DP Economics HL 2.5 Elasticity of Demand

DP Economics HL 2.5 Elasticity of Demand - Full notes

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DP Economics HL | 2.5 Elasticity of Demand

DP ECONOMICS · UNIT 2: MICROECONOMICS

2.5

Elasticity of Demand

Full notes for HL · IB-style

Contents

1	What elasticity measures
2	Price elasticity of demand: meaning and calculation
3	The range of PED values and their diagrams
4	Determinants of PED
5	PED and total revenue
6	Applications of PED for firms and governments
7	Income elasticity of demand (YED)
8	PED along a straight-line demand curve (HL only)
9	PED calculations: practice
10	PED and total revenue
11	PED along a linear demand curve
12	Determinants of PED: applied
13	PED and indirect taxes
14	Income elasticity of demand: calculations
15	YED and the economy
16	Cross-price elasticity (extension)
17	Using elasticity in business decisions
18	Mixed review: worked problems
19	Additional exam-style practice
20	Elasticity and government policy
21	Common misconceptions and links
22	Exam-style question with markscheme
23	Check your understanding
24	Summary and topic map

These are full teaching notes. Read each section in order, try the Think about it question before you read on, and do every Quick check before moving to the next section.

Before you start

Rate yourself on each statement now, and again after you've worked through the notes. Shade R (not yet), A (getting there) or G (confident).

I can…	R	A	G
explain what elasticity means
calculate PED and interpret its sign and size
draw demand curves showing elastic, inelastic, unit elastic, perfectly elastic and perfectly inelastic demand
explain the determinants of PED with examples
explain the relationship between PED and total revenue
apply PED to pricing decisions and to indirect taxation
calculate and interpret YED for normal, inferior and luxury goods
explain the significance of YED for producers and for the structure of the economy
explain why PED varies along a straight-line demand curve
relate the midpoint of a linear demand curve to maximum total revenue

Section 8 is Additional Higher Level content. Every other section is common to SL and HL.

Guiding questions

Why does a price rise increase a firm's revenue in one market and reduce it in another? Why do governments tax petrol and cigarettes so heavily? Why do some industries grow faster than others as countries get richer?

How this topic is examined

Elasticity turns up throughout the course: in tax incidence (2.7), in the analysis of commodity markets and development (Unit 4), and in the J-curve (HL). Paper 2 regularly asks you to calculate PED or YED from data and interpret the result.

Paper 1 questions often ask you to explain why a government taxes goods with inelastic demand, or to evaluate the usefulness of PED to firms. The marks come from linking the value of PED to an outcome: revenue, tax revenue or consumption.

Command term	What the examiner wants
Define	the precise meaning, ideally in the IB wording, in one or two sentences
Draw / Sketch	a fully labelled diagram with every axis, curve, equilibrium and change labelled
Explain	a causal chain linked to economic theory, usually supported by a diagram
Analyse	break a situation into its parts and trace the effects of each
Evaluate / Discuss	weigh up arguments, question assumptions and reach a justified conclusion using real-world examples
Calculate	use the formula with % changes, show the sign, and interpret the value in words

How to use these notes

Each section teaches one part of the syllabus in full. You'll see these boxes throughout; each has one job:

Box	What it's for
Think about it	a question to get you thinking before a section; the answer comes in the section
Key point	the one idea you must not forget
Common mistake	an error examiners see every year, and how to avoid it
In the real world	where the economics shows up outside the classroom
Try this	something quick you can do yourself to test the idea
Worked example	full solutions with IB-style marks (M1 method, A1 answer, R1 reasoning)
Quick check	short questions to test yourself at the end of each section

1 What elasticity measures

Elasticity tells you not just which way quantity moves, but how much.

Think about it

If a cinema and a petrol station both raised prices by 20%, which would lose more customers? Why?

The law of demand tells us that a price rise reduces quantity demanded. But it does not tell us by how much. For a firm deciding whether to raise its price, or a government deciding whether a tax will cut consumption, the size of the response is what matters.

Elasticity measures the responsiveness of one variable to a change in another. It is always expressed in percentage changes so that goods measured in different units (litres, kilograms, tickets) can be compared. In this topic you meet two elasticities of demand: price elasticity of demand (PED), which measures responsiveness to the good's own price, and income elasticity of demand (YED), which measures responsiveness to consumers' income.

