How price elasticity of demand works
When a coffee shop raises its latte price, two things happen at once: each cup earns more, and fewer cups sell. Elasticity is the number that says which force wins. It compares the percentage change in quantity to the percentage change in price, so it works the same whether you sell ten-dollar books or ten-thousand-dollar machines. A result above 1 in magnitude means buyers are price-sensitive — demand is elastic. Below 1, they mostly shrug — demand is inelastic. Marketers use it to set prices, economists use it to predict tax effects, and every intro-econ problem set uses it constantly.
The midpoint formula
E = %ΔQ ÷ %ΔP
%ΔQ = (Q₂ − Q₁) ÷ [(Q₁ + Q₂) ÷ 2] × 100
%ΔP = (P₂ − P₁) ÷ [(P₁ + P₂) ÷ 2] × 100
where P₁, Q₁ are the initial price and quantity andP₂, Q₂ the new ones. Dividing by the averagerather than the starting value makes the answer identical whichever direction the price moves — the reason the midpoint method is the textbook standard. Classify on the absolute value: |E| > 1 elastic, |E| < 1 inelastic, |E| = 1 unit elastic.
Worked example
Take the classic problem: a price rise from $10.00 to $12.00 cuts sales from 100 to 80 units. Here is the midpoint calculation, step by step:
| Step | Amount |
|---|---|
| Price changemidpoint method: change ÷ average of the two prices = 18.18% | $10.00 → $12.00 |
| Quantity changemidpoint method: change ÷ average of the two quantities = -22.22% | 100 → 80 units |
| ÷ Elasticity = %ΔQ ÷ %ΔP-22.22% ÷ 18.18% | -1.2222 |
| Revenue checkan elastic response means the price rise costs more sales than it gains per unit | $1,000.00 → $960.00 |
| = |E| of 1.2222 — demand is elasticeach 1% price change moves quantity about 1.2222% | 1.2222 |
Computed with this calculator's default settings — open the tool above and you'll see the same numbers, then swap in your own price and quantity data.
Elasticity, revenue, and who bears a tax
The revenue test built into this calculator is more than a classroom trick. Because total revenue is price × quantity, elasticity tells a business which way a price change moves the top line before it happens: elastic demand punishes price rises, inelastic demand rewards them. The same logic decides tax incidence — governments tax inelastic goods like fuel and cigarettes precisely because quantity barely falls, and the burden lands mostly on buyers. When you hear that a firm "has pricing power", elasticity below 1 is the formal version of that claim.
Elasticity feeds directly into margin math: pair it with ourmargin calculatorto see what a price change does to profit rather than revenue, check a price cut's promotional math with thepercentage discount calculator, or model the volume needed to break even after a price move with thebreak-even point calculator.
Frequently asked questions
What is price elasticity of demand?
Price elasticity of demand measures how strongly the quantity demanded of a good responds to a change in its price. It is the percentage change in quantity divided by the percentage change in price. A magnitude above 1 means demand is elastic (quantity moves more than proportionally), below 1 means inelastic (quantity barely responds), and exactly 1 means unit elastic. Because price and quantity move in opposite directions along a demand curve, the raw coefficient is negative; textbooks classify on its absolute value.
Why use the midpoint (arc) method?
The simple point method divides each change by its starting value, which gives a different elasticity depending on whether the price rose or fell between the same two points. The midpoint method divides by the average of the two values instead, so the answer is identical in both directions. That symmetry is why AP Economics and most intro textbooks require the midpoint formula for elasticity between two points.
How does elasticity affect total revenue?
Total revenue is price times quantity, so a price change pulls revenue in two directions at once: a higher price earns more per unit but sells fewer units. When demand is elastic the quantity effect wins, so raising price lowers revenue. When demand is inelastic the price effect wins, so raising price raises revenue. At unit elasticity the two effects cancel exactly and revenue does not change. This "revenue test" is the fastest way to read an elasticity result.
What makes demand for a good elastic or inelastic?
The main drivers are substitutes, necessity, budget share, and time. Goods with close substitutes (one brand of cereal) are elastic because buyers can switch; necessities with no substitutes (insulin, gasoline in the short run) are inelastic. Items that consume a large share of income tend to be more elastic than trivial purchases, and almost everything becomes more elastic over longer time horizons as buyers find alternatives.
Can elasticity be positive?
For ordinary goods, price elasticity of demand is negative — price up, quantity down. A positive coefficient would mean people buy more as the price rises, which is the theoretical territory of Giffen and Veblen goods, and in practice usually signals a data problem (something else, like income or fashion, changed at the same time as the price). Cross-price and income elasticities, by contrast, are routinely positive.
Sources
- OpenStax, Principles of Economics — Price Elasticity of Demand and Price Elasticity of Supply
- Marshall, Principles of Economics (1890) — Book III, on elasticity of wants (Library of Economics and Liberty)
The official figures this page quotes are drawn from the primary sources above — check them (or a qualified professional) before relying on a result.
Disclaimer: This calculator is foreducation and illustration only. Elasticity computed from two observed points assumes nothing else changed between them — real-world estimates control for income, substitutes, and seasonality. Results are a textbook calculation, not a demand study, and nothing here is pricing, financial, or tax advice.