Price elasticity of demand (PED) | IGCSE Class 10 Economics Notes

This note covers price elasticity of demand (PED): its definition, the formula used to calculate it, how the numerical result is interpreted, how demand curves are drawn to show different values of PED, the key influences on whether demand is elastic or inelastic, the relationship between PED and total spending or revenue, and the significance of PED for the decisions made by consumers, producers and government.

What is price elasticity of demand?

Price elasticity of demand (PED) measures how responsive the quantity demanded of a good is to a change in its own price.

Demand for some goods changes considerably even for small price changes, while demand for other goods is barely affected by price changes. PED is a single number that captures this responsiveness, allowing comparison between goods.

Definition: Price elasticity of demand. Price elasticity of demand is defined as the percentage change in quantity demanded of a good divided by the percentage change in its price.

Because the demand curve slopes downward, an increase in price normally causes a fall in quantity demanded, so the raw value of PED is negative. For simplicity, economists usually refer to the absolute value of PED (ignoring the minus sign) when describing how responsive demand is.

Why percentage changes, not raw changes?

Using percentage changes, rather than the raw change in quantity and the raw change in price, matters for comparison between different markets.

Different goods are measured in different units, so a rise of 10 units in demand for a good sold by the kilogram cannot be compared directly with a rise of 10 units for a good sold by the litre or by the item. A ten-unit rise might be huge for one good and tiny for another.

Expressing both the change in quantity and the change in price as percentages of their original values removes the units, so PED can be used to compare the responsiveness of demand for completely different goods, such as rice and jewellery, on the same scale.

This is why PED, rather than simply the slope of a demand curve on a diagram, is the measure used to decide how a producer, consumer or government should respond to a price change. A steep or flat line drawn on a diagram only gives a rough visual impression, and that impression depends on the scale chosen for the axes, whereas the percentage-based PED figure does not change with the scale of the diagram.

PED as a pure number

PED has no units attached to it, because a percentage divided by a percentage leaves a plain number. This means a PED of 0.5 for rice can be compared directly with a PED of 2 for a particular brand of perfume, even though the two goods are sold in completely different markets and measured in different units.

How is PED calculated?

PED is found using the following formula.

PED = %ΔQd ÷ %ΔP

where Qd is quantity demanded, P is price, and the Greek letter Δ (delta) means "the change in". The percentage changes themselves are calculated as:

Change in quantity = Q2 − Q1

Change in price = P2 − P1

Here Q1 is the original quantity demanded and P1 is the original price, while Q2 and P2 are the new quantity demanded and new price. The change in quantity, ΔQ, is Q2 minus Q1, and the change in price, ΔP, is P2 minus P1. Each change is then turned into a percentage of its original value.

%ΔQd = (ΔQ ÷ Q1) × 100

%ΔP = (ΔP ÷ P1) × 100

Working through the formula step by step

1. Record the original price (P1) and original quantity demanded (Q1), and the new price (P2) and new quantity demanded (Q2).
2. Find the change in quantity, ΔQ = Q2 − Q1, and the change in price, ΔP = P2 − P1.
3. Convert each change into a percentage of its original value: %ΔQd = (ΔQ ÷ Q1) × 100, and %ΔP = (ΔP ÷ P1) × 100.
4. Divide %ΔQd by %ΔP to find PED, then take the absolute value (drop the minus sign) to describe how responsive demand is.

Worked example 1. At a price of $5 per unit, 15 units of a good are demanded. When the price rises to $7 per unit, demand falls to 12 units. Calculate the PED.

Answer: %ΔQd = (12 − 15) ÷ 15 × 100 = −3 ÷ 15 × 100 = −20%. %ΔP = (7 − 5) ÷ 5 × 100 = 2 ÷ 5 × 100 = +40%.

PED = −20 ÷ 40 = −0.5. Taking the absolute value, PED = 0.5, so demand is price inelastic.