Quick check

1. What does elasticity measure?

2. Why are percentage changes used?

Answers: 1. the responsiveness of one variable to a change in another 2. so goods in different units can be compared

2 Price elasticity of demand: meaning and calculation

PED compares the percentage change in quantity with the percentage change in price.

Think about it

A game's price falls from $50 to $40 and weekly sales rise from 200 to 280. Is that a big response or a small one? How could you put a number on it?

Price elasticity of demand (PED) is a measure of the responsiveness of the quantity demanded of a good to a change in its price. It is calculated as:

PED = percentage change in quantity demanded ÷ percentage change in price

Each percentage change is found as (new − original) ÷ original × 100. Because price and quantity demanded move in opposite directions (the law of demand), PED is almost always negative. Economists usually judge elasticity by the absolute value (ignoring the minus sign), but you should show the sign in calculations.

The size of the number tells you how responsive demand is. If PED is −2, a 1% change in price causes a 2% change in quantity demanded in the opposite direction: quantity is twice as responsive as price. If PED is −0.5, quantity changes by only half as much as price.

WORKED EXAMPLE 1 Calculating PED

A shop cuts the price of a video game from $50 to $40, and weekly sales rise from 200 to 280. Calculate PED and interpret the result.

Solution

%ΔQd = (280 − 200) ÷ 200 × 100 = +40%M1

%ΔP = (40 − 50) ÷ 50 × 100 = −20%M1

PED = 40 ÷ (−20) = −2A1

The absolute value is greater than 1, so demand is price elastic: quantity demanded changed proportionally more than priceR1

Always put the quantity change on top. Dividing price by quantity gives −0.5 and the opposite conclusion.

WORKED EXAMPLE 2 Using PED to predict

Demand for bus travel has PED = −0.4. The bus company raises fares by 15%. Calculate the percentage change in the number of journeys.

Solution

%ΔQd = PED × %ΔPM1

= −0.4 × 15 = −6%: journeys fall by 6%A1

Common mistake

Quoting PED as a positive number without comment, or writing 'PED = 2, so price and quantity move together'. Show the negative sign and interpret it as an inverse relationship.

Quick check

1. State the formula for PED.

2. Price rises 10% and quantity demanded falls 5%. Calculate PED.

3. Why is PED usually negative?

Answers: 1. %ΔQd ÷ %ΔP 2. −0.5 3. price and quantity demanded move in opposite directions

3 The range of PED values and their diagrams

Five cases: elastic, inelastic, unit elastic and the two extremes.

Absolute value of PED	Description	Meaning	Example
greater than 1	price elastic	%ΔQd > %ΔP	a particular brand of cereal, foreign holidays
less than 1	price inelastic	%ΔQd < %ΔP	petrol, cigarettes, salt
equal to 1	unit elastic	%ΔQd = %ΔP	a theoretical case
0	perfectly inelastic	quantity does not change at all	a life-saving drug with no substitute (approximately)
infinity	perfectly elastic	any price rise reduces quantity to zero	an identical product in a perfectly competitive market

Figure 1. Price elastic demand: a small price change causes a large change in quantity.

Figure 2. Price inelastic demand: a large price change causes only a small change in quantity.

Figure 3. The extreme cases: perfectly elastic (horizontal), perfectly inelastic (vertical) and unit elastic (a rectangular hyperbola).

On a diagram, an elastic demand curve is drawn relatively flat and an inelastic one relatively steep. Be careful: the slope of a straight line is not the same as its elasticity (at HL you will see that elasticity changes along a straight line). For SL purposes, drawing elastic demand flatter and inelastic demand steeper, over the relevant range, is the expected convention.

Unit elastic demand is drawn as a curve called a rectangular hyperbola: every point on it gives the same total revenue, because price and quantity change in exactly offsetting proportions.

Quick check

1. Draw (or describe) a perfectly inelastic demand curve.

2. What does PED = 0 mean?

3. What shape is a unit elastic demand curve?

Answers: 1. vertical line 2. quantity does not respond to price at all 3. rectangular hyperbola

4 Determinants of PED

Substitutes matter most; necessity, budget share and time explain the rest.

Think about it

Why do you think demand for petrol is inelastic in the short run, but much more elastic over ten years?

Number and closeness of substitutes. This is the most important determinant. If a good has many close substitutes, a price rise sends consumers elsewhere, so demand is elastic. A single brand of shampoo has many substitutes and highly elastic demand; shampoo as a whole has fewer substitutes and less elastic demand. How widely a good is defined matters: demand for 'food' is very inelastic, demand for 'Brand X frozen pizza' is very elastic.

