Price elasticity of demand measures how much quantity demanded changes when price changes. A PED above 1 means elastic demand (buyers are sensitive), below 1 means inelastic (buyers keep buying regardless of price). This single ratio tells businesses whether a price hike will raise or kill revenue, and tells governments how much tax a market will actually absorb.
On this page
- The formula and what it tells you
- The midpoint formula and why it matters
- A worked example: a coffee shop's pricing decision
- What drives elasticity: four determinants
- Availability of substitutes
- Necessity vs. luxury
- Time horizon
- Share of the household budget
- The negative-sign convention
- What it means in practice
In April 2009, the federal excise tax on cigarettes nearly tripled overnight, rising from $0.39 to $1.01 per pack under the Children's Health Insurance Program Reauthorization Act. Policymakers had two goals: raise revenue for children's health coverage and reduce smoking rates. They succeeded at the first more than the second. Cigarette consumption fell, but modestly, far less than the price increase might suggest. The reason comes down to a single concept: cigarettes have inelastic demand. Buyers are not very sensitive to price changes, so a large price increase produces a smaller-than-expected drop in quantity and a larger-than-expected gain in revenue.
Understanding that ratio, how much quantity responds when price changes, is price elasticity of demand, and it is one of the most practically useful measurements in economics.
The formula and what it tells you
Price elasticity of demand (PED) is defined as:
PED = % change in quantity demanded ÷ % change in price
Because the law of demand tells us quantity and price move in opposite directions, the ratio is negative. Economists typically report the absolute value, a PED of 2 rather than -2, since the direction is already known. The magnitude is what matters.
- PED > 1: elastic demand. Quantity changes by a larger percentage than price. A 10% price increase causes more than a 10% drop in quantity. Buyers are sensitive and adjust significantly.
- PED < 1: inelastic demand. Quantity changes by a smaller percentage than price. A 10% price increase causes less than a 10% drop in quantity. Buyers are not very responsive.
- PED = 1: unit elastic demand. Quantity and price change by exactly the same percentage. Total revenue stays constant when price changes.
Two special cases sit at the extremes. Perfectly inelastic demand (PED = 0) means quantity never changes regardless of price, a vertical demand curve. No real good is perfectly inelastic, but insulin for a type 1 diabetic approaches it. Perfectly elastic demand (PED = ∞) means consumers will buy any quantity at the going price but nothing above it, a horizontal demand curve. This describes competition between identical commodities where buyers can switch instantly.
The midpoint formula and why it matters
There is a problem with the basic formula: the percentage change you calculate depends on which direction you run it. If price rises from $10 to $12, the increase is 20%. If it falls from $12 back to $10, the decrease is 16.7%. The same $2 move produces different percentages depending on which point you call the base. This makes the basic formula asymmetric and direction-dependent.
The midpoint formula (also called the arc elasticity formula) fixes this by using the average of the two values as the denominator:
PED = [(Q₂ − Q₁) / ((Q₁ + Q₂) / 2)] ÷ [(P₂ − P₁) / ((P₁ + P₂) / 2)]
In plain terms: calculate the percentage change in quantity using the midpoint of the two quantities as the base; calculate the percentage change in price using the midpoint of the two prices as the base; divide.
The midpoint formula produces the same elasticity number whether you're measuring a price increase or decrease between the same two points, which makes it standard in economic analysis and in any setting where consistent measurement matters.
A worked example: a coffee shop's pricing decision
A coffee shop currently sells 600 cups per day at $4.00 each. The owner considers raising the price to $4.60, a meaningful increase. A rival coffee shop estimates that a similar price hike reduced their volume by 9%.
