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Microeconomics guide, Unit 2, step 9 of 28Previous stepNext step

Step 9: Elasticity

By the EconTutorials team. 11-minute read with 6 practice questions.
SyllabusAP Micro 2.3–2.5 · Cambridge 2.2–2.3 · IB 2.5–2.6
In 30 seconds
  • Elasticity measures how much one variable responds when another changes, using percentage changes.
  • Price elasticity of demand: \( \text{PED} = \%\Delta Q_d \div \%\Delta P \). If \( |\text{PED}| > 1 \) demand is elastic; if \( |\text{PED}| < 1 \) it is inelastic.
  • The total revenue test: if a price rise makes total revenue fall, demand is elastic; if total revenue rises, demand is inelastic.
  • Three more measures: PES (supply, always positive), YED (income: normal or inferior) and XED (other good’s price: substitutes or complements).
Video lesson coming soonA short animated lesson for this step will appear here.

What elasticity means

Imagine two shops raise prices by 10% on the same day. The petrol station sees almost no change in sales: people still have to drive to work. The trainers shop sees sales fall sharply: customers go to a rival or wait for a sale. Both shops faced the Law of Demand, but the size of the response was very different. Elasticity is the tool that measures that size.

In Step 7 you learned which direction price and quantity move. Elasticity tells you how far. Businesses use it to set prices, and governments use it to decide what to tax.

Key termPrice elasticity of demand (PED): the responsiveness of quantity demanded to a change in price, measured as the percentage change in quantity demanded divided by the percentage change in price.

Calculating price elasticity of demand

You always work with percentage changes, so that the answer does not depend on units (cups, litres, dollars or riyals).

\[ \text{PED} = \frac{\%\Delta Q_d}{\%\Delta P}, \qquad \%\Delta = \frac{\text{new} – \text{old}}{\text{old}} \times 100 \]

Because price and quantity demanded move in opposite directions, PED is always negative. Economists usually report the absolute value, \( |\text{PED}| \), and read it like this:

  • \( |\text{PED}| > 1 \): elastic. Quantity changes by a bigger percentage than price.
  • \( |\text{PED}| < 1 \): inelastic. Quantity changes by a smaller percentage than price.
  • \( |\text{PED}| = 1 \): unit elastic. Quantity changes by the same percentage as price.
Worked example

A bubble tea shop raises its price from $5 to $6. Daily sales fall from 200 cups to 140 cups. Calculate PED and say whether demand is elastic or inelastic.

Step 1\( \%\Delta P = \frac{6 – 5}{5} \times 100 = +20\% \)
Step 2\( \%\Delta Q_d = \frac{140 – 200}{200} \times 100 = -30\% \)
Step 3\( \text{PED} = \frac{-30}{20} = -1.5 \), so \( |\text{PED}| = 1.5 > 1 \)

Demand is elastic: a 20% price rise caused a 30% fall in sales. There are plenty of other drinks nearby, so customers switch.

Five cases, and the total revenue test

\( |\text{PED}| \) can be anywhere from zero to infinity. Five cases come up again and again in exams:

CaseValueDemand curveExample from the book
Perfectly inelastic0VerticalLife-saving insulin
InelasticBetween 0 and 1SteepPetrol
Unit elastic1Curve where TR stays constantRevenue unchanged when price changes
ElasticGreater than 1FlatLuxury handbags
Perfectly elasticInfiniteHorizontalWheat from one farm in a competitive market

Steeper usually means more inelastic and flatter means more elastic. Be careful, though: slope and elasticity are not the same thing. Along a straight-line demand curve the slope stays fixed but elasticity changes.

Total revenue is price times quantity: \( TR = P \times Q \). When a firm raises its price, it earns more on each unit but sells fewer units. Which effect wins depends on elasticity:

  • Inelastic demand: a price rise increases TR (quantity barely falls).
  • Elastic demand: a price rise decreases TR (quantity falls a lot).
  • Unit elastic: TR stays the same.

