Price elasticity of supply (PES) | IGCSE Class 10 Economics Notes

This note covers price elasticity of supply (PES): what it means, how it is calculated and interpreted, how different supply curve diagrams show different values of PES, the factors that make supply elastic or inelastic, the role of the time period, and why PES matters for the decisions of producers, consumers and government.

What is price elasticity of supply?

The price elasticity of supply of a good measures the responsiveness of quantity supplied to changes in the price of the good. It tells us by how much producers change the amount they offer for sale when the price changes.

Definition and direction of change

Supply curves are normally drawn sloping upwards, so a rise in price is usually followed by a rise in quantity supplied, and PES is normally a positive number. Only when the supply curve is vertical does a price change produce no change in quantity supplied at all.

Definition: Price elasticity of supply. PES measures the percentage change in quantity supplied divided by the percentage change in price that caused it.

Why PES has no unit

Because PES compares two percentage changes, it has no unit of measurement. A PES value can therefore be compared directly between completely different goods, for example wheat and mobile phones, even though the two are sold in different units and at different prices. This is the same reason that price elasticity of demand has no unit: ratios of percentages cancel out the underlying units of price (dollars) and quantity (tonnes, boxes, units and so on), leaving a pure number that can be read off and compared across markets.

How is PES calculated?

PES is defined as the percentage change in quantity supplied divided by the percentage change in price.

PES = %ΔQs ÷ %ΔP

Defining the symbols

Before using the formula, every symbol in it must be defined. Q₁ is the original quantity supplied and P₁ is the original price, before the change being studied. Q₂ is the new quantity supplied and P₂ is the new price, after the change.

ΔQ = Q2 − Q1

ΔP = P2 − P1

Here ΔQ (read "delta Q") is simply the change in quantity supplied, and ΔP is the change in price, each found by subtracting the old value from the new value. A positive ΔQ or ΔP means a rise; a negative value means a fall.

Working out each percentage change

The percentage change in quantity supplied and the percentage change in price are each calculated against the original (old) value, not the new one.

%ΔQs = (ΔQ ÷ Q1) × 100

%ΔP = (ΔP ÷ P1) × 100

Combining the two percentage formulas gives a single working formula that avoids calculating each percentage separately.

PES = (ΔQ ÷ ΔP) × (P1 ÷ Q1)

Worked examples using the formula

Worked example 1. The market for cricket balls is perfectly competitive. When the price of a cricket ball is $10, 200 cricket balls are produced in aggregate by firms in the market. When the price rises to $30, 1,000 cricket balls are produced.

Answer: Percentage change in quantity supplied = (1000 − 200) ÷ 200 × 100 = 400. Percentage change in price = (30 − 10) ÷ 10 × 100 = 200. PES = 400 ÷ 200 = 2.

Note: the same calculation in another currency. This same calculation can equally be set in any currency, with price rising from 10 to 30 units and quantity rising from 200 to 1,000 cricket balls. Because PES has no unit, the same percentage changes, 400% and 200%, are obtained whatever currency the price is quoted in, giving the identical answer, PES = 2.

Worked example 2. A firm earns a revenue of $50 when the market price of a good is $10. The market price increases to $15 and the firm now earns a revenue of $150. Find the price elasticity of the firm's supply.

Answer: Quantity supplied is revenue ÷ price. Old quantity = $50 ÷ $10 = 5 units.

New quantity = $150 ÷ $15 = 10 units. %ΔQs = (10 − 5) ÷ 5 × 100 = 100. %ΔP = (15 − 10) ÷ 10 × 100 = 50. PES = 100 ÷ 50 = 2.

A calculation question of this kind always gives a pair of old and new values for price and a pair for quantity (or revenue, from which quantity can be derived), so that both percentage changes can be worked out before the final division. Candidates should always state which value is the old (Q₁, P₁) value and which is the new (Q₂, P₂) value before substituting into the formula, since using the new value as the base by mistake gives a wrong answer.

How do we interpret the numerical value of PES?

Once PES has been calculated, the number itself tells us how strongly producers react to a price change.

