Price Elasticity of Demand Formula
Defines price elasticity of demand (PED) as the ratio of the percentage change in quantity demanded to the percentage change in price, and shows how to calculate it, always reporting the result as a positive value despite the negative raw calculation. The key insight is that PED is a pure number (no units) that measures responsiveness, allowing comparison across completely different goods. Contains: text explanation, the standard percentage-change formula, the midpoint formula, a worked example calculation, and an exam-tip callout on the sign convention.
Price elasticity of demand (PED) measures how responsive quantity demanded of a good is to a change in its own price. It answers the question: if price rises by 10%, does quantity demanded barely move, or does it collapse? Because PED expresses both quantity and price changes as percentages rather than absolute units, it lets economists compare the responsiveness of totally different goods — say, bread and diamonds — on the same scale.
Basic PED formula: percentage change in quantity demanded divided by percentage change in price.
Because demand curves slope downward, a price rise causes quantity demanded to fall (and vice versa), so the raw calculation of PED is mathematically negative. By convention, PED is always reported as a positive number — economists simply ignore the negative sign (or take the absolute value) because the direction of the relationship is already known from the law of demand; what matters for analysis is the magnitude of the response.
Midpoint (arc elasticity) formula, used for greater accuracy when the price change is large.
The basic percentage-change formula uses the original price and quantity as the base for calculating percentage change. This can give different answers depending on whether price rises or falls between the same two points. The midpoint formula avoids this inconsistency by using the average of the two prices and the average of the two quantities as the base, giving one consistent PED value regardless of the direction of change. This is especially useful when the price change under consideration is large.
Calculating PED with the basic formula
- A firm raises the price of a good from 12. Quantity demanded falls from 200 units to 150 units.
- % change in quantity demanded = (150 − 200)/200 × 100 = −25%
- % change in price = (12 − 10)/10 × 100 = +20%
- PED = −25% ÷ 20% = −1.25
- Express as a positive value: PED = 1.25
- Since 1.25 > 1, demand is elastic — quantity demanded changes proportionally more than price.
Exam tip: On Paper 2 calculation questions, always state your final PED answer as a positive number even if your working produces a negative sign — examiners expect the absolute value as the final answer, with a brief note on what it means (elastic/inelastic).
Common mistake: Forgetting to convert changes into percentages before dividing. PED is never calculated as the raw ratio of to (absolute unit changes) — both changes must first be expressed relative to their original (or midpoint) values.
- PED = % change in quantity demanded ÷ % change in price
- PED is always expressed as a positive number, even though the raw calculation is negative
- Use the midpoint formula for large price changes to avoid inconsistent results depending on direction
- PED has no units — it is a pure ratio, allowing comparison across different goods
- PED > 1 = elastic; PED < 1 = inelastic; PED = 1 = unit elastic (covered in more depth elsewhere in this subtopic)
Midpoint Formula for PED
Explains why the standard PED formula gives inconsistent results depending on the direction of a price change, and how the midpoint (arc) formula solves this by using average price and quantity as the base for percentage changes. The key insight is that the basic formula's percentage change depends on which point is treated as the 'original' value, causing the same price move to yield different PED values for a rise versus a fall, whereas the midpoint formula produces one consistent value regardless of direction. Contains: text explanation, formula, worked example comparing basic vs midpoint calculations, exam tip, and a common-mistake callout.
The basic PED formula divides the percentage change in quantity demanded by the percentage change in price, using the original price and quantity as the denominator for each percentage change. This works well for small changes, but it creates a problem for large ones: the answer you get depends on whether you treat the change as a price rise or a price fall, because the 'original' value is different in each direction.
For example, a movement from $10 to $20 is a 100% increase (using $10 as the base), but the reverse movement from $20 to $10 is only a 50% decrease (using $20 as the base). Since the size of the price change in percentage terms differs depending on direction, the calculated PED for the exact same pair of points on a demand curve will differ depending on whether the price is said to have risen or fallen. This is a genuine flaw in the basic formula, not just a rounding issue -- and it becomes more serious the larger the price change is.
The midpoint (arc) formula for PED: percentage changes are calculated using the average of the two quantities and the average of the two prices as the base, rather than the original value alone.
By using the average of the two prices and the average of the two quantities as the denominator, the midpoint formula treats a movement between two points symmetrically -- it gives exactly the same PED value whether price is rising or falling between those two points. This makes it far more reliable when a price change is large (e.g. a doubling or halving), which is precisely when the basic formula's directional inconsistency is at its worst.
For small price changes (a few per cent), the basic formula and the midpoint formula give almost identical results, because the original value and the average value are very close together. The midpoint formula only matters -- and is only required -- when the price change being analysed is large.
Comparing the basic formula and the midpoint formula
- Suppose price rises from P_1 = \10P_2 = $20Q_1 = 100Q_2 = 60$ units.
- Basic formula (using original values as the base): %ΔQ = (60-100)/100 × 100 = -40%. %ΔP = (20-10)/10 × 100 = +100%. PED = |-40/100| = 0.4.
- Midpoint formula: average Q = (100+60)/2 = 80; average P = (10+20)/2 = 15. %ΔQ = (60-100)/80 × 100 = -50%. %ΔP = (20-10)/15 × 100 = +66.7%. PED = |-50/66.7| = 0.75.
