Calculating the price elasticity of demand
Price elasticity tells you by what percentage quantity changes when the price rises by one percent. It decides whether a price rise increases or reduces revenue.
Formulas and rules
- ε = (% change in quantity) / (% change in price)
- Point elasticity with Q = a − b·p: ε = −b × p / Q
- Arc elasticity (midpoint method): divide the changes by the midpoints
- |ε| > 1 elastic: a price rise lowers revenue
- |ε| < 1 inelastic: a price rise raises revenue
- Maximum revenue with linear demand: ε = −1
Your turn
Three problems on this topic. Type numbers like 12.5 or 1,250 and elasticities with their sign.
Task
A cinema changes its ticket price from €34.00 to €27.00. Weekly tickets sold change from 340 to 350. Work out the arc elasticity (midpoint method) and the change in revenue.
Arc elasticity (with sign, 2 decimals)
Change in weekly revenue in € (fall with a minus)
Demand in this range is …
Numbers like 12.5 or 1,250; elasticities with their sign (−0.75); percentages as a number (12.5). Round to 2 decimal places.
Worked example
Demand for a good is Q_d = 355 − 5p. The price is currently €21.00. Work out the price elasticity of demand at this point.
Worked solution
- 1.Quantity: 355 − 5 × 21 = 250
- 2.ε = (dQ/dp) × (p/Q) = −5 × 21 / 250 = −0.42
- 3.|ε| < 1: inelastic, quantity reacts less than the price → revenue rises when the price rises
Typical mistake: Taking the slope −b as the elasticity. Elasticity depends on the point: slope times p/Q.
A cinema changes its ticket price from €29.00 to €25.00. Weekly tickets sold change from 280 to 340. Work out the arc elasticity (midpoint method) and the change in revenue.
Worked solution
- 1.Change in quantity relative to the midpoint: (340 − 280) / 310 = 19.35 %
- 2.Change in price relative to the midpoint: (25 − 29) / 27 = −14.81 %
- 3.ε = −1.31
- 4.Revenue before €8,120.00, after €8,500.00 → change €380.00
Typical mistake: Dividing the changes by the starting values instead of the midpoints. Then the answer depends on the direction of the change; the midpoint method avoids that.
Common questions
Why is price elasticity negative?
When the price rises, the quantity demanded falls. Many textbooks quote the absolute value; work with the sign and compare the absolute value with 1.
Is elasticity the same everywhere on a straight line?
No. The slope is constant, the elasticity is not: at the top (high price, small quantity) demand is elastic, at the bottom inelastic.