A producer facing this inelastic demand could raise price and increase total revenue, from $5 × 15 = $75 to $7 × 12 = $84, since quantity demanded falls by a smaller percentage than the price rises.

Worked example 2. A good is demanded at 25 units when its price is $4 per unit. The price increases to $5 per unit and demand falls to 20 units. Calculate the PED.

Answer: %ΔQd = (20 − 25) ÷ 25 × 100 = −20%. %ΔP = (5 − 4) ÷ 4 × 100 = +25%. PED = −20 ÷ 25 = −0.8.

The absolute value, 0.8, is less than 1, so demand is inelastic. A producer could consider raising the price further, since demand for this good remains relatively unresponsive to price over this range.

A common slip in the calculation

A frequent error is dividing by the new value of price or quantity instead of the original value. The formula always uses the original price (P1) and the original quantity (Q1) as the base for each percentage change, because the percentage change describes the movement away from the starting point.

How is the result of a PED calculation interpreted?

The numerical value of PED tells a producer or analyst how strongly quantity demanded reacts to a price change.

Demand for essential goods is often found to be inelastic, while demand for luxury goods is seen to be highly responsive to price changes, giving a PED greater than 1.

Elasticity is not fixed for a good

The demand for a particular good can be elastic, unitary elastic or inelastic at different prices along the same downward-sloping demand curve, so the PED calculated at one price and quantity does not necessarily apply at another point on the same curve.

The dividing line at PED = 1 matters in practice because it marks the point at which total revenue is at its highest, a relationship explored fully later in this note.

A result such as PED = 0.5 means that a 10% rise in price would be expected to reduce quantity demanded by only around 5%, so revenue would be expected to rise.

A result such as PED = 2 means the opposite: a 10% rise in price would be expected to reduce quantity demanded by around 20%, so revenue would be expected to fall.

Worked example 3. A good has a PED of 1.4. Its price is raised by 5%. By roughly what percentage would quantity demanded be expected to fall, and would this be described as elastic or inelastic demand?

Answer: PED = %ΔQd ÷ %ΔP, so %ΔQd = PED × %ΔP = 1.4 × 5% = 7%.

Quantity demanded would be expected to fall by roughly 7%, a larger percentage than the 5% price rise.

Because the absolute value of PED, 1.4, is greater than 1, this is elastic demand, so a producer should be cautious about raising price, since total revenue is likely to fall.

Interpreting the number correctly, rather than simply labelling a good as elastic or inelastic, is what allows the PED calculation to support an actual pricing or taxation decision.

What do demand curves of different elasticities look like?

The shape and slope of a demand curve on a diagram give a visual impression of elasticity, although the actual numerical value still depends on the percentage changes used.

Two demand curves are drawn on separate price-quantity diagrams, price on the vertical axis and quantity on the horizontal axis.

The relatively elastic curve is drawn flatter: for a given rise in price shown on the vertical axis, there is a large fall in quantity demanded shown on the horizontal axis.

The relatively inelastic curve is drawn steeper: the same rise in price produces only a small fall in quantity demanded.

The two extreme cases

At the extremes, a perfectly inelastic demand curve is drawn as a vertical straight line: whatever the price, the quantity demanded stays at the same level, so a price change never leads to a change in demand, and PED is always 0.

A perfectly elastic demand curve is drawn as a horizontal straight line at a fixed price: at any other price, quantity demanded drops to zero, so PED is infinite.

The perfectly inelastic curve is a vertical line at a fixed quantity, showing PED = 0. The perfectly elastic curve is a horizontal line at a fixed price, showing PED = infinity.

A curve shaped like a rectangular hyperbola (bowed towards the origin) has PED = 1 (unitary elastic) at every point, because a given percentage change in price along it always produces an equal percentage change in quantity.

How do I draw these demand curves?

