Difficulty: Introductory | Prerequisites: Basic algebra; familiarity with supply and demand graphs.
Price elasticity of demand sits at the centre of how economists think about consumer behaviour. It quantifies how sensitive the quantity demanded of a good is to a change in its own price, and it underpins everything from tax incidence analysis to pricing strategy. You need a solid handle on elasticity before tackling topics such as consumer surplus, monopoly pricing, and welfare analysis later in the course. If the only thing you remember from this unit is that "elastic" means buyers are price-sensitive and "inelastic" means they are not, you are already halfway there.
Price elasticity of demand measures the percentage change in quantity demanded divided by the percentage change in price. Along a straight-line demand curve, elasticity varies from elastic at the top to inelastic at the bottom, with unit elasticity at the midpoint. Economists use elasticity rather than slope because elasticity is unit-free and allows comparison across different goods and markets.
Price elasticity of demand (PED)
The percentage change in quantity demanded divided by the percentage change in price. In simple terms, it tells you how much buyers pull back (or pile in) when the price moves.
Elastic demand
A PED with an absolute value greater than 1. Quantity responds more than proportionally to a price change. Think of it as buyers being very sensitive to price.
Inelastic demand
A PED with an absolute value less than 1. Quantity responds less than proportionally to a price change. In simple terms, buyers mostly keep buying even when the price goes up.
Unit elastic demand
A PED with an absolute value of exactly 1. The percentage change in quantity exactly matches the percentage change in price. Total expenditure is at its maximum here.
Total expenditure (total revenue from the buyer's side)
Price multiplied by quantity (P × Q). Whether a price increase raises or lowers total expenditure depends entirely on whether demand is elastic or inelastic at that point.
Demand curve slope
The ratio ΔP/ΔQ (or ΔQ/ΔP depending on convention). The slope is constant along a linear demand curve, but elasticity is not, which is one of the key insights of this topic.
A linear demand curve such as Q = 100 – 50P has a constant slope, but elasticity changes at every point.
At the top of the curve (low Q, high P), demand is elastic (|PED| > 1). A small percentage price cut leads to a large percentage increase in quantity.
At the bottom of the curve (high Q, low P), demand is inelastic (|PED| < 1). Price changes barely move the quantity demanded in percentage terms.
The midpoint of the curve is the unit-elastic point (|PED| = 1).
The formula for point elasticity is: PED = (dQ/dP) × (P/Q).
On a linear curve, dQ/dP is constant. But the ratio P/Q changes as you move along the curve.
Near the vertical intercept, P is large and Q is small, so P/Q is large and |PED| > 1.
Near the horizontal intercept, P is small and Q is large, so P/Q is small and |PED| < 1.
This is why a constant slope does not mean constant elasticity.
Total expenditure = P × Q.
When demand is elastic, a price decrease raises total expenditure (the quantity gain more than offsets the price drop).
When demand is inelastic, a price decrease lowers total expenditure (the price drop outweighs the quantity gain).
Total expenditure is maximised at the unit-elastic point.
For the curve Q = 100 – 50P, the unit-elastic midpoint is at P = 1 and Q = 50, giving maximum expenditure of 50.
The slope of a demand curve is measured in specific units (e.g. "kilograms per pound sterling"). Change the unit of measurement and the slope changes.
Elasticity is a pure number with no units. It measures percentage changes, so it allows comparison across goods, markets, and countries.
Example: Comparing the price sensitivity of demand for bread in the UK (measured in loaves and pounds) versus rice in Japan (measured in kilograms and yen) is meaningless using slopes. Elasticity makes the comparison straightforward.
Slope also does not distinguish between a movement from £1 to £2 and a movement from £100 to £101; both are a £1 change. Elasticity captures that the first is a 100% increase while the second is roughly a 1% increase.
If a consumer spends all income on two goods and demand for one good is elastic, a rise in that good's price increases spending on it less than proportionally, but the consumer's budget is now squeezed.
Whether the consumer buys more or less of the other good depends on the interplay between the substitution effect and the income effect.
A common exam trap: the statement "if demand for good A is elastic, a price rise for A necessarily means less spending on good B" is not automatically true. It depends on the magnitudes of the effects.
