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.

Elasticity varies along a straight-line demand curve.

Slope is constant on a straight line but elasticity uses relative percentage changes, so it is more elastic near the price intercept and less elastic near the quantity intercept.

Example

The same one-unit price movement can represent a large percentage quantity change at one point and a small one elsewhere.

Read the point on the curve before predicting revenue or responsiveness.

Do not infer constant elasticity from a constant slope.

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.

Demand for primary commodities is generally more price inelastic than demand for manufactured products: a percentage price change tends to cause a smaller percentage change in commodity quantity demanded.

Primary inputs may be necessary for production, form a small share of the final product's price and have few close short-run substitutes. Manufactured products are often more differentiated and face more brands, models or alternative goods, making substitution easier.

Example

A food manufacturer may keep buying nearly the same quantity of a basic grain after a moderate price rise because reformulating production takes time, while consumers can switch more readily between competing manufactured snack brands.

This is a general tendency, not a rule for every product. Market definition, available substitutes, income share and time can make a particular commodity elastic or a manufactured good inelastic.

Do not infer export-revenue volatility without separately analysing supply shifts, PED and the percentage price and quantity changes.

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.

YED helps firms plan for changing incomes.

Firms use income responsiveness to anticipate which products expand or contract during booms and downturns, alongside costs and competition.

Example

A premium travel firm with high positive YED may see demand fall faster than income during a recession.

Combine the elasticity estimate with the expected income change and the firm’s product mix.

Forecasting from YED assumes other major determinants do not shift at the same time.

YED also explains sectoral change: as average incomes rise, demand tends to grow less than proportionately for necessities and more than proportionately for income-elastic services and luxuries, shifting employment and output toward those sectors. Firms combine estimated YED with an income forecast to plan capacity, product mix and risk; coefficients can change across income ranges and over time.