2.5 Elasticities of demand

Elasticity measures percentage responsiveness.

Elasticity compares a percentage change in one variable with a percentage change in another, so it is unit-free and comparable across scales.

Example

A 5% price rise causing a 10% fall in quantity gives |PED|=2, indicating elastic demand.

Write the percentage changes first, then interpret magnitude and sign in the decision context.

Elasticity is not the same as slope; percentage bases and the chosen interval matter.

Relative elasticity compares percentage quantity responses for a given percentage change in the causal variable. On demand diagrams drawn with the same axis scales and from a common point, a flatter curve is relatively more price elastic and a steeper curve relatively less elastic—but elasticity is not identical to visual slope, so calculate when data are provided.

$PED=(\%\Delta Q_d)/(\%\Delta P)$. It is normally negative because price and quantity demanded move oppositely; many decisions use the absolute magnitude while retaining the sign when asked.

Calculate each percentage change using the base specified by the data or examination convention, divide, and classify: $|PED|<1$ inelastic, $=1$ unit elastic, and $>1$ elastic. The theoretical magnitude ranges from zero to infinity.

Example

If price rises from $10 to$11, the percentage price change is $10\%$. If quantity demanded falls from 200 to 170, the percentage quantity change is $-15\%$. Thus $PED=-15\%/10\%=-1.5$, so demand is elastic.

State the sign convention and calculation base. Midpoint reasoning appears only in local HL evidence and is not inserted into this shared SL/HL card unless the question explicitly supplies that convention.

PED is measured over a stated price interval and market definition; it can change at another point on the same curve.

PED predicts how a price change affects total revenue.

When demand is elastic, quantity changes proportionally more than price; when inelastic, price changes dominate revenue.

Example

A 10% price rise with a 20% quantity fall reduces revenue because the 2× quantity response outweighs price.

Compare percentage changes rather than assuming every price rise raises revenue.

The unit-elastic case leaves revenue approximately unchanged only under the stated local conditions.

Classification and revenue map using $|PED|$: perfectly inelastic $=0$ (vertical), inelastic $0<|PED|<1$, unit elastic $=1$, elastic $|PED|>1$, and perfectly elastic tends to infinity (horizontal). If demand is elastic, price and total revenue move in opposite directions; if inelastic, they move together; at unit elasticity, a small price change leaves total revenue unchanged.

Determinants of PED explain why buyers respond differently.

Substitutes, necessity, habit, budget share and time affect how easily consumers can change quantity demanded after a price change.

Example

A branded medicine may have inelastic short-run demand but become more elastic when substitutes or time to adjust increase.

Name the determinant and the direction of its effect before assigning an elasticity.

These are tendencies, not universal values; market segment and time horizon matter.

Four syllabus determinants: more and closer substitutes make demand more elastic; greater necessity makes it more inelastic; a larger proportion of income makes it more elastic; and more adjustment time usually makes it more elastic. Firms use PED for pricing and revenue forecasts, while governments use it to anticipate tax effects on consumption and revenue. Apply tendencies to a defined market and time period.

Income elasticity classifies demand across the income cycle.

YED=% change in quantity demanded/% change in income; positive values indicate normal goods and negative values inferior goods.

Example

If income rises 8% and demand for restaurant meals rises 12%, YED=1.5, a normal income-elastic good.

State the sign and magnitude, then connect it to forecasting or consumption patterns.

YED can differ across households and income ranges; it is not a permanent label for a product.

YED classes: $YED<0$ inferior; $0<YED<1$ normal and income-inelastic, commonly necessities; $YED>1$ normal and income-elastic, commonly services or luxuries. An Engel curve plots income vertically or horizontally as labelled against quantity demanded: necessities rise less than proportionately, luxuries more than proportionately, and inferior-good demand falls over the relevant income range. Rearrange the formula to find a missing percentage change.