- Now check the reverse direction with the basic formula, treating $20 as the original price: %ΔQ = (100-60)/60 × 100 = +66.7%. %ΔP = (10-20)/20 × 100 = -50%. PED = |66.7/-50| = 1.33.
- Notice the basic formula gives two different answers (0.4 vs 1.33) for the same two points depending on direction, while the midpoint formula gives a single consistent value (0.75) regardless of which point is called 'first'.
Common mistake: Students often apply the basic PED formula to a large price change (e.g. price doubling) and treat the resulting value as definitive, without recognising that swapping which price is 'original' would change the answer. Always check whether the price change described is large -- if so, use the midpoint formula, and state that you are doing so.
Exam tip: On Paper 2 quantitative questions, if you are given two price-quantity pairs with a substantial gap between them, use the midpoint formula and show both the average P and average Q in your working -- examiners award method marks for correctly identifying and applying the averages, not just for the final PED value.
- Basic PED formula uses the original price/quantity as the base, so it gives different results depending on the direction of change.
- Midpoint formula uses the average of P1 & P2 and average of Q1 & Q2 as the base, giving one consistent PED value regardless of direction.
- Midpoint formula matters most for large price changes; for small changes, basic and midpoint formulas give nearly identical results.
- Midpoint PED = [(Q2-Q1)/((Q2+Q1)/2)] ÷ [(P2-P1)/((P2+P1)/2)].
- Always express PED as a positive value, and show the averages used as working for method marks.
Elastic Demand (PED > 1)
Explains elastic demand (PED > 1), where a percentage change in price produces a proportionally larger percentage change in quantity demanded, typically seen with luxury goods and non-essential items that have close substitutes or absorb a large share of income. The key insight links this responsiveness to total revenue: for elastic goods, raising price cuts total revenue because the fall in quantity outweighs the price rise, so firms selling elastic goods generally cut prices to boost revenue. Contains: text explanation, PED formula, worked example calculating an elastic PED value and its revenue effect, and a common-mistake callout on sign and magnitude.
When demand is elastic, the price elasticity of demand (PED) is greater than 1, meaning quantity demanded changes proportionally more than price. A small percentage change in price triggers a larger percentage change in the quantity that consumers are willing and able to buy. Graphically, an elastic demand curve is relatively flat (though not perfectly horizontal), reflecting how sensitive buyers are to price movements.
Goods and services that tend to exhibit elastic demand share common characteristics: they usually have several close substitutes, are considered luxuries or non-essentials rather than necessities, and often take up a significant proportion of a consumer's income. Examples include branded clothing, international holidays, restaurant dining, and consumer electronics — if the price rises, consumers can relatively easily switch to a substitute, delay the purchase, or simply do without.
PED is conventionally reported as a positive number, even though the underlying calculation yields a negative value because price and quantity demanded move in opposite directions. When |PED| > 1, demand is elastic.
Four factors typically push PED above 1, making demand elastic:
- Availability of substitutes: many close substitutes make it easy for consumers to switch away when price rises.
- Necessity vs luxury: luxuries are more easily postponed or forgone than necessities.
- Proportion of income: when a good takes up a large share of a consumer's budget, price changes are felt strongly, prompting bigger changes in quantity demanded.
- Time period: demand tends to become more elastic over a longer time horizon, as consumers find substitutes or adjust habits (for example, switching to a fuel-efficient car after a sustained rise in petrol prices, even though demand for petrol is inelastic in the short run).
For elastic goods (PED > 1), a rise in price causes total revenue to fall, and a fall in price causes total revenue to rise. This is because the proportional change in quantity demanded outweighs the proportional change in price, so the effect on revenue is dominated by the quantity change. This is why firms selling luxury or highly substitutable goods often use price cuts, sales, or discounts to increase total revenue.
Calculating PED for a luxury good
- A restaurant raises the price of a premium dining experience from 100, a 25% increase.
- Quantity demanded falls from 200 meals per week to 120 meals per week, a 40% decrease.
- PED = %ΔQd ÷ %ΔP = (−40%) ÷ (25%) = −1.6, reported as PED = 1.6.
- Since 1.6 > 1, demand is elastic: quantity demanded fell proportionally more than price rose.
- Check the revenue effect: original TR = 16,000; new TR = 12,000. Total revenue fell, confirming the expected relationship for elastic demand — the price rise was not a good pricing strategy for maximizing revenue.
Common mistake: Students sometimes think a larger PED number automatically means the good is more of a 'necessity' or assume elastic demand only applies to expensive items. In fact, elasticity depends on substitutability, the proportion of income spent, and time period — not price level alone. A cheap but highly substitutable snack brand can have PED > 1, while an expensive good with no substitutes (some prescription medicines) can be inelastic.
- Elastic demand: PED > 1 — quantity demanded changes proportionally more than price.
- Typical of luxury goods, non-essentials, and goods with close substitutes or a high share of income spent.
- PED is always expressed as a positive value despite the negative price–quantity relationship.
- If PED > 1, a price increase causes total revenue to fall, and a price decrease causes total revenue to rise.
- Demand tends to become more elastic in the long run as consumers find substitutes or adjust behaviour.