Cambridge A Level Economics: Price, income and cross elasticity of demand (9708) – Revision Notes

These notes condense section 2.2 (outcomes 2.2.1 to 2.2.8) of the Cambridge International AS & A Level Economics 9708 syllabus for examination in 2026, 2027 and 2028. Topic 2 is AS Level content and is assumed knowledge for A Level Papers 3 and 4. For full explanations read the study guide, then test yourself with the practice questions. The price system revision notes cover the rest of topic 2. All figures here are invented and illustrative.

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2.2.1 and 2.2.2: definitions and formulae

Measure	Definition	Formula
PED	Responsiveness of quantity demanded to a change in the good’s own price	%ΔQd ÷ %ΔP
YED	Responsiveness of demand to a change in income	%ΔQd ÷ %Δincome
XED	Responsiveness of demand for A to a change in the price of B	%ΔQd of A ÷ %ΔP of B

Percentage change = (new − old) ÷ old × 100.

Method in steps

1. Work out the percentage change in quantity (or demand).
2. Work out the percentage change in the other variable: own price, income, or the other good’s price.
3. Divide the first by the second, keeping the sign.
4. Name the type of good or the elasticity band, then answer the question asked.

Reminder. Price 8 to 10 cu (+25%), quantity 200 to 170 (−15%). PED = −15 ÷ 25 = −0.6, inelastic.

Reminders for YED and XED. Income 2,000 to 2,500 cu (+25%) and demand 50 to 57.5 units (+15%): YED = +0.6, a necessity. The price of B falls 5 to 4 cu (−20%) and demand for A rises 400 to 460 (+15%): XED = −0.75, complements. Note the denominators: income for YED, the other good’s price for XED.

2.2.3: sign and size

Coefficient	Value	Meaning
PED	Normally negative	Law of demand: price and quantity move opposite ways
YED	Positive	Normal good
YED	Above +1	Income elastic (“luxury”)
YED	Between 0 and +1	Income inelastic (“necessity”)
YED	Negative	Inferior good
XED	Positive	Substitutes: B’s price up, demand for A up
XED	Negative	Complements: B’s price up, demand for A down
XED	Zero	Unrelated

• Larger size of XED means a closer relationship between the goods.
• Elasticity uses relative (percentage) changes, so a 1 cu rise is large for a 2 cu good and small for a 20 cu good.
• Elasticity has no units.

2.2.4: descriptions of PED (using size)

Term	Size of PED	Curve
Perfectly inelastic	0	Vertical
(Highly) inelastic	0 to 1	Steep
Unitary	1	Rectangular hyperbola
(Highly) elastic	Above 1	Shallow
Perfectly elastic	Infinity	Horizontal

Do not say “0.9 is elastic”. Below 1 is inelastic, even when close to 1.

2.2.5: PED along a straight-line demand curve

• Slope is constant. PED changes along the line.
• Point PED = (1 ÷ slope) × (P ÷ Q), where slope = change in P ÷ change in Q.
• High price, low quantity: elastic. Midpoint: unitary. Low price, high quantity: inelastic.
• PED is minus infinity where the line meets the price axis and zero where it meets the quantity axis.
• Total revenue is highest at the midpoint, where PED is unitary.

Worked reminder. Demand Q = 60 − P.

Price	Quantity	Point PED	Total revenue
45	15	−3.0	675
30	30	−1.0	900
15	45	−0.33	675

Here slope in terms of P against Q is −1, so point PED = −P ÷ Q. At P = 45, PED = −45 ÷ 15 = −3.

For a large change, the base matters. State the base you use, or use a small change.

2.2.6: factors affecting each elasticity

Elasticity	Higher (more elastic) when	Lower (more inelastic) when
PED	Many close substitutes; narrow definition; luxury; large share of income; long time period	Few substitutes; broad definition; necessity or habit; small share of income; short time period
YED	Good is a luxury; buyers are on lower incomes who aspire to it	Good is a necessity; buyers already consume plenty
XED (size)	Goods are close substitutes or closely tied complements; narrow definitions	Goods are loosely linked; broad definitions

A good can change character: a basic food may have positive YED at low incomes and negative YED once buyers can afford alternatives.

2.2.7: PED and total expenditure (total revenue)

Total expenditure = price × quantity.