1. Draw the axes: price on the vertical axis and quantity demanded on the horizontal axis, and label both.
2. For relatively elastic demand, draw a flat downward-sloping line and label it D; for relatively inelastic demand, draw a steep downward-sloping line and label it D.
3. For perfectly inelastic demand, draw a vertical straight line at a fixed quantity; for perfectly elastic demand, draw a horizontal straight line at a fixed price.
4. For unitary elastic demand, draw a curve bowed towards the origin like a rectangular hyperbola, so that price times quantity is the same at every point.
5. Mark a price change with a movement along the curve, and read off the resulting change in quantity demanded to compare the responsiveness of the curves.

Draw four small price-quantity diagrams side by side. In the first, a flat downward-sloping line labelled D shows elastic demand. In the second, a steep downward-sloping line labelled D shows inelastic demand. In the third, a vertical line labelled D shows perfectly inelastic demand. In the fourth, a horizontal line labelled D shows perfectly elastic demand. Label price P on the vertical axis and quantity Q on the horizontal axis in each.

What determines whether demand is elastic or inelastic?

The price elasticity of demand for a good depends mainly on the nature of the good and the availability of close substitutes.

Necessities versus specific varieties

For example, demand for food as a whole does not change much even if food prices rise, because food is a necessity.

However, demand for one particular variety of a food item within a broader category, such as one specific variety of pulses, is more elastic, because consumers can switch to another close variety of pulses if its price rises, even though demand for pulses as a whole stays inelastic. The broader the category, the fewer substitutes it has, and so the more inelastic its demand tends to be.

Worked example 4. Good A has many close substitutes and is a luxury. Good B has no close substitutes and is a necessity. Which good is likely to have the higher PED, and why?

Answer: Good A is likely to have the higher PED. It has close substitutes, so buyers can switch away easily when its price rises, and it is a luxury, so buyers can more easily postpone or reduce purchases.

Good B, with no substitutes and classed as a necessity, is likely to have a low PED, because buyers continue to buy it even if the price rises.

A producer selling Good B could therefore raise price to increase total revenue, whereas a producer selling Good A should avoid raising price and instead compete on quality or branding.

How is PED related to total revenue?

A firm's total revenue (also called total spending by consumers on the good) depends both on price and on quantity sold.

Total revenue = P × Q

Whether total revenue rises or falls when price changes depends on how elastic demand is at that price.

On a price-quantity diagram with a downward-sloping demand curve, total revenue at any point equals the area of the rectangle formed by price (vertical side) times quantity (horizontal side).

Towards the top of the curve, where demand is elastic, a price rise shrinks this rectangle; towards the bottom of the curve, where demand is inelastic, a price rise enlarges this rectangle.

Total revenue is at its maximum at the midpoint of the curve, where PED = 1.

Working through a revenue change

Worked example 5. A firm sells 500 units a week at $4 per unit, giving total revenue of $2,000. It raises the price to $5 per unit, and weekly sales fall to 420 units.

Calculate the firm's total revenue before and after the price change, and explain whether demand is elastic or inelastic over this range.

Answer: Total revenue before the change = $4 × 500 = $2,000. Total revenue after the change = $5 × 420 = $2,100. %ΔQd = (420 − 500) ÷ 500 × 100 = −16%. %ΔP = (5 − 4) ÷ 4 × 100 = +25%.

PED = −16 ÷ 25 = −0.64, so the absolute value of PED is 0.64, which is less than 1, meaning demand is inelastic over this range.

This is consistent with the table above: when price rises and demand is inelastic, total revenue rises, which matches the rise from $2,000 to $2,100 seen here.

Because total revenue increased after the price rise, raising the price to $5 would increase the firm's revenue, although the firm would still need to weigh any change in costs before deciding on its final price.

Why does PED matter for consumers, producers and government?

Knowing the PED of a good is useful for the decisions made by each type of economic agent.

How do consumers use PED?

Consumers facing a price rise in a good with inelastic demand, such as a necessity with few substitutes, will end up spending a larger share of their income on it, since they cannot easily cut back the quantity bought.

