IB DP Economics: Elasticity of demand – Revision Notes

These notes follow the IB Diploma Programme Economics guide (first assessment 2022, published February 2020), the course examined from the 2022 session onwards. They cover sub-topic 2.5, Elasticity of demand, for SL and HL, with HL-only points marked. Full explanations and worked examples are in the study guide; test yourself with the practice questions.

Course links: IB DP Economics hub, the printable checklist and the free diagnostics.

Formulas

Measure	Formula	Use
Percentage change	(new - old) / old x 100	Always from the starting value
PED	%Qd / %P, where Qd is quantity demanded	Responsiveness to own price
YED	%Qd / %Y, where Y is income	Responsiveness to income
Total revenue (TR)	Price x quantity	Compare before and after
Missing quantity	% change in quantity = PED x % change in price	Then apply to old quantity

Calculate means a numerical answer with working shown. Paper 1 does not allow calculators, so keep the numbers friendly in practice.

PED: degrees and diagrams

Size of PED	Name	Demand curve
0	Perfectly inelastic	A vertical line
Between 0 and 1	Relatively inelastic	Steep
1	Unitary	Rectangular hyperbola (TR constant)
Between 1 and infinity	Relatively elastic	Flat
Infinity	Perfectly elastic	Horizontal line

Raw PED is negative on a downward-sloping demand curve. Decide whether you quote the sign or the size, and be consistent.

Method

1. Work out the price change as a percentage.
2. Work out the quantity change as a percentage.
3. Divide quantity by price.
4. Classify by size (below 1, 1, above 1).
5. Compare total revenue before and after if asked.

Worked reminder. Price 60 to 66 (+10%); quantity 700 to 595 (-15%). PED = -15 / 10 = -1.5, so elastic.

HL only: PED along a straight line

• A straight demand curve has constant slope but changing PED.
• Upper section: elastic (size above 1). Midpoint: unitary. Lower section: inelastic.
• The midpoint, where PED is unitary, gives maximum revenue.
• Example for Q = 100 - 5P: PED size is 2.33 between prices 14 and 16 and 0.25 between prices 4 and 6.

Determinants of PED

Determinant	More elastic when	More inelastic when
Substitutes	Many, close	Few, distant
Necessity	Luxury or want	Necessity
Share of income	Large share	Small share
Time	Long period	Short period

Always apply the determinant to the good in the question. A named factor with no link to the case earns little.

PED and total revenue

Demand	Price rises	Price falls
Elastic	TR falls	TR rises
Unitary	No change	No change
Inelastic	TR rises	TR falls

Worked reminder. A fictional cinema cuts its ticket price from 12 to 10 (-16.67%) and weekly attendance rises from 600 to 780 (+30%). PED = 30 / -16.67 = -1.8, elastic. Revenue rises from 7,200 to 7,800.

Diagram: draw the demand curve, then two shaded rectangles from the origin to each price-quantity point. Label the rectangle gained and the rectangle lost, and say which is larger.

Importance of PED (AO3)

For	Use	Limit
Firms	Choose price to raise revenue; forecast sales after a change	Revenue is not profit; rivals react; estimates are uncertain
Governments	Choose goods for indirect taxes; predict effect on consumption	Burden on low-income households; other policies may be needed

Conclude with a judgement and say what would change it (time period, accuracy of data, the objective).

HL only: primary commodities

PED is generally lower for primary commodities than for manufactures because:

• fewer close substitutes, and often necessities or essential inputs;
• a small share of the cost of the final good;
• demand derived from the final product.

Manufactures face branded rivals and can be differentiated, so buyers switch more easily.

YED

YED	Meaning	Type of good
Positive	Demand rises with income	Normal
Negative	Demand falls as income rises	Inferior
Between 0 and 1	Income inelastic	Necessities
Above 1	Income elastic	Services and luxury goods

Worked reminder. Income 2,000 to 2,200 (+10%). Restaurant meals 20 to 26 (+30%): YED = +3.0. Instant noodles 30 to 27 (-10%): YED = -1.0, inferior.

Engel curve. Put income up the side and quantity along the base.

• Income elastic good: flatter than a line from the origin to the point.
• Income inelastic normal good: steeper than that line.
• Inferior good: slopes backwards.

