Business Economics · Consumer demand and behaviour

Price, Income and Cross Elasticity of Demand Explained

Updated 11 October 2026 · Fact-checked

Elasticity of demand measures how much quantity demanded changes in percentage terms when price, income or another good's price changes by one percent. Divide the % change in quantity demanded by the % change in the driver. The sign and size tell you the good type and the effect on revenue.

Understand Price, Income and Cross Elasticity of Demand

Elasticity answers one question: how strongly do buyers react? The slope of a demand curve depends on units, so it is a poor measure. Elasticity uses percentage changes, so it has no units and you can compare goods.

Price elasticity of demand (PED) is the % change in quantity demanded divided by the % change in the good's own price. Because demand slopes downward, PED is normally negative. Many texts quote the absolute value. State which convention you use. If |PED| > 1, demand is elastic. If |PED| < 1, it is inelastic. If |PED| = 1, it is unit elastic.

Elasticity links to revenue. Total revenue = price × quantity. If demand is elastic, a price rise cuts quantity by a larger percentage, so revenue falls. If demand is inelastic, a price rise increases revenue. At unit elasticity, revenue does not change. Price cuts work the other way round.

Income elasticity of demand (YED) is the % change in quantity demanded divided by the % change in consumer income. A positive YED means a normal good. A negative YED means an inferior good. Among normal goods, YED > 1 marks a luxury (necessity-type goods have YED between 0 and 1).

Cross elasticity of demand (XED) is the % change in quantity demanded of good A divided by the % change in the price of good B. Positive XED means substitutes. Negative XED means complements. Near zero means the goods are unrelated. Here the price that changes belongs to the other good.

Key rules to remember

Price elasticity of demand (point or simple form): PED = (%ΔQ) ÷ (%ΔP) = (ΔQ ÷ Q) ÷ (ΔP ÷ P); Normally negative. For a linear demand curve, the value changes along the curve.
Arc (midpoint) PED: PED = [(Q₂ − Q₁) ÷ ((Q₁ + Q₂) ÷ 2)] ÷ [(P₂ − P₁) ÷ ((P₁ + P₂) ÷ 2)]; Gives the same answer for a rise or a fall between two points. Use it when the question says midpoint or arc.
Point PED from a demand function: PED = (dQ/dP) × (P ÷ Q); For linear Q = a − bP, dQ/dP = −b.
Income elasticity of demand: YED = (%ΔQ) ÷ (%ΔY); YED > 1 luxury; 0 < YED < 1 normal necessity; YED < 0 inferior.
Cross elasticity of demand: XED = (%ΔQ of A) ÷ (%ΔP of B); Positive: substitutes. Negative: complements. Sign depends on the pair, not on one good alone.
Revenue rule: |PED| > 1: price up, revenue down. |PED| < 1: price up, revenue up. |PED| = 1: revenue unchanged.; Reverse the direction for a price cut.

How to solve Price, Income and Cross Elasticity of Demand questions

Use this order for any numerical or interpretive question on elasticity.

1Identify which elasticity is asked: price, income or cross. Note which variable changes and which quantity responds.
2Write down the old and new values of the driver and of quantity demanded.
3Calculate percentage changes. Use the simple formula on the original value unless the question asks for the midpoint or arc method.
4Divide % change in quantity by % change in the driver. Keep the sign.
5Interpret the sign and size: elastic or inelastic; normal, inferior or luxury; substitute or complement.
6If revenue is asked, apply the revenue rule, or compute P × Q before and after to check.
7State your convention (signed value or absolute value) and the answer in a clear sentence.

Quickest way: Sign first, then size

When to use it: Use this in multiple-choice questions where you must classify a good or predict revenue.

Read the sign first. For PED expect negative. For YED, negative means inferior. For XED, positive means substitutes.
Compare the size to 1 for PED and YED.
For revenue, ask: does quantity move by more or less in percentage than price? More means revenue moves opposite to price. Less means it moves with price.
Check the answer with a quick P × Q calculation if numbers are given.