The five cases

• When the supply curve is vertical, supply is completely insensitive to price and the elasticity of supply is zero: this is perfectly inelastic supply.
• When the value of PES is positive but less than 1, supply is inelastic supply: quantity supplied changes by a smaller percentage than price.
• When PES equals exactly 1, supply is unitary elastic: quantity supplied changes by the same percentage as price.
• When PES is greater than 1, supply is elastic supply: quantity supplied changes by a larger percentage than price.
• When supply can respond to even the smallest price change with an unlimited change in quantity, supply is said to be perfectly elastic supply, with the supply curve drawn as a horizontal line.

In worked example 1 above, PES = 2, so the cricket ball market shows elastic supply: a 200% rise in price produced a larger, 400% rise in quantity supplied.

Reading the summary table

What do supply curve diagrams for different PES look like?

Supply curves can be drawn to show each of the five cases of PES, and the shape of the line tells you at a glance whether supply is elastic, inelastic or unit elastic.

Drawing the five cases

Three panels each show price on the vertical axis and output on the horizontal axis.

In the first panel, the straight-line supply curve cuts the price axis in its positive range and, when extended, cuts the quantity axis at a point M in the negative range; for any point S on this curve, the distance Mq₀ is greater than Oq₀, so PES is greater than 1 (elastic supply).

In the second panel, the supply curve is a straight line through the origin, so point M coincides with the origin and PES equals exactly 1 at every point (unitary elastic supply).

In the third panel, the straight-line supply curve cuts the quantity axis at a point M in the positive range, so Mq₀ is less than Oq₀ and PES is less than 1 at every point on the curve (inelastic supply).

Perfectly elastic and perfectly inelastic supply

Two further diagrams each plot price on the vertical axis and output on the horizontal axis.

A completely vertical supply curve shows that the same quantity is supplied whatever the price, so PES is zero (perfectly inelastic supply).

A completely horizontal supply curve, drawn at a fixed price, shows that any quantity can be supplied at that one price, so PES is infinite (perfectly elastic supply).

These diagrams are useful because a supply curve's steepness alone does not reveal its elasticity: two lines with different steepness can both pass through the origin and both have unitary elastic supply at every point, while the position of the intercept on the price axis or the quantity axis is what actually determines whether supply is elastic or inelastic at a given point.

Interpreting a supply diagram in an answer

When a diagram is asked for, label the axes (price on the vertical axis, quantity on the horizontal axis), draw the supply curve with the correct intercept, and then state in words what the shape shows. A vertical line means quantity supplied does not change at all when price changes, so PES is zero. A horizontal line means producers will supply any amount at one price but nothing at a lower price, so PES is infinite. A line through the origin means the percentage change in quantity equals the percentage change in price, so PES is 1. A line cutting the price axis means quantity supplied changes by a larger percentage than price, so supply is elastic, and a line cutting the quantity axis means it changes by a smaller percentage, so supply is inelastic.

What determines whether supply is elastic or inelastic?

Several features of a firm's or an industry's production decide how far quantity supplied can change when price changes.

Determinants linked to capacity and cost

• Spare capacity. A firm with unused factory space, machinery and labour can raise output quickly when price rises, giving a more elastic supply; a firm already working at full capacity cannot, giving inelastic supply.
• Ease of storing stocks. If a firm can hold finished goods in store and release them onto the market when price rises, supply is more elastic; goods that are perishable or very costly to store make supply more inelastic.
• Ease of switching resources between uses. If labour and capital can be moved easily from making one good to another, supply of that good is more elastic; highly specialised resources that cannot be redeployed make supply inelastic.
• Number of producers and ease of entry. A good produced in a market where new firms can enter easily tends to have more elastic supply in the longer term, because entry adds to total output when price is attractive.
• Rate at which costs rise with output. If marginal cost rises only slowly as output expands, firms can expand output with only a small further rise in price needed, giving elastic supply; if marginal cost rises steeply, supply is more inelastic.

The minimum supply price

A firm's willingness to supply more also depends on whether price covers its costs. A firm will not offer any output at all below its minimum supply price, the lowest price at which it is willing to produce, so quantity supplied is completely unresponsive to small price changes below that price.