Necessity or luxury. Necessities, goods people feel they must have, tend to have inelastic demand: people keep buying basic food, medicines and electricity even when prices rise. Luxuries tend to have elastic demand because consumers can postpone or forgo them.

Proportion of income spent on the good. If a good takes a tiny share of income (salt, matches), even a large percentage price rise makes little difference to the budget, so demand is inelastic. If it takes a large share (a car, rent, a holiday), a price rise forces consumers to think hard, so demand is more elastic.

Time period. Demand becomes more elastic over time. Immediately after a petrol price rise, people still need to drive to work; over months and years they buy more fuel-efficient cars, move closer to work, or switch to public transport. Habits and long-term contracts take time to change.

Habit and addiction. Habit-forming and addictive goods, such as cigarettes, alcohol and caffeine, tend to have inelastic demand, because consumers find it hard to cut back even when prices rise.

Determinant	More elastic when...	More inelastic when...
Substitutes	many close substitutes	few or no substitutes
Necessity	a luxury	a necessity
Share of income	a large share of income	a small share of income
Time	a long time period	a short time period
Habit / addiction	not habit-forming	habit-forming or addictive

Common mistake

Saying 'demand for petrol is inelastic because it is a necessity' and stopping. Better: 'demand for petrol is inelastic in the short run because there are few substitutes for driving to work, so a 50% price rise reduced sales by only 5%'. Link the determinant to evidence.

Quick check

1. Why is demand for one brand of cola more elastic than demand for soft drinks in general?

2. Why is demand for salt inelastic?

3. Why does PED increase over time?

Answers: 1. one brand has many close substitutes 2. small share of income; few substitutes 3. consumers find substitutes and change habits

5 PED and total revenue

Whether a price rise raises revenue depends entirely on PED.

Think about it

A football club wants more ticket revenue. Should it raise or lower prices? What would you need to know?

Total revenue (TR) is the amount a firm receives from selling its product: TR = price × quantity sold. Total revenue is the same as total consumer spending on the good. When a firm changes its price, two effects pull in opposite directions: each unit sold brings in a different amount (the price effect), and a different number of units is sold (the quantity effect). PED tells you which effect wins.

If demand is elastic, the percentage change in quantity is larger than the percentage change in price. A price cut therefore increases revenue (the extra units sold more than make up for the lower price), and a price rise reduces revenue. Price and total revenue move in opposite directions.

If demand is inelastic, the percentage change in quantity is smaller than the change in price. A price rise increases revenue and a price cut reduces it. Price and total revenue move in the same direction.

If demand is unit elastic, the two effects exactly cancel, and total revenue does not change.

PED	Price rise	Price fall
Elastic (> 1)	TR falls	TR rises
Inelastic (< 1)	TR rises	TR falls
Unit elastic (= 1)	TR unchanged	TR unchanged

Figure 4. Total revenue is the rectangle price × quantity. With elastic demand the new rectangle (blue) is larger; with inelastic demand it is smaller.

WORKED EXAMPLE 3 PED and total revenue

A shop cuts the price of a game from $50 to $40 and sales rise from 200 to 280 a week (PED = −2). Calculate the change in total revenue and explain it.

Solution

TR before = 50 × 200 = $10 000A1

TR after = 40 × 280 = $11 200A1

TR rises by $1 200A1

Demand is elastic, so the 40% rise in quantity outweighs the 20% fall in priceR1

Key point

Elastic: price and revenue move in opposite directions. Inelastic: they move in the same direction. This one rule answers most PED questions about firms.

Quick check

1. Demand is inelastic. What happens to TR if price rises?

2. Why does TR stay constant when demand is unit elastic?

3. A cinema's demand is elastic. Should it raise or lower prices to increase revenue?

Answers: 1. TR rises 2. percentage changes in price and quantity cancel 3. lower prices

6 Applications of PED for firms and governments

PED guides pricing, tax policy and the analysis of commodity markets.

6.1 Firms: pricing decisions

Firms use estimates of PED to set prices. A firm facing inelastic demand, for example because its brand is strong or it has few competitors, can raise prices and increase revenue. A firm facing elastic demand is cautious about price rises and may use price cuts or promotions to increase sales and revenue.

