How this instrument works
Price elasticity of demand measures how sharply the quantity people buy reacts to a change in that same good's own cost — nothing else moves in this ratio, not income, not a rival's rate, only two figures for the good itself and the two quantities sold at each one. This sheet uses the midpoint (or arc) method: instead of picking one of the two figures as the base for the percentage change, it divides by the average of the two and the average of the two quantities. That choice matters because a plain percentage change gives a different answer depending on which figure you call the start — a rise from $10 to $12 is +20%, but the same move read backward from $12 to $10 is −16.7%. Averaging both endpoints in the denominator removes that asymmetry, so the same two points return the same size of answer whichever direction the calculation runs.
A retail pricing manager reaches for this figure before approving a markdown: if the cut is expected to land in elastic territory, above 1 in absolute size, the extra volume it draws should more than offset the lower per-unit price and total revenue should rise; in inelastic territory the same cut just gives away margin on units that would have sold anyway. Gasoline, prescription insulin, and highway tolls typically test inelastic, because buyers keep paying when there is no easy substitute or the purchase is not optional. Restaurant meals, a name-brand snack sitting next to a cheaper store brand, and leisure air travel typically test elastic, because a substitute or a postponed trip is one cost increase away. Economists estimating a demand curve from two observed price-quantity pairs, and analysts modeling how much revenue a targeted excise tax will actually raise, run this identical arithmetic.
The result describes one arc between two specific points, not the whole demand curve — a good can test elastic near one cost range and inelastic near another, so a reading taken far from the range actually under consideration is a poor guide there. It also cannot separate a pure price effect from a demand shift that happened at the same time: if a competitor launched a cheaper alternative the same week the cost changed, the quantity drop this formula attributes to that change includes some of the competitor's pull too. And because the two figures must differ for the ratio to exist at all, this measures a move between two points, never a single fixed level.
- Enter Initial quantity demanded and Initial price, $ — the units sold and the amount charged before the change you want to test.
- Enter New quantity demanded and New price, $ — the units sold and the cost after the change, whether observed or hypothetical.
- Read Price elasticity of demand and check the sign first — demand curves normally slope down, so an increase paired with a quantity drop returns a negative number.
- Compare the size of that number to 1: above 1 means demand is elastic, below 1 means inelastic — that comparison decides whether the move raises or lowers total revenue.
- Hold the quantities fixed and nudge either input to see how much the reading shifts when the two points sit closer together or farther apart.
Worked example — a price rise from $10 to $12
Start at Initial quantity demanded 100 and Initial price, $ 10.00. That figure then rises to New price, $ 12.00 and New quantity demanded falls to 80. The midpoint percentage change in quantity is (80 − 100) divided by ((100 + 80) ⁄ 2), or −20 ⁄ 90, about −22.2%. The midpoint percentage change in cost is (12 − 10) divided by ((10 + 12) ⁄ 2), or 2 ⁄ 11, about 18.2%.
Price elasticity of demand is then −22.2 divided by 18.2, about −1.22 (more precisely −1.222222…). Because the size of that number exceeds 1, demand tested elastic over this range: quantity fell by a larger percentage than cost rose, so total revenue actually moved from 100 × $10 = $1,000 before the change to 80 × $12 = $960 after it — the $12 sticker sold fewer total dollars than the $10 one, the opposite of what a seller assuming a higher charge always collects more money would expect.
Questions
Why does this use the midpoint method instead of the original price as the base?
Because a plain percentage change gives two different answers for the same two points depending on which one gets called the starting price — a $10-to-$12 move is +20% read forward but −16.7% read backward. The midpoint method divides by the average of the two prices and two quantities instead, so the size of the result comes out the same regardless of which direction you calculate, which is what lets two people compare elasticities computed from the same pair of points.
What does it mean when demand tests as elastic, with the reading above 1 in size?
It means quantity demanded moves by a larger percentage than cost does, so a price increase shrinks total revenue and a price cut grows it — the opposite of assuming a higher sticker figure always means more money collected. Goods with easy substitutes or postponable purchases, like restaurant meals or leisure travel, typically test elastic.
What does an inelastic reading, below 1 in size, mean for revenue?
It means quantity barely moves when cost does, so a price increase raises total revenue and a price cut lowers it, because the small drop in units sold is outweighed by the higher amount collected on each unit still sold. Goods with few substitutes or non-optional purchases, such as gasoline, prescription insulin, or highway tolls, typically test inelastic.
Why is the elasticity value negative in the worked example?
Because demand curves slope downward: cost rose and quantity fell, so the two percentage changes carry opposite signs and their ratio comes out negative. Elasticity is often discussed by its size alone for convenience, but the sign is doing real work — a positive reading between two price-quantity pairs for the same good would be the unusual case worth double-checking, not the default.
How is this different from cross-price or income elasticity of demand?
This instrument relates a good's quantity demanded to its own price; cross-price elasticity relates one good's quantity to a different good's cost, and income elasticity relates quantity to a buyer's earnings instead of either one. All three divide one midpoint percentage change by another, but which two quantities go into the ratio, and so what question the sign answers, differs in each case.
What is the most common mistake people make when reading this number?
Assuming a price increase always raises revenue. Whether it does depends entirely on where the reading falls relative to 1 in size — above 1 and that same increase loses more in volume than it gains per unit, so revenue falls; below 1 and the reverse holds. Skipping that comparison and reasoning straight from a higher charge to more money is the error this calculation exists to catch.
References
- OpenStax, Rice University — Principles of Microeconomics, price elasticity of demand
- U.S. Small Business Administration — Manage Your Business guide
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.