This helps explain why a supply curve is often drawn as having a positive minimum price below which no output is offered, with the rising part of the curve beginning only once price reaches that minimum. Over a market with many firms of differing costs, the lowest-cost firms begin supplying at a lower price than higher-cost firms, so as price rises past each firm's minimum cost level, additional firms join in, which also makes aggregate market supply more elastic than the supply curve of any one firm taken alone.

Shifts in supply are separate from elasticity

Firms respond to a rise in the price of an input, such as a wage rise, by raising their marginal cost at every level of output, which shifts the whole supply curve to the left so that less is supplied at any given price; a fall in input prices or an improvement in technology that lowers marginal cost shifts the supply curve to the right, so that more is supplied at any given price.

These shifts are separate from elasticity, but they show how the underlying cost conditions that make supply elastic or inelastic can themselves change over time. A government policy such as a tax charged on every unit sold also raises a firm's cost at each level of output and shifts its supply curve to the left, whereas a subsidy paid per unit lowers cost and shifts supply to the right; neither a tax nor a subsidy by itself changes the shape of the curve or the value of PES, but both affect the quantity supplied and the price actually received by producers at the new equilibrium.

Why does time matter for PES?

The time period allowed for producers to respond is one of the strongest influences on PES.

Short run supply

In the short run, a firm cannot vary all of its factors of production: at least one factor, typically capital such as machinery or factory buildings, is fixed.

This limits how much output can be raised even if price rises a great deal, so short-run supply tends to be more inelastic. A firm facing a sudden rise in price may only be able to use existing machinery more intensively, for example by running extra shifts, rather than installing new capacity straight away.

Long run supply

In the long run, a firm can vary every factor of production, including building new capacity or installing new machinery, and new firms can also enter the industry.

This greater flexibility allows quantity supplied to respond by a larger percentage to the same price change, so long-run supply tends to be more elastic than short-run supply for the same good.

This distinction matters most for goods that take a long time to produce, such as agricultural crops that depend on a growing season or manufactured goods that need new factories to be built; for these goods the gap between short-run and long-run elasticity of supply is particularly wide. A crop that can only be sown once a year, for instance, cannot increase its quantity supplied within the current growing season no matter how much price rises, so its short-run supply is close to perfectly inelastic.

What is the significance of PES for producers?

Knowing the elasticity of supply helps a producer judge how output and revenue will respond if the market price changes.

Elastic supply and spare capacity

If supply is elastic, a producer can increase output by a relatively large percentage in response to even a modest rise in price, which is useful when trying to meet a sudden rise in demand without the price rising too far.

If supply is inelastic, the same rise in demand mostly raises price rather than output, because producers cannot expand quantity supplied quickly; this matters for goods such as those that need specialist skills, long production times or scarce raw materials, where producers must plan well in advance to be able to respond to price changes at all.

Planning ahead using PES

Producers who understand their own PES can plan capacity decisions, such as whether to hold spare capacity or stocks, in good time so that they are able to benefit from price rises rather than missing out on sales while competitors expand output faster.

Worked example 3. The market price of a good changes from $5 to $20. As a result, the quantity supplied by a firm increases by 15 units. The price elasticity of the firm's supply is 0.5. Find the initial and final output levels of the firm.

Answer: %ΔP = (20 − 5) ÷ 5 × 100 = 300. Since PES = %ΔQs ÷ %ΔP, 0.5 = %ΔQs ÷ 300, so %ΔQs = 150.

Since %ΔQs = (ΔQ ÷ Q₁) × 100 and ΔQ = 15, 150 = (15 ÷ Q₁) × 100, so Q₁ = 10 units. Final output = 10 + 15 = 25 units.

What is the significance of PES for consumers and government?

Significance for consumers

For consumers, PES affects how much the price of a good is likely to rise following a rise in demand, for example a seasonal rise in demand for a good.

If supply is elastic, consumers can expect producers to meet the extra demand with extra output, so the price rise is relatively small; if supply is inelastic, consumers face a much larger rise in price for the same rise in demand, because output cannot expand quickly to meet it.

Significance for government

For government, PES helps predict the effect of policies that change costs or incentives for producers, such as a tax on a good or a subsidy to producers.

