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Educerie · IB Diploma · Economics
Unit 2 Microeconomics · 2.5 Elasticities of demand
What you must be able to do
| You must be able to | Level | What it looks like in the exam |
|---|---|---|
| Explain what elasticity means and draw relatively elastic and relatively inelastic demand | SL, HL | "Using a diagram, distinguish between price elastic and price inelastic demand" (4 marks) |
| State the PED formula and calculate PED from data | SL, HL | Paper 2: "Calculate the PED for good X" (2 marks). Show the working |
| Name the degrees of PED and their theoretical range | SL, HL | "Distinguish between perfectly elastic and unitary elastic demand" (4 marks) |
| Draw perfectly elastic, perfectly inelastic and unitary elastic demand | SL, HL | Any diagram question on elasticity |
| Explain the four determinants of PED | SL, HL | "Explain two factors that determine the PED for…" (4 marks) |
| Link PED to total revenue, and draw the link | SL, HL | Paper 2 calculation, and Paper 1 part (b) evaluation of a firm's pricing |
| Calculate a price change, a quantity demanded or a total revenue from PED and data | SL, HL | Paper 2, two or three marks, working shown |
| Explain why PED matters to firms and to governments | SL, HL | Paper 1 part (b), 15 marks, where you must evaluate |
| Explain and draw how PED changes along a straight-line demand curve | HL only | Paper 1 part (a) or Paper 3 |
| Explain why PED for primary commodities is generally lower than for manufactured products | HL only | Paper 1 part (b), or a Paper 3 data extract on commodity prices |
| State the YED formula, calculate YED, and read its sign and size | SL, HL | Paper 2 calculation plus one sentence of interpretation |
| Draw Engel curves for a necessity, a luxury and an inferior good | SL, HL | "Using an Engel curve, explain…" |
| Explain why YED matters to firms and to the structure of an economy | HL only | Paper 1 part (b), or Paper 3 |
Before you start
You need the demand curve from 2.1 and the difference between a movement along it and a shift of it, because every elasticity in this subtopic is measured along one curve. You also need normal and inferior goods from 2.1, since the sign of YED is exactly that distinction written as a number. Percentages are the only maths here, and you must be able to work one out from two figures.
1The idea in one paragraph
The demand curve tells you which way quantity moves when price moves. It does not tell you by how much, and "by how much" is where the money is. Elasticity is a number that answers it: divide the percentage change in the quantity by the percentage change in whatever caused it. Divide by the percentage change in price and you have price elasticity of demand. Divide by the percentage change in income and you have income elasticity of demand. Everything else in this subtopic is what those two numbers are worth once you have them.
2Elasticity, and the first of the two numbers
Elasticity is a measure of responsiveness: how much one variable changes when another one changes, written as a ratio of two percentage changes. Because both parts of the ratio are percentages, the units cancel and the answer is a plain number. That is the point of it. You can put the elasticity of a market measured in litres next to one measured in cinema tickets and the comparison still means something.
Figure 1 shows what responsiveness looks like on a diagram. The price falls by the same amount in both panels. In the left panel buyers move a long way; in the right panel they barely move at all.
The left panel is relatively elastic demand and the right panel is relatively inelastic demand. Say relatively, because those two words are a comparison and not a measurement. The measurement is this.
Price elasticity of demand (PED) measures how much the quantity demanded of a good responds to a change in its own price.
PED = percentage change in quantity demanded ÷ percentage change in price
Now do one. A bakery sells 800 loaves a week at €2.00 and puts the price up to €2.20. Sales fall to 760 loaves.
| Before | After | Change | Percentage change | |
|---|---|---|---|---|
| Price | €2.00 | €2.20 | +€0.20 | +0.20 ÷ 2.00 = +10% |
| Quantity demanded | 800 | 760 | −40 | −40 ÷ 800 = −5% |
PED = −5% ÷ +10% = −0.5
Three things about that answer.
The percentage change is always measured from the starting figure. Divide by 800, not by 760, and divide by 2.00, not by 2.20. The starting figure is the one before the change.
The sign is negative and you keep it. Price went up and quantity went down, so one of the two percentages is negative and the answer is negative. PED is negative for almost every good, because of the law of demand. Write the minus sign. Then, when you compare elasticities with each other, compare the sizes and ignore the sign: that is what the bars in the |PED| notation mean.
0.5 is smaller than 1, so this demand is price inelastic. The quantity moved less, in percentage terms, than the price did.
The formula also runs backwards, and Paper 2 often asks it that way. If you are told PED and one percentage change, you can find the other.
percentage change in quantity demanded = PED × percentage change in price
If the bakery's PED stays at −0.5 and it raises the price by a further 6%, quantity demanded changes by −0.5 × 6% = −3%: 760 loaves falls to about 737. Keep the sign in the multiplication and the direction comes out on its own.
3The degrees of PED, and the range they sit in
Three values of PED have names of their own, and each has a shape you must be able to draw. Figure 2 draws all three.
Perfectly elastic demand, PED = ∞. The curve is horizontal. At that one price buyers will take any quantity, and at a price one cent higher they will take nothing at all. No real market looks like this, but it is the limiting case, and it turns up again when you study a single firm in a very competitive market.