Common mistakes in Price, Income and Cross Elasticity of Demand

Using the absolute change instead of the percentage change.
Students confuse elasticity with the slope of the demand curve.
Fix: Always divide each change by the base value before taking the ratio.
Calling a good elastic because PED = −0.4 is 'smaller than −1'.
The negative sign makes −0.4 look less than −1 numerically.
Fix: Compare the absolute value with 1. |−0.4| = 0.4 < 1, so demand is inelastic.
Saying revenue rises when price rises for any good.
Students remember the inelastic case and apply it everywhere.
Fix: Check |PED| first. A price rise raises revenue only when demand is inelastic.
Using the change in the good's own price for cross elasticity.
The formula looks like PED.
Fix: For XED the denominator is the % change in the price of the other good.
Labelling a good luxury just because YED is positive.
Positive YED only shows a normal good.
Fix: Luxury needs YED > 1. Inferior needs YED < 0.
Mixing midpoint and simple methods, or assuming PED is constant along a straight-line demand curve.
The slope is constant, so students think elasticity is too.
Fix: Use the method asked. On a linear curve, PED is larger in absolute value at high prices and smaller at low prices.

Worked examples

Example 1

The price of a packet of tea rises from ₹100 to ₹110. Quantity demanded falls from 500 to 450 packets per week. Calculate PED (simple method on original values) and state the effect on total revenue.

Show the solution

%ΔP = (110 − 100) ÷ 100 = +10%.
%ΔQ = (450 − 500) ÷ 500 = −10%.
PED = −10% ÷ +10% = −1. Demand is unit elastic.
Revenue before = ₹100 × 500 = ₹50,000.
Revenue after = ₹110 × 450 = ₹49,500.
Revenue falls slightly because the simple method is based on the original values and the change is not infinitesimal. The rule says no change only for a very small price change.

Answer: PED = −1 (unit elastic on the simple method). Revenue falls from ₹50,000 to ₹49,500, so over a discrete 10% change the result is only approximately unchanged.

Example 2

When consumer income rises by 8%, demand for good X rises by 12% and demand for good Z falls by 4%. When the price of good W rises by 5%, demand for good X falls by 3%. Classify X and Z, and describe the relationship between X and W.

Show the solution

YED for X = 12% ÷ 8% = 1.5. This is positive and greater than 1, so X is a normal luxury good.
YED for Z = −4% ÷ 8% = −0.5. This is negative, so Z is an inferior good.
XED of X with respect to W = −3% ÷ 5% = −0.6.
A negative XED means that when W's price rises, demand for X falls. X and W are complements, with a fairly weak link.

Answer: X has YED = 1.5 (luxury). Z has YED = −0.5 (inferior). XED between X and W = −0.6, so they are complements.

Exam tips

Write the formula and the signed result. Then interpret in words, because marks are often given for the conclusion.
In multiple-choice questions, check whether the options use signed or absolute values before you choose.
For revenue questions, a quick P × Q before and after catches sign errors.
Know the three sign tests: YED < 0 inferior, YED > 1 luxury, XED > 0 substitutes.
Written questions often link elasticity to pricing decisions. Explain what a firm should do with price, not just the number.

Practice questions from Consumer demand and behaviour

Price, Income and Cross Elasticity of Demand in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Price, Income and Cross Elasticity of Demand: frequently asked questions

What is the formula for price elasticity of demand?

PED = % change in quantity demanded ÷ % change in price. It is usually negative because price and quantity move in opposite directions. Many questions quote the absolute value, so state your convention.

How do I tell normal, inferior and luxury goods apart?

Use income elasticity. A negative YED is an inferior good. A positive YED is a normal good. If YED is also above 1, the good is a luxury.

Are substitutes positive or negative in cross elasticity?

Substitutes have positive cross elasticity, because a rise in the price of one good raises demand for the other. Complements have negative cross elasticity.

How does elasticity affect total revenue?

If demand is elastic, raising price lowers revenue and cutting price raises it. If demand is inelastic, raising price raises revenue. At unit elasticity, small price changes leave revenue unchanged.