How to Calculate Price Elasticity of Demand (Midpoint Method)
Price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price, using the midpoint method on AP exams.
The Price Elasticity of Demand formula
Calculator
Enter the old and new price and quantity; get the midpoint %ΔQ, %ΔP, PED, and the elasticity verdict.
The starting price. The worked example uses a rise from $4 to $6.
Quantity at the new price. It normally moves opposite to price.
Quantity and price move by the same percentage, so total revenue does not change.
- % change in quantity demanded
- −40%
- % change in price
- 40%
- Elasticity verdict
- Unit elastic
How to calculate Price Elasticity of Demand, step by step
- 1Find the % change in quantity (midpoint). (Q₂ − Q₁) ÷ ((Q₁ + Q₂) ÷ 2).
- 2Find the % change in price (midpoint). (P₂ − P₁) ÷ ((P₁ + P₂) ÷ 2).
- 3Divide. PED = %ΔQ ÷ %ΔP. Take the absolute value to classify elasticity.
- 4Interpret. |PED| > 1 = elastic, < 1 = inelastic, = 1 = unit elastic.
Worked example: Price Elasticity of Demand
Price rises from $4 to $6 and quantity falls from 120 to 80. %ΔQ = (80−120)/100 = −40%; %ΔP = (6−4)/5 = 40%. PED = −40% ÷ 40% = −1 → unit elastic.
Why the midpoint formula exists
Ordinary percentage change gives two different answers for the same pair of points, depending on which one you start from. Take the worked example: price $4 with quantity 120, and price $6 with quantity 80.
Starting from the $4 point, quantity falls 40/120 = 33.3% while price rises 2/4 = 50%, so elasticity is 0.67 and demand looks inelastic. Starting from the $6 point, quantity rises 40/80 = 50% while price falls 2/6 = 33.3%, so elasticity is 1.5 and the same stretch of the same curve now looks elastic.
The midpoint formula divides by the average of the two values instead of by whichever came first, which gives 40/100 = 40% and 2/5 = 40%, so elasticity is exactly 1 from either direction. That is the whole reason to use it, and it is why AP questions specify it.
The total revenue test, and why it works
Elasticity tells you what a price change does to revenue, which is usually the point of the question.
Check it on the same numbers. At $4 and 120 units, revenue is $480. At $6 and 80 units, revenue is also $480. Elasticity came out to exactly 1, and revenue did not move. That is not a coincidence: unit elastic means the percentage fall in quantity exactly cancels the percentage rise in price.
From there the rest follows. If demand is elastic, quantity moves proportionally more than price, so raising the price loses revenue and cutting it gains revenue. If demand is inelastic, quantity moves proportionally less, so raising the price gains revenue. This gives you a way to answer without computing anything: if a firm raises its price and revenue rises, demand was inelastic over that range.
Elasticity changes along a straight-line demand curve
A common wrong instinct is that a straight demand curve has one elasticity because it has one slope. It does not. Slope and elasticity are different things, and elasticity falls continuously as you move down the curve.
Near the top, price is high and quantity is small, so a small absolute change in quantity is a large percentage change while the same absolute change in price is a small percentage one. Demand is elastic there. Near the bottom the position reverses and demand is inelastic. Exactly halfway down, elasticity is 1, and that is also the quantity where total revenue is at its maximum.
So a question asking whether demand is elastic has to tell you where on the curve you are. When one asks for the revenue-maximising price, the answer is the midpoint of the demand curve, where elasticity equals 1.
Price Elasticity of Demand questions
Why use the midpoint method?
It gives the same elasticity whether price rises or falls between two points, because it divides by the average of the start and end values instead of the starting value.
What makes demand more elastic?
More substitutes, the good taking a larger share of income, it being a luxury, and a longer time horizon all make demand more elastic.
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