If supply is inelastic, a tax raises price only a little relative to the amount by which the government wants to discourage production, and the tax tends to raise government revenue reliably because quantity supplied falls by less; if supply is elastic, the same tax causes a much larger fall in quantity supplied.

Governments setting a maximum price or a minimum price on a good must also consider the elasticity of supply, because an inelastic supply curve means that even a large gap between the set price and the market price produces only a small shortage or surplus of the good, whereas an elastic supply curve produces a much larger shortage or surplus for the same price gap.

Worked example 4. At the market price of $10, a firm supplies 4 units of output. The market price increases to $30. The price elasticity of the firm's supply is 1.25. What quantity will the firm supply at the new price?

Answer: %ΔP = (30 − 10) ÷ 10 × 100 = 200. Since PES = %ΔQs ÷ %ΔP, 1.25 = %ΔQs ÷ 200, so %ΔQs = 250.

Since %ΔQs = (ΔQ ÷ 4) × 100, 250 = (ΔQ ÷ 4) × 100, so ΔQ = 10 units. New quantity supplied = 4 + 10 = 14 units.

Going beyond the syllabus

These ideas extend the unit and are not needed for the questions on it.

Tax incidence and elasticity

PES is closely related to price elasticity of demand, and the two together decide how the burden of a tax on a good is shared between buyers and sellers, and how much of a price change caused by a shift in demand or supply falls on price rather than on quantity.

Where supply is very inelastic and demand is elastic, most of a tax tends to fall on the seller, because the seller cannot easily reduce the quantity it offers to avoid the tax and so must absorb more of the cost through a lower price received.

Where supply is elastic and demand is inelastic, most of a tax tends to fall on the buyer, because the seller can reduce output in response to the tax while buyers continue to demand roughly the same quantity even at a higher price.

This link is useful for understanding real-world government decisions about which goods to tax, since a government that wants a tax to fall mainly on producers rather than consumers, or that wants to be sure a tax raises reliable revenue without a large fall in quantity traded, needs to know the elasticity of supply as well as the elasticity of demand for the good concerned before setting the rate of the tax.

How does the geometric method measure PES?

For a straight-line supply curve, a simple geometric rule links the position of the line to the value of PES at any point S on it.

The rule looks at where the straight line, if extended, would cut the quantity axis, at point M, compared with the distance Oq₀ along the quantity axis to the point directly below S.

PES at S = Mq0 ÷ Oq0

What happens when price falls below minimum average variable cost?

A profit-maximising firm will not supply any positive quantity at all if the price is below the minimum of its average variable cost in the short run, or below the minimum of its average cost in the long run; below that minimum price, output is zero, so quantity supplied is completely unresponsive to small price changes in that range.

Glossary

• Price elasticity of supply: the percentage change in quantity supplied divided by the percentage change in price that caused it.
• Elastic supply: supply where PES is greater than 1, so quantity supplied changes by a larger percentage than price.
• Inelastic supply: supply where PES is between 0 and 1, so quantity supplied changes by a smaller percentage than price.
• Unitary elastic supply: supply where PES equals exactly 1, so quantity supplied changes by the same percentage as price.
• Perfectly elastic supply: supply where any quantity can be offered at one fixed price, shown as a horizontal supply curve, with PES infinite.
• Perfectly inelastic supply: supply where the same quantity is offered whatever the price, shown as a vertical supply curve, with PES equal to zero.
• Quantity supplied: the amount of a good that producers are willing and able to offer for sale at a given price.
• Spare capacity: unused machinery, factory space or labour that allows a firm to raise output quickly.
• Short run: the time period in which at least one factor of production, typically capital, cannot be varied.
• Long run: the time period in which every factor of production can be varied and firms can enter or leave the industry.
• Marginal cost: the increase in total cost from producing one more unit of output.
• Minimum supply price: the lowest price at which a firm is willing to offer any output at all.
• Stocks: finished goods held by a producer that can be released onto the market when price rises.
• Subsidy: a payment from government to producers that lowers their costs and encourages a higher quantity supplied.

