Price Elasticity of Demand
Measure how sharply quantity demanded responds to a price change, using the midpoint (arc) method.
PED = -1.22 — demand is elastic.
Price elasticity of demand measures how much quantity demanded responds to a price change: PED = %ΔQ ÷ %ΔP. Raising price from $10 to $12 while quantity falls from 100 to 80 gives |PED| ≈ 1.22 — elastic, because a 1% price rise cuts quantity demanded by more than 1%.
What price elasticity of demand tells you
Price elasticity of demand (PED) is the percentage change in quantity demanded divided by the percentage change in price. It is a unitless ratio: a PED of −1.22 means that, in this range, quantity demanded changes by 1.22% for every 1% change in price. Because demand curves slope downward, the raw value is almost always negative — price and quantity move in opposite directions — so economists usually compare the absolute value, |PED|.
The size of |PED| is what matters. If |PED| is greater than 1, demand is elastic: buyers are sensitive to price, and quantity swings by a larger percentage than price. If it is less than 1, demand is inelastic: quantity barely moves, as with necessities. Exactly 1 is unit elastic, where the two percentage changes match.
Midpoint method: %ΔQ = (Q₂ − Q₁) ÷ ((Q₁ + Q₂) ÷ 2) and %ΔP = (P₂ − P₁) ÷ ((P₁ + P₂) ÷ 2)
Worked example
A shop raises a product’s price from $10 to $12, and weekly units sold fall from 100 to 80.
- 1 Find the percentage change in quantity. %ΔQ = (Q₂ − Q₁) ÷ ((Q₁ + Q₂) ÷ 2) = (80 − 100) ÷ 90 = −0.2222.
- 2 Find the percentage change in price. %ΔP = (P₂ − P₁) ÷ ((P₁ + P₂) ÷ 2) = (12 − 10) ÷ 11 = 0.1818.
- 3 Divide %ΔQ by %ΔP. PED = −0.2222 ÷ 0.1818 = −1.22.
- 4 Take the absolute value. |−1.22| = 1.22, so |PED| ≈ 1.22.
- 5 Read the label. Because |PED| > 1, demand over this price range is elastic.
Reading the elasticity value
Compare the absolute value |PED|. The sign is almost always negative because demand slopes downward.
| |PED| range | Label | What it means | Typical example |
|---|---|---|---|
| 0 | Perfectly inelastic | Quantity does not change at all when price moves | Life-saving medicine like insulin |
| Between 0 and 1 | Inelastic | Quantity changes by a smaller percentage than price | Gasoline, salt, utilities |
| Exactly 1 | Unit elastic | Quantity and price change by the same percentage | A borderline case between the two |
| Greater than 1 | Elastic | Quantity changes by a larger percentage than price | Soft drinks, restaurant meals, holidays |
Why the midpoint method, and what the sign means
The midpoint method removes direction bias. If you divide each change by the starting value, a price rise from $10 to $12 and a fall from $12 to $10 give different elasticities for the same pair of points. Dividing by the average of the two values — the midpoint — makes the calculation symmetric, so you get the same |PED| whether price rose or fell. That is why intro courses call it the arc (or midpoint) elasticity.
The total-revenue test is the practical payoff. When demand is elastic, a price cut raises total revenue because the percentage jump in quantity outweighs the lower price; a price increase lowers revenue. When demand is inelastic, the opposite holds — raising price raises revenue. At unit elasticity, revenue is unchanged. Knowing |PED| tells a seller which way to move price.
A negative sign is normal. Price and quantity demanded move in opposite directions, so PED itself is usually negative; the tool reports both the signed value and |PED| so you can classify it without worrying about the minus.