\text{PED} = \frac{\%\Delta Q}{\%\Delta P} = \frac{dQ}{dP} \times \frac{P}{Q}\text{Total Expenditure} = P \times QFor Q = 100 – 50P:
Slope: dQ/dP = –50 (constant)
Midpoint: P = 1, Q = 50
Maximum total expenditure: 1 × 50 = 50
For P = 27 – Q²:
Total expenditure: TE = P × Q = 27Q – Q³
Maximise by setting dTE/dQ = 0: 27 – 3Q² = 0, so Q = 3
Corresponding price: P = 27 – 9 = 18
Maximum total expenditure: 18 × 3 = 54
Firms use price elasticity to set prices. If demand for a product is inelastic (think insulin for diabetics or petrol in the short run), a price increase raises total revenue. If demand is elastic (budget airlines, streaming subscriptions with many competitors), cutting the price draws enough new buyers to more than compensate. Governments use elasticity estimates to predict how much revenue a tax will raise and how much of the tax burden falls on consumers versus producers.
Students often think a steeper demand curve means more inelastic demand. Not necessarily: steepness depends on the axis scales and units. Elasticity, being unit-free, is the correct measure.
Students confuse "elastic demand" with "the demand curve shifts." Elasticity describes movement along a curve, not a shift of the entire curve.
A common error is assuming elasticity is constant along a linear demand curve. The slope is constant; elasticity is not.
Students sometimes believe that if demand is elastic, a price rise always reduces total expenditure. This is correct for total expenditure on that good, but the effect on spending on other goods depends on additional factors (income and substitution effects).
⚠️ Expect to be asked to identify elastic, inelastic, and unit-elastic regions on a linear demand curve. Know where each region falls without calculation.
⚠️ The total-expenditure test is a favourite exam shortcut: if demand is elastic, a price drop raises total expenditure; if inelastic, it lowers it.
⚠️ "Why elasticity instead of slope?" is a common short-answer question. Hit these three points: unit-free, comparable across goods, captures proportional change.
⚠️ True/false questions about elastic demand and budget constraints are tricky. Read the statement carefully before assuming the conjecture is true.
True or false: Elasticity is constant along a linear demand curve.
Fill in the blank: Total expenditure is maximised at the ____-elastic point on a demand curve.
True or false: A demand curve with a slope of –2 is always more elastic than one with a slope of –1.
Fill in the blank: Economists prefer elasticity over slope because elasticity is ____-free.
True or false: When demand is elastic, raising the price increases total expenditure.
Answers: 1. False. 2. Unit. 3. False. 4. Unit. 5. False.
Q: Consider the demand curve Q = 100 – 50P. At which point is total expenditure maximised, and why?
A: At the midpoint, where P = 1 and Q = 50. This is the unit-elastic point. Below this price, demand is inelastic, so a price cut reduces total expenditure. Above this price, demand is elastic, so a price cut raises total expenditure. The maximum lies at the boundary between the two regions.
Q: Why do economists use elasticity rather than slope to measure responsiveness of demand to price?
A: Slope depends on the units of measurement for price and quantity. Change from litres to gallons, or from dollars to euros, and the slope changes even though nothing has happened to the underlying demand relationship. Elasticity is a ratio of percentages, making it unit-free. This allows comparison across entirely different goods and markets.
Q: True or false and explain: Mike spends all income on tennis balls and basketball tickets. His demand for tennis balls is elastic. When the price of tennis balls rises, he necessarily consumes fewer basketball tickets.
A: The conjecture is not necessarily true. If demand for tennis balls is elastic, a price increase causes a more-than-proportional drop in quantity, meaning Mike's total spending on tennis balls actually falls. That would leave more income available for basketball tickets, not less. The statement conflates the direction of the price change with its effect on total expenditure. The correct reasoning: elastic demand + price rise = lower spending on that good = potentially more income available for the other good.
Q: What price maximises total expenditure along the demand curve P = 27 – Q²?
A: Total expenditure = P × Q = 27Q – Q³. To maximise, take the derivative with respect to Q and set it to zero: dTE/dQ = 27 – 3Q² = 0, so Q = 3. The corresponding price is P = 27 – 9 = 18. Maximum total expenditure is 54.
This material connects directly to consumer surplus and producer surplus: the size of each depends on elasticity. It also underpins tax incidence analysis, where the more inelastic side of the market bears more of the tax burden. Later in the course, monopoly pricing relies on the inverse-elasticity rule (the Lerner index), so a firm grasp of PED is essential groundwork.
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