Elasticity of Demand

The law of demand tells us that a fall in price raises quantity demanded — but by how much? For some goods demand changes a lot when price changes; for others hardly at all. Price elasticity of demand (E_d) measures the responsiveness of quantity demanded to a change in price. More precisely, it is the percentage change in quantity demanded divided by the percentage change in price:

E₃ = (% change in quantity demanded) ÷ (% change in price)

Since price and quantity move in opposite directions, elasticity is technically negative, but we usually ignore the sign and look at the size of the number. Based on its value, demand has different degrees of elasticity:

• Perfectly elastic (E = ∞) — demand changes infinitely at a given price; the demand curve is horizontal. (A rare, theoretical case.)
• Highly (more than unit) elastic (E > 1) — quantity changes more than price; flat-ish curve (e.g. luxuries).
• Unit elastic (E = 1) — quantity changes exactly in proportion to price.
• Less (inelastic) than unit (E < 1) — quantity changes less than price; steep curve (e.g. necessities like salt).
• Perfectly inelastic (E = 0) — quantity does not change at all when price changes; the demand curve is vertical. (Also rare/theoretical.)

So a large elasticity (E > 1) means demand is very responsive (elastic); a small elasticity (E < 1) means demand is unresponsive (inelastic).

The most common way to calculate elasticity is the percentage method (also called the proportionate method). The formula is:

E₃ = (ΔQ ÷ Q) × 100   ÷   (ΔP ÷ P) × 100 = (ΔQ ÷ ΔP) × (P ÷ Q)

where ΔQ is the change in quantity, ΔP is the change in price, and Q and P are the original quantity and price.

Worked example. When the price of a good falls from ₹10 to ₹8, the quantity demanded rises from 40 units to 60 units. Find the price elasticity of demand.

• ΔP = 8 − 10 = −2; original P = 10. So % change in price = (−2 ÷ 10) × 100 = −20%.
• ΔQ = 60 − 40 = 20; original Q = 40. So % change in quantity = (20 ÷ 40) × 100 = 50%.
• E = 50% ÷ (−20%) = −2.5, and ignoring the sign, E = 2.5.

Since E = 2.5 is greater than 1, the demand for this good is elastic — quantity demanded responded strongly (a 20% price cut raised quantity by 50%). The percentage method is exact and works for any pair of price–quantity values, which is why it is the standard method in examinations.

Another way to judge elasticity, without exact numbers, is the total expenditure (total outlay) method, given by Alfred Marshall. It looks at what happens to the consumer's total spending (Total Expenditure = Price × Quantity) when the price changes:

• If a fall in price raises total expenditure (and a price rise lowers it), demand is elastic (E > 1). Price and total expenditure move in opposite directions.
• If total expenditure stays the same when price changes, demand is unit elastic (E = 1).
• If a fall in price lowers total expenditure (and a price rise raises it), demand is inelastic (E < 1). Price and total expenditure move in the same direction.

For example, if the price of a luxury drops and people spend much more on it overall, its demand is elastic; if the price of salt drops and total spending on salt falls (because we buy hardly any more), its demand is inelastic.

Finally, factors affecting elasticity: (1) nature of the good — necessities (salt, medicine) are inelastic, luxuries are elastic; (2) availability of substitutes — more substitutes make demand more elastic; (3) proportion of income spent — goods on which we spend a large share of income are more elastic; (4) number of uses — goods with many uses are more elastic; (5) time period — demand is usually more elastic in the long run, as people find alternatives; and (6) habit — habitual goods (like cigarettes for a smoker) tend to be inelastic.