Two measures of price elasticity of demand

Price elasticity of demand measures how far quantity demanded responds to a change in the good's own price. Two common ways of measuring it are set out below, each with an example of our own.

Measure 1: the percentage (proportionate) method.

• Formula. Ep = (% change in quantity demanded) ÷ (% change in price), that is, (change in quantity ÷ original quantity) ÷ (change in price ÷ original price). The answer is negative for a normal good, and its size (the sign ignored) shows how responsive demand is.
• The mid-point refinement. Measured from the original price and quantity, the answer depends on whether the price rises or falls between the same two points. The mid-point (arc) method avoids this by using the average of the two prices and the average of the two quantities as the base.
• Example. A Jaipur bakery cuts the price of a cake from Rs 500 to Rs 400 and its daily sales rise from 20 to 30.
  • From the original point: change in quantity = 10, so 10/20 = 50%; change in price = -100, so -100/500 = -20%. Elasticity = 50 / (-20) = -2.5.
  • Mid-point method: average quantity 25 and average price 450, so (10/25) / (-100/450) = 0.40 / (-0.222) = -1.8.
  • Either way the size exceeds 1, so demand for the cake is elastic.

Measure 2: the total expenditure (total revenue) method.

• Rule. Total expenditure on a good (the seller's total revenue) is price x quantity. Compare it before and after a price change:
  • Elastic demand (size above 1): expenditure moves opposite to price, rising when price falls and falling when price rises.
  • Unitary elastic demand (size 1): expenditure stays the same.
  • Inelastic demand (size below 1): expenditure moves with price, falling when price falls and rising when price rises.
• Example. In the bakery case expenditure rises from 500 x 20 = Rs 10,000 to 400 x 30 = Rs 12,000 when price falls: demand is elastic, which agrees with Measure 1. By contrast, if a Pune metro pass rises from Rs 500 to Rs 600 and passes sold fall from 1,000 to 950, spending rises from Rs 5,00,000 to Rs 5,70,000 as price rises: demand is inelastic.
• Limit. This method tells only the class of elasticity (elastic, unitary or inelastic), not its exact value.

Conclusion. The percentage method gives a number for the elasticity (with the mid-point version giving the same answer whichever way the price moves), while the total expenditure method gives a quick test of whether demand is elastic, unitary or inelastic from what happens to spending.