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Knowing that demand slopes downward tells you the direction a price change moves quantity; price elasticity of demand tells you the magnitude. That distinction — direction versus magnitude — is what elevates microeconomics from description to genuine analysis. PED is among the most heavily examined ideas at A-Level because it unlocks two of the subject's most important applications: how firms set prices to maximise revenue, and how the burden of an indirect tax is shared between producers and consumers. This lesson develops the formula, the full range of elasticity values with diagrams, the determinants, the crucial PED–revenue relationship, and the synoptic links to tax incidence.
This lesson maps to AQA 7136 section 4.1.3 — elasticities of demand (price elasticity of demand). It is examined in Paper 1 (Markets and market failure), frequently as a calculation within a data-response, and in 25-mark essays on pricing or taxation. It is strongly synoptic: PED determines the incidence of an indirect tax (a later micro lesson and a Paper 1/3 staple), drives firms' pricing and revenue decisions in the theory of the firm, and underlies the analysis of commodity-price volatility and government revenue in Paper 2 and Paper 3. All four AOs apply, with AO2 (selecting the right elasticity for the context) and AO4 (recognising that conclusions "depend on" the elasticity) carrying heavy weight.
Key Definition: Price elasticity of demand (PED) measures the responsiveness of the quantity demanded of a good to a change in its own price, ceteris paribus.
Alfred Marshall (1890) introduced elasticity precisely because the slope of a demand curve, expressed in £ and units, cannot be compared across goods measured in different units. Elasticity solves this by using percentage changes, which are unit-free and therefore comparable. Consider why this matters: the slope of the demand curve for cars (measured in thousands of pounds per car) and the slope for apples (measured in pence per apple) are not remotely comparable as raw numbers, yet a percentage measure lets us say meaningfully that "a 10% price rise reduces quantity demanded by 4% for cars but by 25% for apples," and hence that demand for apples is the more elastic. This unit-free quality is what makes elasticity one of the most portable and widely used tools in the whole subject — it travels across goods, markets and even countries, allowing genuine comparison where raw slopes cannot.
PED is the percentage change in quantity demanded divided by the percentage change in price:
PED=%ΔP%ΔQd
Because of the law of demand (price and quantity move in opposite directions), PED is always negative. By convention we usually quote the absolute value (its size, ignoring the sign) when classifying demand as elastic or inelastic — but you should still state that the true value is negative.
Suppose a coffee shop raises the price of a latte from £3.00 to £3.30 and daily sales fall from 200 to 180.
Step 1 — percentage change in price.
%ΔP=3.003.30−3.00×100=+10%
Step 2 — percentage change in quantity demanded.
%ΔQd=200180−200×100=−10%
Step 3 — apply the formula.
PED=+10%−10%=−1.0
The absolute value is 1.0, so demand is unit elastic at this point: quantity demanded changed in exactly the same proportion as price.
Exam Tip: Always show the formula, substitute the numbers, and interpret the result. Examiners award method marks even if the arithmetic slips, and a bare number with no interpretation ("elastic" / "inelastic") leaves marks on the table.
| PED (absolute) | Description | Meaning | Curve shape |
|---|---|---|---|
| 0 | Perfectly inelastic | Quantity demanded does not change at all | Vertical |
| 0 < PED < 1 | Inelastic | Quantity changes proportionately less than price | Steep |
| 1 | Unit elastic | Quantity changes in the same proportion as price | Rectangular hyperbola |
| > 1 | Elastic | Quantity changes proportionately more than price | Shallow/flat |
| ∞ | Perfectly elastic | Any price rise sends quantity demanded to zero | Horizontal |
A subtle but examinable point: along a single straight-line demand curve, PED is not constant. It is elastic near the top (high price, low quantity), unit elastic at the midpoint, and inelastic near the bottom (low price, high quantity). This is because elasticity depends on the ratio P/Q at each point, not just the constant slope.
Exam Tip: A steeper curve is broadly more inelastic when comparing curves on the same axes, but PED is a percentage measure that varies point-to-point. Avoid the lazy claim that "steep = inelastic everywhere."
The limiting cases are worth visualising because they appear in theory and, approximately, in reality. A perfectly inelastic demand curve (PED = 0) is vertical: the same quantity is bought whatever the price, because there is no substitute and the good is an absolute necessity in the relevant range — a life-saving medicine to the patient who needs it is the textbook illustration. A perfectly elastic demand curve (PED = ∞) is horizontal: at the going price consumers will buy any quantity, but the smallest price rise sends quantity demanded to zero because perfect substitutes are instantly available. The perfectly elastic case is the model of demand facing a single firm in perfect competition, where the firm is a price-taker: charge a penny more than the market price and you sell nothing, because identical output is available elsewhere. Real demand curves lie between these extremes, but the extremes anchor the scale and sharpen intuition: the closer a good is to "no substitutes and essential," the nearer demand approaches vertical; the closer it is to "perfect substitutes," the nearer it approaches horizontal.
The single most important determinant. Many close substitutes → consumers switch easily → elastic. Few or no substitutes → inelastic. A particular chocolate brand has many rivals (elastic); insulin for a diabetic has no close substitute (highly inelastic).
Necessities (bread, water, electricity) tend to be inelastic — they must be bought whatever the price. Luxuries (foreign holidays, designer clothing) tend to be elastic — they can be foregone.