Using the midpoint formula:
- Average price = ($4.00 + $4.60) / 2 = $4.30. Price change = $0.60. % price change = 0.60 / 4.30 = 13.95%
- Quantity falls by 9%, so new quantity = 600 × 0.91 = 546 cups
- Average quantity = (600 + 546) / 2 = 573. Quantity change = -54. % quantity change = -54 / 573 = -9.42%
- PED = 9.42% / 13.95% ≈ 0.68 (inelastic)
Because demand is inelastic, the price increase should raise total revenue:
- Before: 600 cups × $4.00 = $2,400/day
- After: 546 cups × $4.60 = $2,512/day
- Revenue gain: +$112/day, or roughly +$41,000 per year
If instead the rival shop had estimated a 20% volume drop, PED would be approximately 1.43 (elastic) and the calculation reverses: 480 cups × $4.60 = $2,208/day, a revenue decline. Same price increase, opposite financial outcome.
What drives elasticity: four determinants
Availability of substitutes
This is the single strongest predictor of elasticity. When a good has many close substitutes, buyers can and do switch when price rises, so demand is elastic. When there are no substitutes, buyers have no exit and demand is inelastic.
Gasoline at the market level is relatively inelastic because there is no substitute for fuel in internal combustion vehicles in the short run. A specific gas station is highly elastic, because the station two blocks away is a near-perfect substitute. Bureau of Labor Statistics Consumer Expenditure Survey data shows that households in urban areas, where alternatives to driving exist, exhibit higher elasticity in gasoline spending than rural households with no viable substitutes.1
Necessity vs. luxury
Necessities are inelastic. Buyers cannot walk away from insulin, heating fuel, or basic food regardless of price. Luxuries are elastic. Fine dining, premium electronics, and vacations can all be postponed, reduced, or replaced. When incomes fall, demand for discretionary spending falls far more sharply than demand for necessities, reflecting higher elasticity in those categories.
Bureau of Economic Analysis personal consumption data shows this asymmetry clearly in spending patterns across the 2008-2009 recession: spending on necessities held relatively stable while discretionary categories collapsed, the behavioral signature of elastic vs. inelastic demand at aggregate scale.2
Time horizon
Short-run demand is almost always more inelastic than long-run demand, because time enables substitution. When gasoline prices surged in 2022, drivers could not immediately sell their cars and buy e-bikes, so their short-run elasticity was very low. Over years, car purchase decisions, commuting patterns, and residential locations adjusted. The long-run elasticity of gasoline demand is roughly two to three times the short-run figure.
This time-dependence means the same good can have genuinely different elasticities depending on the time frame of analysis, a critical nuance when applying elasticity estimates to real pricing or policy decisions.
Share of the household budget
Goods that represent a trivial portion of spending are relatively inelastic even without strong necessity arguments. Table salt, toothpicks, a $.99 app: even a 50% price increase costs the average household almost nothing in absolute terms. The price change registers but doesn't motivate serious search for alternatives. Conversely, goods that consume a significant budget share (housing, car payments, health insurance) have higher elasticity because the absolute dollar stakes make shopping around worthwhile.
The negative-sign convention
One note on interpretation: because demand curves slope downward, price elasticity of demand is always negative in its raw form. A price increase causes a quantity decrease; the ratio of two numbers with opposite signs is negative.
Economists almost universally drop the negative sign and report the absolute value, relying on context to convey that demand is being discussed. A PED of "2" means a 10% price increase reduces quantity demanded by 20%. The inverse relationship is understood. When comparing elasticities across goods, the convention is consistent: a higher absolute value means more price-sensitive demand.
What it means in practice
For businesses, elasticity determines whether a price increase raises or lowers revenue. A firm with inelastic demand (a pharmaceutical company, a regulated utility, a business with strong switching costs) can raise prices and increase revenue. A firm with elastic demand (a commodity retailer, a streaming service with many competitors) risks revenue loss from price hikes.
For tax policy, elasticity determines who bears the burden. When the federal government imposes an excise tax on cigarettes, the inelastic demand for cigarettes means consumers absorb most of the tax in higher prices; they don't reduce consumption enough to shift the burden back to manufacturers.3 The IRS excise tax framework applies to dozens of product categories, and the intended revenue yield of any such tax is only achievable if the elasticity of demand is correctly estimated. Tax a highly elastic good at a high rate and the quantity base collapses: government collects far less than projected because buyers simply stop buying.
Elasticity does not tell you what price to charge or what tax to set. But it is the mechanism that determines what actually happens after you do.