This leaves less income for other goods, so a rise in the price of a necessity with inelastic demand hits consumers on low incomes hardest, because such goods take up a larger share of what they earn.

Where a good has close substitutes, demand for it is elastic, so if the price of one brand rises, consumers can switch to a rival brand and avoid paying the higher price.

How do producers use PED?

1. Producers deciding whether to raise or lower price need to know PED, because, as shown above, the effect of a price change on total revenue depends entirely on whether demand is elastic or inelastic at that price.
2. A producer facing inelastic demand can raise price to increase total revenue, whereas a producer facing elastic demand would lower price to increase total revenue, or compete on non-price factors such as quality and branding.
3. A producer launching a new product with many existing close substitutes should expect relatively elastic demand, and should therefore price cautiously and focus on building brand loyalty rather than relying on price rises to raise revenue.

How does government use PED?

Government uses PED when designing indirect taxes: taxing a good with inelastic demand, such as tobacco or fuel, raises more tax revenue reliably and causes only a small fall in quantity sold, because consumers keep buying despite the higher price.

Government can also use PED to judge how effective a subsidy will be at increasing consumption of a good it wishes to encourage: subsidising a good with elastic demand produces a larger increase in quantity bought for a given fall in price than subsidising a good with inelastic demand.

A government deciding between taxing a necessity or a luxury to raise a fixed amount of revenue should generally choose the good with the more inelastic demand, since the quantity sold, and so the size of the market, will shrink by less once the tax is in place.

Going beyond the syllabus

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

How does elasticity vary along a single straight-line demand curve?

Along an ordinary straight-line downward-sloping demand curve, elasticity is not the same at every point: it is highest (approaching infinity) near the top of the curve where price is high and quantity is low, falls to 1 at the midpoint of the curve, and falls further towards 0 near the bottom of the curve where price is low and quantity is high.

This means a single demand curve for one good can show elastic demand at high prices and inelastic demand at low prices, which is why economists always state the price range to which a particular PED figure applies.

How is elasticity measured geometrically along a straight-line demand curve?

Elasticity along a straight-line demand curve can also be measured geometrically: at any point, PED equals the ratio of the length of the demand curve below that point to the length above it.

This geometric method is not required for this topic but helps explain why elasticity changes continuously along a single straight demand curve rather than staying constant.

It also helps explain why a firm cannot simply assume that one PED figure applies across its whole range of possible prices.

Why do firms re-estimate PED after each price change?

A firm that calculates PED = 0.6 at its current price and quantity, and uses this to justify a price rise, cannot assume the same figure of 0.6 would still apply after several further price rises, because elasticity typically rises as price rises further up a straight-line demand curve.

In practice, firms often re-estimate PED after each significant price change, using fresh data on quantity demanded at the new price, rather than relying on a single historical estimate indefinitely.

This is one reason why real pricing decisions usually combine PED evidence with other market research rather than treating the formula as the only input.

Glossary

• Price elasticity of demand (PED): the percentage change in quantity demanded of a good divided by the percentage change in its price.
• Elastic demand: demand where PED is greater than 1, so quantity demanded changes by a larger percentage than price.
• Inelastic demand: demand where PED is less than 1, so quantity demanded changes by a smaller percentage than price.
• Unitary elastic demand: demand where PED equals 1, so quantity demanded changes by exactly the same percentage as price.
• Perfectly elastic demand: demand where PED is infinite; any price rise above a fixed price causes quantity demanded to fall to zero.
• Perfectly inelastic demand: demand where PED is 0; quantity demanded does not change at all when price changes.
• Total revenue: the total amount received by sellers from sales of a good, equal to price multiplied by quantity sold.
• Substitute good: a good that can be used in place of another to satisfy a similar want.
• Necessity: a good considered essential for everyday life, for which demand tends to be inelastic.
• Luxury good: a good not considered essential, for which demand tends to be elastic.
• Percentage change: the change in a variable expressed as a proportion of its original value, multiplied by 100.
• Demand curve: a graph showing the quantity of a good consumers are willing and able to buy at each price.
• Indirect tax: a tax imposed on spending, such as on the sale of a good, usually paid to government by the seller.
• Subsidy: a payment by government to a producer or consumer that lowers the price paid or received for a good.

