2.2 Price elasticity, income elasticity and cross elasticity of demand

Price elasticity of demand (PED) measures quantity demanded’s response to price; income elasticity (YED) measures response to income; cross elasticity (XED) measures response to another good’s price.

PED compares a good with its own price, YED with consumer income and XED with a related good. Keep the numerator and denominator matched to the concept.

A fall in the price of a product may change its quantity demanded (PED), while a rise in income may increase demand for a normal good (YED).

Elasticity is not a slope alone: it is a percentage response relative to a percentage change.

PED = % change in quantity demanded / % change in price; YED = % change in quantity demanded / % change in income; XED = % change in demand for A / % change in price of B.

Use a consistent percentage-change method, state the sign and interpret the magnitude. For a finite interval, the midpoint method may avoid choosing one endpoint as the base.

If price rises 10% and quantity demanded falls 20%, PED = −2. A 5% income rise that increases demand 2% gives YED = 0.4.

Do not divide an absolute quantity change by a percentage price change; both parts must be percentage changes.

The sign identifies the direction of the relationship: PED is usually negative, YED is positive for normal goods and negative for inferior goods, and XED is positive for substitutes and negative for complements.

The absolute size measures responsiveness: values above one are elastic, below one inelastic and equal to one unitary. Sign and magnitude must both be reported.

XED = +0.6 suggests substitutes but a relatively weak response; YED = −1.2 suggests an inferior good with more-than-proportional fall in demand as income rises.

A coefficient of −2 is not “less elastic” than +1 because of its sign; compare absolute values for responsiveness.

Perfectly elastic demand has an infinitesimal price change causing an enormous quantity response; perfectly inelastic demand has zero quantity response. Elastic, unitary and inelastic lie between these extremes according to |coefficient| greater than, equal to or less than one.

The label applies to the relevant section or point of the curve, not automatically to the whole market. Revenue implications depend on which side of unit elasticity demand lies.

A PED of −1.5 is elastic; −1.0 is unitary; −0.4 is inelastic. A vertical demand curve is perfectly inelastic in the diagram.

“Elastic” does not mean quantity changes without limit; it means the percentage response is greater than the percentage price change.

Even though the slope of a straight-line demand curve is constant, PED changes along it because elasticity uses percentage changes relative to the current price and quantity.

Near the high-price/low-quantity end, a small quantity change is large relative to quantity, so demand is more elastic. Near the low-price/high-quantity end, it is more inelastic; the midpoint is unitary in the standard linear case.

Moving the same small amount along a linear demand curve can produce a larger percentage quantity response near the quantity intercept than near the price intercept.

Constant slope does not mean constant PED; slope and elasticity are different measures.

PED tends to be larger when close substitutes exist, the good is a luxury rather than a necessity, consumers have time to adjust, or the good takes a large share of income. YED and XED have their own category and relationship determinants.

These are tendencies, not automatic results: brand loyalty, habit, information and market definition can change the response.

Petrol may be inelastic in the short run when commuting alternatives are limited but more elastic in the long run as people change cars or routes.

Do not explain every elasticity solely by “necessity”; time horizon and available substitutes may dominate.

Total expenditure is price multiplied by quantity bought. If demand is elastic, a price rise reduces total expenditure because quantity falls proportionally more; if demand is inelastic, total expenditure rises.

With unitary elasticity, the percentage price and quantity changes offset and total expenditure is approximately unchanged. The result applies over the relevant section and direction of movement.

A 10% price rise with a 20% quantity fall lowers expenditure; a 10% price rise with only a 5% quantity fall raises it.

Do not decide from the price change alone: the demand response and the starting price/quantity determine expenditure.

PED informs pricing and total expenditure; YED helps forecast demand as incomes change; XED indicates how a rival or complement’s price may affect demand.

Use the sign and magnitude with the decision’s objective. A firm seeking revenue may raise price when demand is inelastic, while a government assessing a tax or subsidy must consider related goods and income effects.

A luxury retailer with positive YED may plan for stronger sales in an expansion; a bus operator may find a fare rise raises revenue only if demand is sufficiently inelastic.

Elasticity gives a conditional forecast, not a guaranteed profit result: costs, competition and capacity also matter.