Check this against the bubble tea example: TR fell from \( 5 \times 200 = \$1{,}000 \) to \( 6 \times 140 = \$840 \). A price rise reduced revenue, which confirms that demand is elastic.

Exam tipThe total revenue test is the fastest way to identify elasticity from a data table. Work out TR before and after the price change. If price and TR move in the same direction, demand is inelastic; if they move in opposite directions, it is elastic. In written answers, give the PED value and confirm it with the TR test.

What makes demand elastic or inelastic? SPLAT

The book uses the memory aid SPLAT:

  1. Substitutes. More substitutes means more elastic. If Pepsi gets dearer, people switch to Coke. Insulin has no substitute, so demand is inelastic.
  2. Proportion of income. The bigger the share of your income, the more elastic. A 20% rise in house prices matters a lot; a 20% rise in the price of salt barely registers.
  3. Luxury or necessity. Necessities (food, medicine, utilities) are inelastic. Luxuries (designer clothes, holidays, eating out) are elastic.
  4. Addictiveness or habit. Habit-forming goods (cigarettes, coffee, alcohol) are inelastic.
  5. Time horizon. Demand is more elastic in the long run. When petrol prices jump, drivers cannot switch to an electric car tomorrow, but over several years they can.

This is why governments tax cigarettes heavily. The chapter reports research estimates of PED for cigarettes of about −0.3 to −0.5 in the short run. Because demand is inelastic, smokers keep buying, so the tax raises a lot of revenue while still reducing smoking somewhat.

Three more elasticities: PES, YED and XED

The same “percentage change divided by percentage change” idea works for other relationships.

Price elasticity of supply measures how strongly producers respond to a price change:

\[ \text{PES} = \frac{\%\Delta Q_s}{\%\Delta P} \]

PES is always positive (the Law of Supply). PES above 1 is elastic supply; below 1 is inelastic. Supply is more elastic when there is more time to adjust, when firms have spare capacity, when output can be stored, and when workers and materials can move easily into the industry. Housing is very inelastic in the short run because building takes years.

Income elasticity of demand measures how demand responds to a change in income:

\[ \text{YED} = \frac{\%\Delta Q_d}{\%\Delta Y} \]
  • YED greater than 1: normal good, luxury (sports cars, foreign holidays).
  • YED between 0 and 1: normal good, necessity (bread, electricity, toothpaste).
  • YED negative: inferior good. Demand falls as income rises (bus travel, instant noodles, second-hand clothing).

Cross-price elasticity of demand measures how demand for good A responds to a change in the price of good B:

\[ \text{XED} = \frac{\%\Delta Q_d \text{ of A}}{\%\Delta P \text{ of B}} \]
  • XED positive: substitutes (Pepsi gets dearer, more Coke is bought).
  • XED negative: complements (printers get dearer, fewer ink cartridges are bought).
  • XED zero: unrelated goods.
Common mistakeDividing the wrong way round. The thing that responds (quantity) always goes on top, and the thing that causes the change (price or income) goes underneath. A second common slip is dropping the sign for YED and XED. For PED you may use the absolute value, but for YED and XED the sign is the whole point: it tells you whether the good is normal or inferior, a substitute or a complement.

Practise: 6 questions

Try each one on paper first, then check the worked answer.