Common errors and misconceptions

• Misconception: A steep demand curve on a diagram always means PED equals exactly 0. Correct: A steep curve only means demand is relatively more inelastic than a flatter curve; only a perfectly vertical demand curve gives PED exactly 0.
• Misconception: PED is the same at every point on a given straight-line demand curve. Correct: PED varies along a straight-line demand curve, falling from very high near the top (high price, low quantity) to very low near the bottom (low price, high quantity).
• Misconception: A price rise always increases a firm's total revenue. Correct: A price rise increases total revenue only if demand is inelastic at that price; if demand is elastic, a price rise reduces total revenue.
• Misconception: The minus sign in a PED calculation means the answer is wrong. Correct: The minus sign is expected, because price and quantity demanded usually move in opposite directions; economists normally quote the absolute value.
• Misconception: Elastic demand means a good is expensive, and inelastic demand means a good is cheap. Correct: Elasticity depends on responsiveness to price changes, not on the price level itself; a cheap good with no substitutes can still have inelastic demand.
• Misconception: All necessities have a PED of exactly 0. Correct: Necessities tend to have low PED (inelastic demand), but this is usually a value between 0 and 1, not exactly 0 unless demand is perfectly inelastic.

Exam-style questions with model answers

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

1. Price elasticity of demand measures the responsiveness of quantity demanded of a good to a change in its price.
2. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.

Q2. Market research shows that when the price of a good is $8 per unit, 40 units are demanded, and when the price falls to $6 per unit, 60 units are demanded. Calculate the PED. Show your working. [2 marks]

1. %ΔQd = (60 − 40) ÷ 40 × 100 = +50%, and %ΔP = (6 − 8) ÷ 8 × 100 = −25%.
2. PED = 50 ÷ (−25) = −2, so the absolute value of PED is 2, and demand is elastic over this price range.

Q3. Explain two factors that would make demand for a good more price elastic. [4 marks]

1. If the good has many close substitutes available, buyers can easily switch to another good when its price rises, so a given price rise causes a larger percentage fall in quantity demanded, making demand elastic.
2. If the good is a luxury rather than a necessity, buyers can more easily postpone or reduce their purchases when price rises, again producing a larger percentage change in quantity demanded relative to the percentage price change.

Q4. A firm sells 500 units a week at $4 each. It is considering raising the price to $5, after which it expects weekly sales to fall to 420 units. Calculate the firm's total revenue before and after the price change, and explain whether demand is elastic or inelastic over this range. [6 marks]

1. Total revenue before the change = $4 × 500 = $2,000.
2. Total revenue after the change = $5 × 420 = $2,100.
3. %ΔQd = (420 − 500) ÷ 500 × 100 = −16%.
4. %ΔP = (5 − 4) ÷ 4 × 100 = +25%.
5. PED = −16 ÷ 25 = −0.64, so the absolute value of PED is 0.64, which is less than 1.
6. Demand is therefore inelastic over this range, which is consistent with total revenue rising, from $2,000 to $2,100, when price rose.
7. This matches the general rule that a price rise increases total revenue only when demand is inelastic at that price, confirmed here by the actual rise in revenue.