Common errors and misconceptions

• Misconception: PES is calculated the same way as price elasticity of demand, with a negative sign. Correct: supply curves usually slope upwards, so PES is normally a positive number, not a negative one.
• Misconception: a steeper supply curve always means a smaller PES. Correct: for straight-line supply curves, it is the position of the intercept on the price axis or quantity axis, not the steepness of the line, that decides whether PES is greater than, equal to or less than 1.
• Misconception: percentage changes in PES calculations can be worked out against either the old or the new value. Correct: both the percentage change in quantity and the percentage change in price are calculated against the original (old) value.
• Misconception: an elastic supply curve must mean a large absolute change in quantity. Correct: elasticity compares percentage changes, so a good with a small total market can still have an elastic supply if its percentage response to price is large.
• Misconception: the short run and long run give the same PES for a good. Correct: supply tends to be more inelastic in the short run, when at least one factor of production is fixed, and more elastic in the long run, when all factors can be varied.
• Misconception: a vertical supply curve is simply an example of very inelastic supply. Correct: a vertical supply curve shows perfectly inelastic supply, with PES exactly equal to zero, not merely a low value.
• Misconception: PES is the same as the slope of the supply curve. Correct: PES compares percentage changes, so it is not the slope; any straight supply line through the origin has a PES of 1 at every point, whatever its slope.

Exam-style questions with model answers

Q1. Define price elasticity of supply. [2 marks]

1. Price elasticity of supply measures the responsiveness of quantity supplied to a change in price.
2. It is calculated as the percentage change in quantity supplied divided by the percentage change in price.

Q2. A firm supplies 80 units at a price of $5 and 100 units at a price of $6. Calculate the price elasticity of supply and state what the value shows. [4 marks]

1. %ΔQs = (100 − 80) ÷ 80 × 100 = 25.
2. %ΔP = (6 − 5) ÷ 5 × 100 = 20.
3. PES = 25 ÷ 20 = 1.25.
4. Because PES is greater than 1, supply is elastic: quantity supplied changes by a larger percentage than price.

Q3. Explain two determinants of whether the supply of a good is elastic or inelastic. [4 marks]

1. Spare capacity: a firm with unused machinery or factory space can raise output quickly when price rises, making supply more elastic.
2. Ease of storing stocks: a firm that can hold finished stock and release it when price rises has a more elastic supply than a firm making a good that cannot be stored.
3. A firm already working at full capacity, or making a good that cannot be stored, has a more inelastic supply, because quantity supplied cannot respond quickly to a price change.

Q4. Explain why the price elasticity of supply of a good is usually more inelastic in the short run than in the long run. [4 marks]

1. In the short run at least one factor of production, typically capital, is fixed, so output cannot be expanded by very much even if price rises a great deal.
2. In the long run every factor of production can be varied, including building new capacity, so output can rise by a much larger percentage for the same rise in price.
3. New firms can also enter the industry in the long run, adding further to total output when price is attractive, which is not possible in the short run.
4. This means the same price rise produces a smaller percentage rise in quantity supplied in the short run than in the long run.

Q5. At a market price of $6, a firm supplies 20 units. The price rises to $9 and the price elasticity of supply is 1.5. Calculate the new quantity supplied. [4 marks]

1. %ΔP = (9 − 6) ÷ 6 × 100 = 50.
2. PES = %ΔQs ÷ %ΔP, so 1.5 = %ΔQs ÷ 50, giving %ΔQs = 75.
3. %ΔQs = (ΔQ ÷ 20) × 100, so 75 = (ΔQ ÷ 20) × 100, giving ΔQ = 15 units.
4. New quantity supplied = 20 + 15 = 35 units.

Q6. Analyse how knowledge of the price elasticity of supply of a good can help a government decide whether to set a maximum price on that good. [6 marks]

1. A maximum price is a price set below the market equilibrium price, intended to make the good more affordable.
2. If supply is inelastic, a given gap between the maximum price and the market price causes only a small fall in quantity supplied, so the resulting shortage is relatively small.
3. If supply is elastic, the same gap between the maximum price and the market price causes a much larger fall in quantity supplied, so the resulting shortage is much larger.
4. A government that knows supply is highly elastic may therefore expect a severe shortage, queuing or a black market if it sets a maximum price well below equilibrium.
5. A government that knows supply is inelastic may judge that a maximum price can be set with only a small shortage resulting, making the policy more workable.
6. This shows that the same policy can have very different effects on quantity supplied depending on the price elasticity of supply of the good concerned.

