Lesson preview · Supply, income and cross elasticity

Other elasticities: supply, income and cross

~8 min · Free to read

In 2022, a tonne of cocoa beans (the raw material for chocolate) averaged about 2,400 dollars on world markets. In 2024 the average was about 7,300 dollars: three times as much. A world price like that is a signal to grow more cocoa. But a newly planted cocoa tree usually takes three to five years to give its first crop.

When sellers can’t respond much to a higher price, economists call their supply inelastic.

Key Term

Price elasticity of supply (PES)

Price elasticity of supply (PES) measures how strongly sellers respond to a change in price:

$P E S = \frac{%Δ Q _{s}}{%Δ P}$

$%Δ$ means “percentage change in”. The top is the percentage change in quantity supplied (the amount sellers offer). The bottom is the percentage change in price.

If the price of apples rises 10% and growers offer 5% more, PES = 5 ÷ 10 = 0.5.

Above 1: elastic. Quantity supplied rises by a bigger percentage than the price.
Below 1: inelastic. It rises by a smaller percentage, like the apples.
Exactly 1: unit elastic. Quantity supplied and price rise by the same percentage.

PES is positive, because sellers offer more when the price rises. Price elasticity of demand (PED) carries a minus sign; PES doesn’t.

Imagine the price of bicycles in a country rises 20% and stays there. How much more bike makers offer depends on how long they have:

Time since the price rise	What makers can do	Rise in quantity supplied	PES
One week	Sell the few bikes already in the warehouse	2%	0.1
One year	Add shifts and hire workers	10%	0.5
Five years	Build new factories; new firms join	30%	1.5

Interactive — One price rise, three time horizons

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Supply curves for one week, one year and five years through the same starting point, with the same 20% price rise marked.

The same price rise gets three different answers. Supply becomes more elastic with time, because firms need time to hire workers, buy machines and build factories. Cocoa farmers face the same pattern with fewer quick options. Until new trees bear fruit, usually three to five years after planting, they can offer only a little more.

Tip

What else makes supply more elastic

Besides time, two things let sellers respond quickly:

Spare capacity: machines and workers that aren’t fully used. A factory running at half speed can add a shift next week.
Stocks: goods already made and stored. A warehouse of tinned soup can meet a price rise today. Fresh strawberries can’t be stored for long.

Some things can’t be made at all. No one can make more land in a city centre, so the supply of city-centre land has a PES close to 0.

Trap · Common Misconception

"A factory working at full capacity is best placed to respond"

A factory at full capacity looks strong, but it has no room left to grow. If the price rises, it can’t make more until it adds machines or space. Full capacity makes supply less elastic, not more.

Elasticity can also measure how buyers respond to things other than price. Imagine average incomes in Country X rise 10%. People buy 15% more restaurant meals and 5% fewer bus journeys.

Key Term

Income elasticity of demand (YED)

Income elasticity of demand (YED) measures how demand responds to income:

$Y E D = \frac{%Δ Q _{d}}{%Δ Y}$

The top is the percentage change in quantity demanded (the amount people buy). The bottom is the percentage change in income; $Y$ is economists’ usual letter for income. Here the sign is the message:

Above 0: a normal good. People buy more as they earn more.
Above 1: a luxury, as a rule of thumb. It is a normal good whose demand grows faster than income. Restaurant meals: 15 ÷ 10 = +1.5.
Between 0 and 1: a necessity, also a normal good. Demand grows, but more slowly than income.
Below 0: an inferior good. People buy less as they earn more. Bus journeys: −5 ÷ 10 = −0.5.

Key Term

Cross elasticity of demand (XED)

Cross elasticity of demand (XED) measures how demand for one good responds to the price of another:

$X E D = \frac{%Δ Q _{d} of good A}{%Δ P of good B}$

Above 0: substitutes, goods that do the same job. Coffee gets 10% pricier and people buy 5% more tea: +0.5.
Below 0: complements, goods used together. Consoles get 10% pricier and game sales fall 8%: −0.8.
Close to 0: unrelated goods.

The sign tells you the type of link. The size tells you how strong it is.

Tip

Why firms care

Firms use income elasticity to plan for a recession, a period when the economy shrinks and incomes fall. A seller of luxuries should expect its sales to fall faster than incomes. A discount grocer selling inferior goods may sell more.

Cross elasticity matters too. A firm whose product has a close substitute knows that a rival’s price cut will cost it customers.

Trap · Common Misconception

"Inferior means low quality"

An inferior good isn’t badly made. The word only says that people buy less of it as they get richer, because they switch to something they like more. A bus is a fine way to travel, but a family that can afford a car may drive instead.

Check yourself · no marks

Sort these four made-up estimates. Which shows a luxury, which an inferior good, which substitutes and which complements?

Instant noodles: YED = −0.3
Cinema tickets and popcorn: XED = −0.6
Cruise holidays: YED = +2.2
Two brands of trainers: XED = +1.8

Commit to one first. Guessing and being wrong beats reading the answer cold.

Practice · 1 / 6

Wrong answers cost no XP

Check your understanding of supply, income and cross elasticity:

The price of bicycle helmets rises by 20%. Over the next year, helmet makers increase the quantity they supply by 30%. What is the price elasticity of supply?

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