EasyQ1. The price of a bus pass rises by 10% and the number sold falls by 5%. Calculate PED and say whether demand is elastic or inelastic. Show worked answer
\( \text{PED} = \frac{-5}{10} = -0.5 \)
\( |\text{PED}| = 0.5 < 1 \), so demand is inelastic. Quantity responds by a smaller percentage than price.
EasyQ2. A good has YED = −0.4. What type of good is it? Show worked answer
YED is negative, so it is an inferior good. When incomes rise, people buy less of it and switch to better alternatives.
MediumQ3. A gym raises its monthly fee from $40 to $50. Members fall from 400 to 280. (a) Calculate PED. (b) Calculate total revenue before and after. (c) Are your answers consistent? Show worked answer
(a) \( \%\Delta P = \frac{50-40}{40} \times 100 = 25\% \). \( \%\Delta Q_d = \frac{280-400}{400} \times 100 = -30\% \). \( \text{PED} = \frac{-30}{25} = -1.2 \). \( |\text{PED}| = 1.2 > 1 \): elastic.
(b) Before: \( 40 \times 400 = \$16{,}000 \). After: \( 50 \times 280 = \$14{,}000 \). TR fell by $2,000.
(c) Yes. With elastic demand, a price rise reduces total revenue.
MediumQ4. The price of petrol rises by 20%. Demand for bus travel rises by 4%, and demand for large cars falls by 10%. Calculate XED in each case and state the relationship. Show worked answer
Bus travel: \( \text{XED} = \frac{+4}{20} = +0.2 \). Positive, so petrol (driving) and bus travel are substitutes, though weak ones because the value is small.
Large cars: \( \text{XED} = \frac{-10}{20} = -0.5 \). Negative, so petrol and large cars are complements: they are used together.
MediumQ5. The price of strawberries rises from $2.00 to $2.50 a box. Farmers increase the quantity supplied from 1,000 to 1,100 boxes. Calculate PES and explain the result. Show worked answer
\( \%\Delta P = \frac{2.50-2.00}{2.00} \times 100 = 25\% \)
\( \%\Delta Q_s = \frac{1{,}100-1{,}000}{1{,}000} \times 100 = 10\% \)
\( \text{PES} = \frac{10}{25} = 0.4 \), which is less than 1, so supply is inelastic.
Strawberries take time to grow and cannot be stored for long, so farmers cannot respond quickly to a higher price.
ExamQ6. Average household income rises by 4%. Demand for good A rises by 6%, demand for good B falls by 2%, and demand for good C rises by 1%. (a) Calculate YED for each good. (b) Classify each good. (c) In a recession, income falls by 3%. Estimate the change in demand for good A and explain which good’s sellers should worry most. [6 marks] Show worked answer
(a) A: \( \frac{6}{4} = +1.5 \). B: \( \frac{-2}{4} = -0.5 \). C: \( \frac{1}{4} = +0.25 \). [3 marks, 1 each]
(b) A is a normal good and a luxury (YED > 1). B is an inferior good (YED < 0). C is a normal good and a necessity (0 < YED < 1). [2 marks]
(c) \( \%\Delta Q_d \approx \text{YED} \times \%\Delta Y = 1.5 \times (-3\%) = -4.5\% \). Sellers of A should worry most, because luxury demand is the most sensitive to income; demand for C falls only slightly and demand for B is likely to rise as people trade down. [1 mark]

Check yourself

1. A 15% price rise causes a 30% fall in quantity demanded. PED is:

\( -30 \div 15 = -2.0 \). PED is negative, and its absolute value of 2 means elastic.

2. When demand is inelastic, a price rise makes total revenue:

Quantity falls by a smaller percentage than price rises, so P × Q goes up.

3. The XED between Coke and Pepsi is +0.7. They are:

Positive XED means a dearer Pepsi raises demand for Coke: consumers switch.

Your score: 0 out of 3

The short version

  • PED = %ΔQd ÷ %ΔP. Use the absolute value: above 1 is elastic, below 1 is inelastic.
  • Total revenue test: a price rise raises TR if demand is inelastic and lowers TR if demand is elastic.
  • SPLAT: Substitutes, Proportion of income, Luxury or necessity, Addictiveness, Time horizon.
  • PES is always positive and grows with time, spare capacity, storability and factor mobility.
  • YED: positive for normal goods (above 1 luxury, below 1 necessity), negative for inferior goods. XED: positive for substitutes, negative for complements.

This guide covers the core of the chapter. For the full Chapter 8, with diagrams of all five PED cases, the cigarette-tax case study and 15 exam-style questions with a complete answer key, see the book Economics Made Simple.

Further reading on EconTutorials

Older in-depth articles on this topic from our blog:

Want more questions like these, with worked answers?
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Next: step 10 of 28Consumer and Producer Surplus