HL only: importance of YED

• For firms: forecast sales through the economic cycle and plan the product range as incomes rise.
• Sectoral structure: low-YED agriculture grows more slowly than income and high-YED services faster, so the share of services tends to rise as incomes rise.

Diagrams to be able to draw

1. Relatively elastic and relatively inelastic demand, on the same axes, with the same price fall.
2. Perfectly elastic, perfectly inelastic and unitary demand, each on its own axes.
3. Revenue rectangles for a price change when demand is elastic, and again when it is inelastic.
4. HL only: a straight demand curve with elastic, unitary and inelastic sections labelled.
5. An Engel curve for an income elastic good, an income inelastic good and an inferior good.

Label both axes, name each curve, and mark the starting and finishing price and quantity. The guide’s definition of “draw” asks for a labelled, accurate diagram, so use a ruler for straight lines.

Evaluation prompts for PED and YED answers

Use these to turn description into a judgement.

• Time. Is the PED short-run or long-run? Over a longer period substitutes appear and demand becomes more elastic.
• Data. A PED is an estimate for one range of prices. A different range may give a different value.
• Objective. A firm may want revenue, profit, market share or survival, and each points to a different decision.
• Who is affected. A tax on an inelastic necessity raises revenue but takes a larger share of a low-income household’s income.
• Rivals. A price cut may be copied, which removes the expected rise in quantity.
• Income path. YED matters most when incomes are changing quickly, in a boom, a slump or a long period of growth.

Must-know distinctions

• PED responds to price; YED responds to income.
• Size of PED (without sign) versus signed value: never mix them.
• Elastic demand: price and revenue move in opposite directions. Inelastic: they move together.
• Negative YED means inferior; low positive YED means a necessity.
• Revenue is not profit.

Quick self-test

1. Write the PED formula in words.
2. A seller lifts a fare from 60 to 66 and passengers drop to 595 from 700. Calculate PED and the change in total revenue.
3. A good has PED of -0.5. Price rises 10% from a base quantity of 400. Find the new quantity.
4. What does a perfectly inelastic demand curve look like, and what is its PED?
5. Demand is inelastic. A firm cuts price. What happens to revenue?
6. Income rises 5% and quantity demanded of a good rises 10%. Calculate YED and classify the good.
7. Income rises from 1,000 to 1,200 and quantity falls from 80 to 72. Calculate YED and classify the good.
8. YED is 1.5 and income rises 4%. By how much does quantity demanded change?
9. PED is -2.5 and price falls 6%. By how much does quantity demanded change?
10. HL only: at which point on a straight downward-sloping demand curve is total revenue greatest, and what is PED there?
11. HL only: give one reason PED is generally lower for a primary commodity than for a manufactured good.

Answers

1. PED = %Qd / %P, using percentage changes.
2. Price +10%, quantity -15%, so PED = -1.5. Revenue falls from 42,000 to 39,270, a fall of 2,730.
3. Quantity falls 0.5 x 10 = 5%, so new quantity = 400 x 0.95 = 380.
4. A vertical line; PED is zero.
5. Revenue falls, because the quantity increase is proportionally smaller than the price cut.
6. YED = 10 / 5 = +2.0. Positive, so normal; above 1, so income elastic.
7. Income +20%, quantity -10%, so YED = -0.5. Negative, so an inferior good.
8. Quantity rises by 1.5 x 4 = 6%.
9. Quantity rises by 2.5 x 6 = 15%.
10. At the midpoint, where PED is unitary (size 1).
11. Examples: few close substitutes; small share of the final product’s cost; derived demand.

Where marks are usually lost

• Measuring a percentage change against the end value, not the start value.
• Putting price change over quantity change, which inverts PED.
• Giving PED as 0.6 and then calling it elastic.
• Naming a determinant but never tying it to the good given.
• Drawing revenue rectangles without labelling price and quantity axes or the two points.
• Saying “revenue falls” after a price rise without stating that demand must be elastic.
• Treating revenue as profit in an evaluation.
• Calling a good inferior because its YED is small, when it is negative YED that marks inferior goods.
• Leaving the HL straight-line result as “PED is constant because the slope is constant”.

Official syllabus

IB Diploma Programme Economics guide, first assessment 2022, published February 2020, International Baccalaureate Organization. Sub-topic 2.5 Elasticity of demand, within Unit 2: Microeconomics.