Q5. Discuss whether a government should impose a large indirect tax on a good whose demand is price inelastic. [8 marks]

1. A tax on a good with inelastic demand raises price, but quantity demanded falls by a smaller percentage than the price rises, so the government can collect a large and reliable amount of tax revenue.
2. Because sales fall only a little, employment and output in the taxed industry are less disrupted than they would be if demand were elastic.
3. If the good is harmful, such as tobacco, the tax may also discourage some consumption, though the inelastic demand means the fall in quantity is small.
4. However, if the good is a necessity with few substitutes, the tax is likely to be regressive, taking a larger share of income from poorer households who cannot easily cut back their purchases.
5. The tax may also push up costs for firms that use the good as an input, and may encourage a black market or tax avoidance if the tax is very large.
6. On balance, a large tax on an inelastic good is effective for raising revenue, but the government should weigh the fairness of the burden and the risk of avoidance before deciding, and may prefer to tax luxuries or harmful goods rather than basic necessities.

Q6. State two determinants of the price elasticity of demand for a good. [2 marks]

1. Whether close substitutes for the good are easily available.
2. Whether the good is a necessity or a luxury.

Q7. At a price of $10 per unit, a firm sells 300 units a week. The firm raises the price to $11 per unit, and weekly sales fall to 270 units. Calculate the PED and state, giving a reason, whether total revenue rose or fell. [4 marks]

1. %ΔQd = (270 − 300) ÷ 300 × 100 = −10%, since the fall of 30 units is divided by the original quantity of 300 units.
2. %ΔP = (11 − 10) ÷ 10 × 100 = +10%, since the rise of $1 is divided by the original price of $10.
3. PED = −10 ÷ 10 = −1, so the absolute value of PED is 1, meaning demand is unitary elastic over this range.
4. Because demand is unitary elastic, total revenue fell only slightly: $10 × 300 = $3,000 before, compared with $11 × 270 = $2,970 after, a very small fall consistent with the rule that unitary elastic demand leaves revenue almost unchanged.

Q8. A good has a PED of 0.3. Explain what this value tells a producer about the likely effect of raising the price of this good. [3 marks]

1. A PED of 0.3 means demand for this good is inelastic, since the value is less than 1.
2. This means that quantity demanded would fall by a smaller percentage than the percentage rise in price, for example a 10% price rise would be expected to reduce quantity demanded by only around 3%.
3. Because quantity demanded falls by proportionally less than price rises, total revenue would be expected to rise if the producer raised the price.

Key takeaways

• Price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price.
• PED is usually negative, but economists normally refer to its absolute value when describing responsiveness.
• Demand is classed as elastic if PED is greater than 1, inelastic if less than 1, and unitary elastic if equal to 1.
• Perfectly inelastic demand is a vertical demand curve with PED equal to 0, and perfectly elastic demand is a horizontal curve with PED equal to infinity.
• Availability of close substitutes, necessity or luxury, the share of income spent, the time period, habit and brand loyalty all influence PED.
• Total revenue equals price multiplied by quantity; whether it rises or falls after a price change depends entirely on elasticity.
• A price rise increases total revenue if demand is inelastic, but reduces total revenue if demand is elastic.
• Producers, consumers and government all use PED, for pricing decisions, for predicting spending, and for designing taxes and subsidies.

Test yourself

What formula is used to calculate price elasticity of demand?

PED equals the percentage change in quantity demanded divided by the percentage change in price.

If PED for a good is 0.3, is demand elastic or inelastic?

Since 0.3 is less than 1, demand for this good is inelastic: quantity demanded changes by a smaller percentage than price.

What shape of demand curve shows perfectly elastic demand?

A horizontal straight line at a fixed price shows perfectly elastic demand, where any price rise causes quantity demanded to fall to zero.

Name two determinants of whether demand for a good is elastic or inelastic.

The availability of close substitutes, and whether the good is a necessity or a luxury.

If demand is elastic, what happens to total revenue when price rises?

Total revenue falls, because quantity demanded falls by a larger percentage than the price rises.

Why might a government prefer to tax a good with inelastic demand?

Because quantity demanded falls only a little after the tax, so the tax raises revenue more reliably with less loss of sales.

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

In the long run buyers have more time to change their habits and find alternatives, so quantity demanded responds more to a price change.