PED	Price rise	Price fall
Elastic (size above 1)	Falls	Rises
Unitary	Unchanged	Unchanged
Inelastic (size below 1)	Rises	Falls

Reminder. PED −2.5 and a price rise of 4% means quantity falls by 2.5 × 4 = 10%. Revenue falls, because 1.04 × 0.90 = 0.936 of the original.

Quick rule. Compare the two percentages. If quantity moves by more than price, the quantity effect wins.

Two-step chain for a pricing answer. First state PED and what it implies for revenue (for example, inelastic demand means a price rise increases revenue). Then qualify it: costs, rivals’ reactions, the time period and the objective of the firm.

Taxes. A government wanting revenue from an indirect tax prefers a good with inelastic demand, because quantity falls by less. A government wanting to reduce consumption finds the same tax less effective on such a good.

2.2.8: implications for decision-making

Elasticity	Who uses it	How
PED	Firms	Set price to raise revenue; check cost effects too
PED	Governments	Judge the revenue and consumption effects of indirect taxes
YED	Firms	Plan output and product range for growth or recession
YED	Governments	Forecast demand patterns as income changes
XED	Firms	Predict the effect of a rival’s price change; price complements together

Evaluation points

• Estimates come from past data and may not hold.
• Ceteris paribus rarely holds: tastes, incomes and other prices change together.
• Short-run and long-run elasticities differ.
• Elasticity varies along a demand curve, so a single value only applies to a price range.
• Revenue is not profit: costs change with output.

Must-know distinctions

Pair	Difference
Slope and elasticity	Slope uses absolute changes and is constant on a straight line. Elasticity uses percentage changes and varies along it.
Elastic and inelastic	Judge by size, not sign: 1.2 is elastic and 0.9 is inelastic.
Substitutes and complements	Positive XED and negative XED respectively.
Normal and inferior	Positive YED and negative YED respectively.
Income elastic and income inelastic	YED above +1 and between 0 and +1 respectively.
Revenue and profit	Revenue is price × quantity. Profit also depends on cost.

Quick self-test

1. Write the formula for XED.
2. Price rises from 8 to 10 cu and quantity falls from 200 to 170. Calculate PED and describe demand.
3. Income rises from 2,000 to 2,500 cu and demand rises from 50 to 57.5 units. Calculate YED and classify the good.
4. The price of B falls from 5 to 4 cu and demand for A rises from 400 to 460. Calculate XED and state the relationship.
5. State the sign of YED for an inferior good.
6. PED is −2.5. The price rises 4%. State the percentage change in quantity demanded.
7. Demand is Q = 60 − P. Calculate PED at P = 45 and state the price that maximises revenue.
8. Demand is inelastic. State what happens to total expenditure if price is cut.
9. YED is +1.5 and incomes rise 6%. State the change in demand.
10. State the PED value and curve shape for perfectly inelastic demand.
11. Give two reasons why demand for one brand of toothpaste is more elastic than demand for toothpaste.

Answers

1. XED = %ΔQd of good A ÷ %ΔP of good B.
2. %ΔP = +25%, %ΔQd = −15%, PED = −0.6. Demand is inelastic.
3. %ΔY = +25%, %ΔQd = +15%, YED = +0.6. Normal good with income inelastic demand (a necessity).
4. %ΔP = −20%, %ΔQd = +15%, XED = −0.75. Complements.
5. Negative.
6. Quantity falls by 10%.
7. PED = −45 ÷ 15 = −3. Revenue is highest at P = 30 (revenue 900), where PED is unitary.
8. Total expenditure falls.
9. Demand rises by 9%.
10. PED = 0. The curve is vertical.
11. Other brands are close substitutes, so buyers can switch if one brand’s price rises. A narrow definition means there are more alternatives than for toothpaste as a whole.

Where marks are usually lost

• Leaving out the sign, or putting it the wrong way, on YED and XED.
• Using the new value as the base without stating it.
• Calling 0.9 elastic, or 1.2 inelastic.
• Dividing the wrong way round (price change over quantity change).
• Using the price of the same good in XED instead of the other good’s price.
• Stating “revenue rises” after a price cut without checking whether demand is elastic.
• Giving factors as a list, without saying which way each factor moves elasticity.
• Ending a decision-making answer with no judgement about the reliability of the estimate.

Official syllabus

Cambridge International AS & A Level Economics 9708 syllabus for examination in 2026, 2027 and 2028, section 2.2 (Cambridge University Press & Assessment).