Hong Life CalculatorsUnderstanding the price elasticity of demand calculator — concept and principle
This calculator measures how strongly the quantity demanded responds to a price change, using the midpoint (arc) method. It classifies demand as elastic, inelastic or unit elastic, shows the percentage changes, the revenue at each price and the revenue change, and gives the simple-percentage elasticity for comparison. Students, pricing managers and small sellers use it to judge whether a price change will raise or lower revenue.
How it is calculated
- % change in quantity = (Q2 − Q1) ÷ ((Q1 + Q2) ÷ 2) × 100
- % change in price = (P2 − P1) ÷ ((P1 + P2) ÷ 2) × 100
- Elasticity = % change in quantity ÷ % change in price
- Revenue = price × quantity at each point
- Simple elasticity = ((Q2 − Q1) ÷ Q1) ÷ ((P2 − P1) ÷ P1)
Elastic: absolute value above 1. Inelastic: below 1. Unit elastic: 1.
The principle
Elasticity compares percentage changes, so it does not depend on units or currency. Because price and quantity usually move in opposite directions, the value is negative; economists often discuss its absolute size. The midpoint method divides each change by the average of the two values, so you get the same answer whether the price goes up or down. Elasticity tells you what happens to revenue: with elastic demand, a price cut raises total revenue because quantity rises proportionally more; with inelastic demand, a price cut lowers revenue.
Worked example
Defaults: price falls from 20 to 18; quantity rises from 1,000 to 1,150.
- % change in quantity = 150 ÷ 1,075 × 100 = 14% (13.95%).
- % change in price = −2 ÷ 19 × 100 = -10.5%.
- Elasticity = 13.95 ÷ (−10.53) = -1.33: Elastic (above 1).
- Revenue: 20 × 1,000 = $20,000; 18 × 1,150 = $20,700; change $700.
- Simple elasticity = 0.15 ÷ (−0.10) = -1.5.
| Quantity sold at the second price | Price elasticity of demand (midpoint) |
|---|---|
| 288 | 10.51 |
| 575 | 5.13 |
| 862 | 1.4 |
| 1,150 | -1.33 |
| 1,438 | -3.41 |
| 1,725 | -5.06 |
| 2,300 | -7.48 |
How to read the result
Because demand is elastic here, the price cut increased revenue. Whether it increased profit depends on costs: 150 extra units must also be produced. Inelastic demand suggests room to raise prices; elastic demand suggests customers are price-sensitive, often because substitutes are easy to find.
Common mistakes
- Using data where other factors, such as advertising or season, also changed.
- Mixing midpoint and simple elasticities.
- Reading the sign as good or bad; it is normally negative.
- Assuming the elasticity is the same at every price.
Frequently asked questions
What does an elasticity of −1.33 mean?
A 1% price change moves quantity by about 1.33% in the opposite direction.
When does a price cut raise revenue?
When demand is elastic, with an absolute elasticity above 1.
Why is the midpoint result different from the simple one?
The simple method uses the first point as the base, so its answer depends on direction; the midpoint method does not.
Sources: OpenStax, Principles of Economics, 3rd ed. (2022), section 5.1 "Price Elasticity of Demand and Price Elasticity of Supply"