2.2 Price elasticity, income elasticity and cross elasticity of demand

Learning objectives

Elasticity measures how responsive demand is to a change in another variable, using percentage changes so that the result has no units.

Measure	What responds?	What changes?	Relationship measured
PED	Quantity demanded of good A	Price of good A	Response to its own price
YED	Demand for good A	Consumer income	Response to income
XED	Demand for good A	Price of good B	Response to another good's price

For XED, the denominator is the percentage change in the price of the other good, not its quantity. Elasticity is also not slope alone: it compares proportional changes relative to their starting values.

PED=\frac{%\Delta Q_d}{%\Delta P}

YED=\frac{%\Delta Q_d}{%\Delta Y}

XED_{A,B}=\frac{%\Delta Q_{d,A}}{%\Delta P_B}

If A's price rises 10% and its quantity demanded falls 20%, $PED=-20/10=-2$ . If income rises 5% and demand rises 2%, $YED=2/5=+0.4$ . If B's price rises 8% and demand for A rises 4%, $XED_{A,B}=4/8=+0.5$ .

Use percentage changes in both numerator and denominator, keep the sign, and label which good changes in XED. A coefficient is unit-free; it is not measured in dollars, units or percent.

An elasticity coefficient contains two kinds of information: its sign shows the direction of the relationship, while its absolute size shows how large the percentage response is relative to the percentage change.

Measure	Sign meaning	Magnitude meaning
PED	Usually negative because price and quantity demanded move oppositely	$\|PED\|>1$ elastic; $\|PED\|<1$ inelastic
YED	Positive: normal good; negative: inferior good	$YED>1$ income-elastic normal/luxury response; $0<YED<1$ income-inelastic normal/necessity response
XED	Positive: substitutes; negative: complements; near zero: weakly related	Larger absolute value means a stronger demand response to the related price

$XED=+0.6$ indicates substitutes with a moderate positive response. $YED=-1.2$ identifies an inferior good whose demand changes more than proportionally in the opposite direction to income.

$-2$ is more responsive than $+1$ because $|-2|>|+1|$ . Compare absolute values for magnitude, but never discard the sign when classifying YED or XED relationships.

Description	Absolute coefficient	Percentage-response meaning	PED limiting shape
Perfectly inelastic	$0$	Quantity demanded does not change	Vertical
(Highly) inelastic	Between $0$ and $1$	Quantity changes proportionally less	Steepness alone is not a reliable test
Unitary elastic	$1$	Quantity changes by the same percentage	Depends on location/curve
(Highly) elastic	Greater than $1$	Quantity changes proportionally more	Steepness alone is not a reliable test
Perfectly elastic	$\infty$	Any quantity can be demanded at one price; a rise above it reduces demand to zero	Horizontal

A PED of $-1.5$ is elastic, $-1.0$ is unitary and $-0.4$ is inelastic because PED categories use absolute magnitude. The description applies at the relevant point or range, not automatically to an entire market curve.

Elastic does not mean unlimited response; only perfectly elastic is the limiting case. A curve's visual steepness cannot by itself identify elasticity unless the scales and location are known.

A straight-line demand curve has constant slope but changing PED because elasticity compares percentage changes relative to the price and quantity at each position.

Position on a standard straight-line demand curve	Relative bases	PED
Near the price-axis intercept	Price high, quantity low	Highly elastic; approaches $\infty$ at the intercept
Midpoint	Price and quantity proportions balance	Unitary, $\|PED\|=1$
Near the quantity-axis intercept	Price low, quantity high	Highly inelastic; approaches $0$ at the intercept

Near the price intercept, a given quantity change is large relative to the small starting quantity, while the corresponding price change is small relative to the high starting price. Near the quantity intercept, the reverse is true.

Constant slope does not mean constant PED. The previous card's example is corrected here: PED is more elastic near the price intercept, not near the quantity intercept.

Elasticity	Main factors	Why responsiveness changes
PED	Number and closeness of substitutes; necessity or luxury; share of income; time to adjust; habit; breadth of market definition	Easier switching, larger budget effects and more adjustment time usually increase $\|PED\|$
YED	Whether the good is normal or inferior; necessity or luxury; consumer income level; time to adjust spending	The sign follows normal/inferior status, while income importance and stage of consumption affect proportional response
XED	Whether goods are substitutes or complements; closeness of the relationship; availability of alternatives; time to switch; market definition	Closer substitutes or complements usually produce a larger absolute cross-price response

Time is especially important when behaviour or durable assets must change. Petrol demand may be inelastic in the short run when commuting options are fixed, but more elastic later as households change vehicles, routes or location.

These are tendencies, not guarantees. A product can be a necessity yet have available substitutes, and XED depends on the particular pair of goods rather than a property of one good alone.

TE=P\times Q

PED magnitude	If price rises	If price falls	Why
Elastic, $\|PED\|>1$	TE falls	TE rises	Quantity changes proportionally more than price
Unitary, $\|PED\|=1$	TE approximately unchanged	TE approximately unchanged	Proportional changes offset
Inelastic, $\|PED\|<1$	TE rises	TE falls	Quantity changes proportionally less than price

A 10% price rise with a 20% quantity fall lowers expenditure because demand is elastic. A 10% price rise with only a 5% quantity fall raises expenditure because demand is inelastic.

Total expenditure by consumers equals sellers' total revenue before considering other receipts, but higher revenue does not necessarily mean higher profit because costs may also change.

Evidence	Decision use	Conditional interpretation
PED	Pricing, sales forecasts, tax effects and expenditure burden	Inelastic demand makes quantity less responsive, but revenue, welfare and profit effects still depend on costs and context
YED	Forecast demand through growth or recession; plan capacity and product mix	Positive high YED makes demand growth-sensitive; negative YED can make demand rise as income falls
XED	Identify substitutes/complements; anticipate rival price changes; consider bundles or competition	Positive XED signals substitution, negative XED complementarity, and magnitude indicates strength

A bus operator considering a fare rise uses PED to estimate the passenger and revenue response. A luxury retailer uses YED when planning for an expansion or recession. An electric-car producer uses XED to assess changes in petrol-car prices or charging costs.

Elasticity is an estimate based on a market definition, time period and past or expected behaviour. It does not guarantee profit or policy success: costs, capacity, competitors, distributional effects and simultaneous changes may alter the outcome.

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—2.3 Price elasticity of supplyRead

2.2 Price elasticity, income elasticity and cross elasticity of demand

Learning objectives

PED, YED and XED measure different demand responses

Calculate PED, YED and XED

Interpret elasticity signs and magnitudes

From perfectly inelastic to perfectly elastic

Why PED changes along straight-line demand

What affects PED, YED and XED?

PED and total expenditure

Use elasticity in business and policy decisions

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