Firms also try to make demand less elastic through advertising and branding, which reduce the number of goods consumers regard as close substitutes. Airlines charge business travellers, whose demand is inelastic because their companies pay and they must travel at specific times, much higher fares than leisure travellers, whose demand is elastic.

6.2 Governments: indirect taxes

Governments rely heavily on indirect taxes on goods with inelastic demand, such as petrol, tobacco and alcohol. Because quantity demanded falls only a little when the tax raises the price, tax revenue (tax per unit × quantity) remains high and predictable.

There is a trade-off. If the aim of the tax is to reduce consumption of a harmful good, inelastic demand makes the tax less effective at that goal. A tax on cigarettes raises plenty of revenue precisely because smokers keep buying. You will analyse this further in 2.7 and 2.8, where the burden (incidence) of a tax depends on elasticity.

6.3 Primary commodities

Many primary commodities, such as coffee, wheat and copper, have price inelastic demand (they are necessities or vital inputs with few substitutes) and also price inelastic supply (2.6). When supply changes because of weather or disease, small shifts in supply cause large price swings, and farmers' incomes become very unstable. This volatility is a major problem for developing countries that depend on a few commodity exports (Unit 4).

In the real world

When fuel prices rose by more than 30% in many countries in 2022, the quantity of fuel bought fell only slightly in the short run, which is consistent with very inelastic demand. Governments' fuel tax revenues stayed high, and several governments cut fuel taxes temporarily to ease the burden on households.

Quick check

1. Why do airlines charge business travellers more?

2. Why do governments tax goods with inelastic demand?

3. Why does inelastic demand make commodity prices volatile?

Answers: 1. their demand is inelastic 2. revenue stays high because quantity falls little 3. small supply shifts cause large price changes

7 Income elasticity of demand (YED)

YED tells you how demand changes as consumers get richer.

Think about it

As average incomes in a country double, which do you think grows faster: spending on rice or spending on restaurant meals? Why?

Income elasticity of demand (YED) measures the responsiveness of demand for a good to a change in consumers' income:

YED = percentage change in quantity demanded ÷ percentage change in income

Unlike PED, the sign of YED matters, because it tells you what type of good it is.

Normal goods have a positive YED: demand rises when income rises. Within normal goods, a YED between 0 and 1 shows income inelastic demand: demand rises, but proportionally less than income. These are often necessities, such as basic food and utilities. A YED greater than 1 shows income elastic demand: demand rises proportionally more than income. These are often luxuries, such as foreign holidays, jewellery and eating out.

Inferior goods have a negative YED: demand falls when income rises, because consumers switch to better alternatives. Examples include bus travel and the cheapest own-brand foods.

YED	Type of good	Example
negative	inferior	bus travel, cheapest own-brand food
0 to 1	normal necessity (income inelastic)	basic food, electricity
greater than 1	normal luxury (income elastic)	foreign holidays, restaurant meals

WORKED EXAMPLE 4 Calculating YED

Average income rises from $40 000 to $44 000. Demand for bus journeys falls from 500 to 450 a week, and demand for restaurant meals rises from 200 to 260. Calculate YED for each and classify the goods.

Solution

%ΔY = (44 000 − 40 000) ÷ 40 000 × 100 = 10%M1

Bus: %ΔQd = −10%, so YED = −10 ÷ 10 = −1: an inferior goodA1 R1

Restaurants: %ΔQd = +30%, so YED = 30 ÷ 10 = 3: an income elastic normal good (luxury)A1 R1

7.1 Why YED matters

For firms. Firms selling income-elastic goods can expect strong growth in sales when the economy grows, but sharp falls in recessions. Firms selling inferior goods may do well in recessions. Knowing YED helps firms plan capacity, stock and marketing over the business cycle.

For the structure of the economy. As economies grow, demand for income-inelastic goods (food, basic agricultural products) grows slowly, while demand for income-elastic goods (manufactures, services such as finance, tourism and health care) grows faster. This is why the share of agriculture in output and employment falls as countries develop, and the share of services rises (the sectoral change you will meet in Unit 4).

For developing countries. Primary commodities tend to have low YED. As world incomes rise, demand for the commodities that many developing countries export grows slowly, so their export earnings grow slowly and their terms of trade may worsen. This is one argument for diversification.

Common mistake

Ignoring the sign of YED. A YED of −0.5 and +0.5 describe completely different goods. Always state whether the good is normal or inferior.

