 x 80/20 = 1.65

So, Ep = 1.65 so it is relatively elastic.

Problem
A consumer purchases 80 units when the price is ₹ 2 per unit and purchases 48 units when the price increases to ₹ 4 per units. What is the price elasticity of demand for the commodity?

Solution
Here,

P1 = 2, Q1 = 80 and P2 = 4 , Q2 = 48

So, by using the formula, Ep= 32/128 X 6/2

So, Ep = 0.75, so it is relatively inelastic.

Total outlay method

This method is also known as Total Expenditure method. We can measure elasticity through a change in expenditure on commodities due to a change in price. With this method, we cannot find out the exact and precise coefficient of elasticity. We can only know whether elasticity is equal to, greater than or lesser than 1.
• If demand is elastic, total outlay or expenditure increases for a fall in price and decreases with rise in price
• If demand is inelastic, total outlay or expenditure falls for a fall in price and rise with rise in price
• If elasticity of demand is unitary, total expenditure does not change for a fall or rise in price
 Changes in price Types of elasticity of demand ep = 1 ep < 1 ep > 1 Fall in price Total outlay remains constant Total outlay falls Total outlay rises Rise in price Total outlay remains constant Total outlay rises Total outlay falls

 Price of pen (P) (₹) Quantity demanded (Q) Total outlay (PxQ) Elasticity of demand (e) 5 2,000 10,000 >1 Relatively elastic 4 3,000 12,000 2 7,000 16,000 5 2,000 10,000 =1 Unitary Elastic 4 2,500 10,000 2 5,000 10,000 5 2,000 10,000 =1 Unitary Elastic 4 2,250 9,000 2 3,100 6,200

Elasticity greater than one (Ep > 1):

When, due to a fall in price, the quantity demanded increases so much so that the total expenditure/outlay increases, price elasticity of demand will be greater than one. Or, if due to an increase in price, the quantity demanded decreases so much so that the total expenditure/outlay decreases, the price elasticity of demand will be greater than one. Thus, price and quantity demanded move in opposite directions. Elasticity is equal to one (Ep = 1)

When, due to a change in the price, the quantity demanded of a good increases so much so that the total expenditure on the good remains the same, the elasticity of demand is equal to one or unity. Elasticity lesser than one (Ep < 1):

If, as a result of a fall in price of a good, the total expenditure decreases, and vice-versa, the price elasticity of demand will be less than unity. Thus, price and quantity demanded move in the same direction.   