Goods absorbing a large share of income (housing, cars) tend to be more elastic, because a price change has a big budget impact. Trivial-cost items (salt, a box of matches) are inelastic — the price barely registers.
Demand is usually more inelastic in the short run and more elastic in the long run, because over time consumers find substitutes and change habits. When petrol prices rise, demand barely moves at first (people must commute) but falls more over years as drivers switch to efficient or electric vehicles and public transport. This time dimension is one of the most important and most often neglected points in PED analysis: a firm or government observing only the short-run response can badly misjudge the eventual effect of a price change. A price rise that looks safely revenue-raising because short-run demand is inelastic may, over several years, prompt enough substitution to turn demand elastic and erode the customer base or tax base. Whenever an exam scenario involves a sustained price change, it is almost always worth distinguishing the short-run from the long-run elasticity explicitly — it is a reliable source of evaluative (AO4) credit.
Habit-forming goods (tobacco, alcohol) tend to be inelastic — consumers keep buying despite price rises. Governments exploit this when setting tobacco duty: high taxes raise substantial revenue precisely because quantity demanded falls only modestly.
Strong brand attachment makes demand more inelastic, because loyal consumers resist switching even when the price rises — a key reason firms invest heavily in branding. Indeed, much of marketing can be understood as an attempt to do two things to the demand curve at once: shift it right (more demand at every price) and make it steeper/more inelastic (so the firm can raise price with less loss of volume). A successful brand both sells more and gains pricing power, which is why advertising and brand-building are so valuable to firms.
In practice these determinants reinforce or offset one another, and the strongest analysis recognises that PED is the net result of several pulls. A good with many close substitutes that also takes a large share of income — a foreign package holiday, say — is doubly elastic. A good with no substitutes, that is habit-forming, takes a tiny share of income, and is a necessity — a prescription medicine for a chronic condition — is multiply inelastic. The dominant determinant is almost always the availability of substitutes, but how you define the market changes the answer: demand for "petrol from a particular station" is far more elastic than demand for "petrol" in general, because the narrower the definition the more substitutes exist. When an exam scenario asks you to judge whether demand is elastic or inelastic, identify the market definition first, then run through the determinants and state which dominates — that disciplined approach earns AO2 application marks.
This is where A-Level decisively goes beyond GCSE. Total revenue (TR) = price × quantity (P × Q). When price changes, P and Q move in opposite directions, so what happens to TR depends entirely on which effect is larger — and that is exactly what PED measures.
| Demand | Price rises | Price falls |
|---|---|---|
| Elastic (PED > 1) | TR falls (Q falls proportionately more) | TR rises (Q rises proportionately more) |
| Inelastic (PED < 1) | TR rises (Q falls proportionately less) | TR falls (Q rises proportionately less) |
| Unit elastic (PED = 1) | TR unchanged | TR unchanged |
The fact that PED varies along a straight-line demand curve has a striking revenue implication. Recall that demand is elastic in the upper section, unit elastic at the midpoint, and inelastic in the lower section. Now trace total revenue as price falls from the top of the curve downward. In the elastic upper region, each price cut raises revenue (quantity rises proportionately more than price falls). At the midpoint, where PED = 1, revenue is at its maximum — a further price cut neither raises nor lowers it at the margin. In the inelastic lower region, each further price cut reduces revenue (quantity now rises proportionately less than price falls). So total revenue rises, peaks at the unit-elastic midpoint, and then falls — a smooth hump. The practical lesson for a firm pursuing revenue maximisation is therefore precise: set price where PED = 1. (A firm pursuing profit maximisation will generally choose a different, higher price, because it must also account for costs — profit maximisation occurs where marginal revenue equals marginal cost, which lies in the elastic region. This is why the revenue-maximising and profit-maximising prices differ, a distinction developed fully in the theory of the firm.) Being able to connect the position on the demand curve, the value of PED, and the behaviour of total revenue in a single chain is exactly the integrated understanding that top answers display.
Stay with the latte. Before the price change, TR = £3.00 × 200 = £600. After, TR = £3.30 × 180 = £594. Revenue is essentially unchanged (the tiny £6 fall reflects rounding around unit elasticity) — exactly what we expect when PED ≈ 1. Now contrast two firms:
Exam Tip: In any PED question, drive the analysis through to total revenue: "Because demand is inelastic (PED < 1), a price increase raises total revenue, since the proportionate fall in quantity demanded is smaller than the proportionate price rise." That sentence is worth real AO3 marks.
PED is decisive for who actually bears an indirect tax — the tax incidence. An indirect (per-unit) tax shifts the supply curve vertically upward by the tax per unit, because at every quantity producers now need the old price plus the tax to be willing to supply. The new equilibrium has a higher price and a lower quantity, but — crucially — the price paid by consumers rises by less than the full tax. The gap between the new consumer price and the original price is the consumer's share of the tax; the rest, the difference between the original price and the (lower) price producers keep after handing over the tax, is the producer's share. How that total tax wedge splits between the two sides is governed by PED.
flowchart TD
A["Government imposes indirect tax (supply shifts up by the tax)"] --> B{"How price-responsive is demand?"}
B -->|Inelastic demand| C["Most of the tax passed to consumers (high consumer incidence) + large tax revenue"]
B -->|Elastic demand| D["Most of the tax absorbed by producers (high producer incidence) + smaller revenue but bigger fall in quantity"]
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