Quick check

1. Define YED.

2. A good has YED = 1.8. Classify it.

3. Why does agriculture's share of output fall as countries develop?

Answers: 1. %ΔQd ÷ %ΔY 2. normal, income elastic (luxury) 3. food has low YED, so demand grows more slowly than income

8 PED along a straight-line demand curve (HL only)

Slope is constant along a straight line; elasticity is not.

HL only

This section is Additional Higher Level content. SL students do not need it.

A common mistake is to think that a straight-line demand curve has the same elasticity everywhere. It does not. PED can be written as (ΔQ ÷ ΔP) × (P ÷ Q). Along a straight line, ΔQ/ΔP (the inverse of the slope) is constant, but P/Q changes: at high prices and low quantities, P/Q is large, so PED is large; at low prices and high quantities, P/Q is small, so PED is small.

So the upper part of a linear demand curve is elastic, the lower part is inelastic, and the midpoint is unit elastic. Total revenue is therefore maximized at the midpoint: above it, a price cut raises revenue; below it, a price cut lowers revenue.

Figure 5. Total revenue along the demand curve P = 10 − Q rises to a maximum at Q = 5, where PED = −1, then falls.

WORKED EXAMPLE 5 PED along a linear demand curve

Demand is P = 10 − Q (P in $, Q in thousands). Calculate PED for a price fall from $8 to $6, and from $4 to $2. Explain the difference.

Solution

$8 to $6: Q rises from 2 to 4 (+100%); P falls 25%; PED = −4M1 A1

$4 to $2: Q rises from 6 to 8 (+33.3%); P falls 50%; PED = −0.67A1

The slope is the same, but at high prices P/Q is larger, so demand is elastic; at low prices it is inelasticR1

Key point

On a straight-line demand curve: elastic above the midpoint, unit elastic at the midpoint (TR maximum), inelastic below.

Quick check

1. Where on a linear demand curve is TR maximized?

2. Why does PED change along a straight line?

Answers: 1. at the midpoint, where PED = −1 2. P/Q changes even though the slope is constant

9 PED calculations: practice

Percentage changes.

PED = % change in quantity demanded/% change in price. Use the formula % change = (new − original)/original × 100. PED is negative for normal demand curves; economists often quote the absolute value.

WORKED EXAMPLE 6 Calculation (standard)

Price rises from $4.00 to $5.00 and quantity demanded falls from 600 to 450. Calculate PED.

Solution

%ΔQ = −25%; %ΔP = +25%M1

PED = −1.0 (unit elastic)A1

WORKED EXAMPLE 7 Inelastic (standard)

Price falls from $20 to $18; quantity rises from 1000 to 1040. Calculate PED.

Solution

%ΔQ = 4%; %ΔP = −10%M1

PED = −0.4 (inelastic)A1

Quick check

1. Price rises 8%; quantity falls 20%. Calculate PED and classify.

2. PED = −0.5; price rises 12%. Predict the change in quantity demanded.

Answers: 1. −2.5: elastic 2. falls 6%

10 PED and total revenue

The revenue test.

If demand is price elastic, a price rise reduces total revenue (TR = P × Q); if inelastic, a price rise increases total revenue; if unit elastic, revenue is unchanged.

PED	Price rise	Price fall
elastic (\|PED\| > 1)	TR falls	TR rises
inelastic (\|PED\| < 1)	TR rises	TR falls
unit elastic	TR unchanged	TR unchanged

WORKED EXAMPLE 8 Revenue (exam level)

In the inelastic example, calculate total revenue before and after.

Solution

Before: 20 × 1000 = $20 000A1

After: 18 × 1040 = $18 720: revenue fallsA1 R1

11 PED along a linear demand curve

Elasticity varies.

Along a straight-line demand curve, PED varies: elastic at high prices (small Q, large %ΔQ), unit elastic at the midpoint, inelastic at low prices. Total revenue is maximized at the midpoint.

WORKED EXAMPLE 9 Midpoint (standard)

Qd = 100 − 2P. At what price is total revenue maximized?

Solution

Midpoint of demand: P = $25 (Q = 50)M1

TR = $1250A1

12 Determinants of PED: applied

Why some goods are inelastic.

Determinant	More elastic if	Example
substitutes	many close substitutes	a particular brand of cola
necessity	luxury	foreign holidays
proportion of income	large share	cars
time	longer time period	petrol in the long run
addictiveness	not habit-forming	cigarettes are inelastic

13 PED and indirect taxes

Who pays?