Q7. Discuss whether a highly inelastic supply of a good is always a disadvantage for its producers. [8 marks]

1. Inelastic supply means producers cannot expand quantity supplied by much even if the price of the good rises sharply, so they may miss out on extra sales when demand rises.
2. However, inelastic supply also means that if demand falls, quantity supplied does not have to fall by as much, so producers may avoid large job losses or wasted capacity.
3. Inelastic supply combined with rising demand tends to push price up by a larger percentage, so existing producers may earn higher revenue per unit sold even without raising output.
4. Whether inelastic supply is a disadvantage therefore depends on whether demand for the good is generally rising or falling, and on how much a producer values stable output over the chance of expanding quickly.
5. A producer who anticipates inelastic supply can build spare capacity or stocks in advance, turning a potential disadvantage into an opportunity to capture higher prices when demand rises.
6. Producers of goods that take a long time to make, such as crops tied to a growing season, may have little choice about their inelastic supply, so the disadvantage is greater for them than for firms that could expand capacity if they chose to invest.
7. On balance, inelastic supply is not always a disadvantage: output and jobs stay steadier when demand falls, and the price producers receive rises sharply when demand rises, although the same inelasticity means the price also falls sharply when demand falls.

Q8. Draw a supply curve that shows perfectly inelastic supply and a supply curve that shows unit elastic supply, and explain what each shows. [4 marks]

1. Both diagrams have price on the vertical axis and quantity supplied on the horizontal axis.
2. Perfectly inelastic supply is a vertical line at one quantity: the quantity supplied does not change whatever happens to price, so PES is zero.
3. Unit elastic supply is a straight line drawn from the origin: any percentage change in price brings the same percentage change in quantity supplied.
4. So PES is 1 at every point on the line through the origin, whatever its slope, while the vertical line shows that producers cannot change output at all in response to price.

Key takeaways

• PES measures the percentage change in quantity supplied divided by the percentage change in price that caused it.
• PES is normally positive because supply curves usually slope upwards.
• A PES of zero means perfectly inelastic supply, shown by a vertical supply curve.
• A PES of exactly 1 means unitary elastic supply, shown by a straight-line supply curve through the origin.
• An infinite PES means perfectly elastic supply, shown by a horizontal supply curve.
• Spare capacity, ease of storing stocks, ease of switching resources, number of producers and the rate at which costs rise all affect whether supply is elastic or inelastic.
• Supply tends to be more inelastic in the short run, when at least one factor of production is fixed, and more elastic in the long run.
• Producers use PES to plan how far output can respond to price changes and to manage capacity and stocks.
• Governments use PES to predict the effect of taxes, subsidies, maximum prices and minimum prices on quantity and price.

Test yourself

What formula is used to calculate price elasticity of supply?

PES equals the percentage change in quantity supplied divided by the percentage change in price.

What value of PES describes perfectly inelastic supply, and what shape of supply curve shows it?

PES equals zero, shown by a completely vertical supply curve, meaning the same quantity is supplied whatever the price.

Why does a straight-line supply curve through the origin always have a PES of 1?

Because the point where the extended line would cut the quantity axis coincides with the origin, making the two distances used in the elasticity ratio equal.

Give two reasons why supply of a good might be elastic.

The firm has spare capacity so it can raise output quickly, and it can store finished stock and release it onto the market when price rises.

Why is supply usually more elastic in the long run than in the short run?

In the long run every factor of production, including capital, can be varied and new firms can enter, so output can respond by a larger percentage to a price change.

How might a government use PES when deciding whether to tax a good?

If supply is inelastic, a tax raises price only a little and reduces quantity supplied by less, making it a more reliable source of revenue.

How does PES affect consumers when demand for a good rises?

If supply is elastic, producers can meet the extra demand with extra output, keeping the price rise small; if supply is inelastic, price rises by much more.