Governments tax goods with inelastic demand (fuel, alcohol, tobacco) because quantity falls little and revenue is high. The burden falls mostly on consumers when demand is more inelastic than supply.

WORKED EXAMPLE 10 Tax choice (exam level)

Explain why governments tax cigarettes heavily.

Solution

Demand is price inelastic, so tax revenue is highR1

Also discourages consumption of a demerit good (though by a small amount)R1

14 Income elasticity of demand: calculations

YED.

YED = % change in quantity demanded/% change in income. YED > 1: income elastic (luxury); 0 < YED < 1: income inelastic (necessity); YED < 0: inferior good.

WORKED EXAMPLE 11 YED (standard)

Incomes rise 5%; demand for restaurant meals rises 12%. Calculate YED and classify.

Solution

12/5M1

= 2.4: income elastic (luxury)A1

Quick check

1. Incomes rise 4%; demand for bus travel falls 2%. Calculate YED.

2. YED for bread is 0.3. Incomes rise 10%. Predict the change in demand.

Answers: 1. −0.5: inferior 2. rises 3%

15 YED and the economy

Sectoral change.

As incomes rise, spending shifts from primary products (low YED) to manufactured goods and services (high YED). This explains the declining share of agriculture in developed economies and the importance of YED for business planning.

WORKED EXAMPLE 12 Primary commodities (exam level)

Explain why countries dependent on primary commodity exports may grow slowly as world incomes rise.

Solution

Primary products have low YEDR1

Demand grows slowly as incomes rise; terms of trade may fallR1

16 Cross-price elasticity (extension)

Substitutes and complements.

XED = % change in quantity demanded of good A/% change in price of good B. Positive for substitutes, negative for complements, near zero for unrelated goods.

WORKED EXAMPLE 13 XED (standard)

The price of coffee rises 10%; demand for tea rises 4%. Calculate XED.

Solution

4/10 = +0.4: weak substitutesA1

17 Using elasticity in business decisions

Pricing strategies.

Firms raise prices when demand is inelastic (airline tickets close to departure) and cut prices when demand is elastic (budget airlines booked early). Price discrimination charges different prices to groups with different PEDs.

Quick check

1. Why do cinemas offer student discounts?

Answers: 1. students have more elastic demand; lower prices raise revenue from them

18 Mixed review: worked problems

Bringing the ideas together.

WORKED EXAMPLE 14 Mixed problem (exam level)

A firm's product has PED = −1.6. It raises price from $50 to $55. Sales were 2000. Calculate the new sales and the change in total revenue.

Solution

%ΔP = 10%; %ΔQ = −16%: new Q = 1680M1 A1

TR: 100 000 → 92 400: falls by $7600A1

19 Additional exam-style practice

Paper 1 and Paper 3.

WORKED EXAMPLE 15 Paper 3 style (exam level)

When price falls from $12 to $9, quantity demanded rises from 300 to 420. (a) Calculate PED. (b) Calculate the change in total revenue. (c) Explain the relationship.

Solution

(a) %ΔQ = 40%; %ΔP = −25%: PED = −1.6A1

(b) 3600 → 3780: +$180A1

20 Elasticity and government policy

Wider applications.

PED informs taxation (inelastic goods raise revenue), subsidies (elastic goods respond more), and minimum prices. YED helps governments plan for changing demand for public services as incomes grow.

Quick check

1. Why is a sugar tax likely to raise revenue but only modestly reduce consumption?

Answers: 1. demand for sugary drinks is relatively inelastic

21 Common misconceptions and links

Students often think…	Actually…
a flat curve is always elastic everywhere	elasticity also depends on P/Q and changes along a straight line
PED is positive	PED is negative; judge size by the absolute value
a price rise always raises revenue	only if demand is inelastic
YED's sign doesn't matter	the sign shows normal or inferior
necessity alone determines PED	substitutes, budget share, time and habit matter too

How 2.5 connects to the rest of the course

Topic	Connection
2.1 Demand	PED measures the responsiveness along the demand curve
2.6 Elasticity of supply	together, PED and PES explain price volatility
2.7 Role of government	tax incidence depends on PED
4.1 Trade and 4.9 Barriers	low PED and YED of commodities and the terms of trade
4.6 Balance of payments (HL)	the Marshall–Lerner condition uses PED for exports and imports

22 Exam-style question with markscheme

Try this under exam conditions (about 15 minutes) before reading the markscheme.

Figure 6. Petrol prices and sales.

Text A. Petrol prices rose sharply in 2022, yet sales fell only slightly. The government considered raising fuel taxes further to fund public transport.

(a) Define the term price elasticity of demand. [2]

(b) Calculate PED for petrol between 2021 and 2022. [2]

(d) Explain why a government might choose to tax petrol, with reference to PED. [3]

(e) Demand for a toll road is P = 12 − 0.01Q. Find the toll that maximizes revenue and the revenue earned. [3]

Markscheme

Part	Answer	Marks
(a)	responsiveness of quantity demanded	A1
	to a change in the good's own price	A1
(b)	%ΔQ = −5%, %ΔP = +50%	M1
	PED = −0.1	A1
(c)	few substitutes in the short run	R1
	necessity for commuting / work	R1
	long-term commitments: car ownership, location	R1
(d)	inelastic: quantity falls little when tax raises price	R1
	tax revenue large and stable	R1
	but little reduction in consumption / emissions	R1
(e)	midpoint: Q = 600, P = $6	M1 A1
	TR = 6 × 600 = $3 600	A1

Examiner's comments. In (b), many candidates reversed the formula. In (d), the best answers noted the trade-off: high revenue but little behavioural change. In (e), weaker answers used the choke price instead of the midpoint.

23 Check your understanding

Section A: multiple choice

1. If price rises by 10% and quantity demanded falls by 20%, PED is

A. −2 B. −0.5 C. −1 D. −20

2. Demand is price inelastic when |PED| is

A. greater than 1 B. equal to 1 C. less than 1 D. infinite

3. If demand is price elastic, a price rise will

A. increase total revenue B. reduce total revenue C. leave revenue unchanged D. increase quantity

4. Which good probably has the most inelastic demand?

A. a brand of cereal B. foreign holidays C. restaurant meals D. insulin

5. A luxury good has YED

A. between 0 and 1 B. greater than 1 C. negative D. zero

6. If incomes rise 5% and demand rises 2%, YED is

A. 0.4 B. 2.5 C. −0.4 D. 10

7. Demand is likely to become more elastic

A. in the immediate period B. when goods are addictive C. when there are fewer substitutes D. over time

8. A perfectly inelastic demand curve is

A. horizontal B. downward sloping C. vertical D. a rectangular hyperbola

9. On a straight-line demand curve, TR is maximized where PED is

A. 0 B. infinite C. −2 D. −1

Section B: structured

10. Explain two determinants of PED. [4]

11. Explain the relationship between PED and total revenue. [4]

12. A 20% rise in incomes leads to a 6% fall in demand for a good. Calculate YED and classify the good. [2]

13. Explain why low YED for primary commodities is a problem for developing countries. [4]

14. Explain why PED varies along a straight-line demand curve. [3]

Answers

1. A 2. C 3. B 4. D 5. B 6. A 7. D 8. C 9. D

10. e.g. substitutes: more substitutes, more elastic; time: longer period, more elastic.

11. Elastic: price and TR move in opposite directions; inelastic: same direction; unit elastic: TR constant.

12. YED = −6 ÷ 20 = −0.3: inferior good.

13. Demand grows slowly as world incomes rise; export earnings grow slowly; terms of trade may decline; need to diversify.

14. PED = (ΔQ/ΔP)(P/Q); slope constant but P/Q falls down the curve; elastic above midpoint, inelastic below.

24 Summary and topic map

Idea	Remember
PED	%ΔQd ÷ %ΔP; usually negative
Elastic / inelastic	\|PED\| > 1 / < 1
Determinants	substitutes, necessity, share of income, time, habit
PED and TR	elastic: opposite directions; inelastic: same direction
Uses	pricing, indirect taxes, commodity volatility
YED	%ΔQd ÷ %ΔY; sign shows normal or inferior
YED > 1	luxury, income elastic
Linear demand (HL)	elastic above midpoint, inelastic below; TR max at midpoint

Before the exam, make sure you…

•put quantity on top of every elasticity formula
•show the sign and interpret it
•link PED to total revenue with numbers
•connect PED to tax revenue and the tax's effect on consumption
•classify goods by the sign and size of YED

Elasticity of Demand on one page

Cover this page with a sheet of paper and try to rebuild it from memory. Whatever you can't recall is what to revise next.

Figure 7. Topic map for Elasticity of Demand.

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