Perfectly inelastic demand, PED = 0. The curve is vertical. The same quantity is bought whatever the price. The quantity is fixed, so the percentage change in quantity is zero, so the whole fraction is zero. A life-saving medicine over a short period is the standard illustration.
Unitary elastic demand, PED = 1. The percentage change in quantity exactly matches the percentage change in price. The curve is a smooth bend, not a straight line, and every point on it traces out the same total revenue. That is why the two dashed rectangles at A and B in panel (c) have the same area.
Those three are the only curves that hold one value of PED from end to end. Every other curve changes its PED as you move along it, and a straight line changes it more than most, which is section 7.
Between the extremes sit the two ranges you will actually use. Figure 3 puts all five on one line.
- Relatively inelastic: |PED| between 0 and 1. Quantity moves proportionately less than price.
- Relatively elastic: |PED| between 1 and ∞. Quantity moves proportionately more than price.
The comparison is always with 1, never with zero. An answer that says "PED is 0.8, so demand is elastic because the number is big" scores nothing.
4What decides whether demand is elastic: the four determinants
The guide names four. Behind all four is one question: how easily can the buyer say no? Figure 4 sets them out with an example of each side.
The number and closeness of substitutes. This is the strongest of the four. If the price of one brand of biscuit rises, buyers reach for the next brand on the shelf and lose nothing, so demand for that brand is elastic. If there is no substitute, as with insulin for a diabetic patient, demand is inelastic. Notice that the same product can be both: demand for one brand of petrol is elastic, demand for petrol is inelastic, because a brand has close substitutes and the product has almost none. Define the market before you judge the elasticity.
The degree of necessity. A necessity is bought whether the price rises or not, so its demand is inelastic: bread, heating, the bus fare to work. A luxury can be put off, so its demand is elastic: a weekend away, a second pair of trainers. Necessity is judged by the buyer, not by you, and it shifts with who the buyer is.
The proportion of income spent on the good. A good that takes a large share of a household's budget is noticed when its price rises, so buyers act, and demand is elastic. Rent is the clearest case. A good that takes a tiny share is not worth reacting to: a 10% rise on a box of matches leaves most buyers doing exactly what they did before, so demand is inelastic.
Time. Demand is more elastic the longer the period you allow. In the month after a petrol price rise the car still runs on petrol and the journey to work still has to happen. Over three years people move house, change car, or change job, and the response is much larger. So the same good has a low short-run PED and a higher long-run PED. When a question gives you a time period, use it.
5PED and total revenue
Total revenue is what sellers receive: price multiplied by quantity sold. On a demand diagram it is a rectangle, from the origin out to the point on the curve.
A price rise pulls total revenue two ways at once. Every unit now sells for more, which adds revenue. Fewer units sell, which takes revenue away. PED decides which of the two is bigger, because PED is precisely the comparison of the two percentage changes. Figure 5 draws the same price rise in an inelastic and an elastic market, so you can compare the rectangle gained with the rectangle lost.
In panel (a) demand is inelastic. The quantity lost is small, so the amber rectangle gained is bigger than the clay rectangle lost, and total revenue rises. In panel (b) demand is elastic. The quantity lost is large, so the rectangle lost is bigger, and total revenue falls.
The bakery from section 2 makes the same point in numbers. Before: 800 × €2.00 = €1,600. After: 760 × €2.20 = €1,672. Demand was inelastic, the price went up, and revenue went up with it.
Figure 6 is the whole relationship on one card. Learn it in this form, because a Paper 2 question will give you a price change and expect the revenue direction in one line.
The trap is to remember it as "raising the price raises revenue". It does not, unless demand is inelastic. Half the marks in this subtopic sit on that "unless".
6Why PED matters to firms and to governments
This is the evaluation line, and the exam asks it as "discuss" or "evaluate", not as "state".
For a firm, PED tells it whether a price change will help. A firm facing inelastic demand can raise its price and take more revenue; a firm facing elastic demand raises its price and loses. The same logic runs a sale in the other direction: cutting the price only raises revenue if demand is elastic, which is why discounting works for fashion and does badly for bread. A firm can also work on its own PED rather than accept it, by building a brand that makes substitutes feel less close.
For a government, two uses pull in opposite directions, and saying so is worth marks.
- If the aim is revenue, tax goods with inelastic demand. Quantity barely falls, so the tax is paid on nearly the same number of units. Fuel, tobacco and alcohol are taxed everywhere for this reason.
- If the aim is to reduce consumption of something harmful, an inelastic good is exactly the wrong target, because the quantity hardly moves. The tax collects money and changes little behaviour.
A government that wants both at once from the same tax is asking for two things that cannot both be large. Say that in an evaluation and you have made the examiner's point for them. PED also decides who ends up paying an indirect tax, which is where 2.7 picks the story up.
Evaluate the number itself as well. Any PED you are given is an estimate from past data, it applies to the price range that data came from, it assumes everything else stayed still, and it will be different over a longer period. A policy built on one decimal place is built on sand.
7HLPED changes as you move down a straight-line demand curve
SL students can skip to section 9. HL students should read this twice, because it is the most commonly misunderstood result in the subtopic.
A straight-line demand curve has a constant slope. It does not have a constant PED. Those are two different things, and the reason is in the formula.
Write PED as the change in quantity over the change in price, times price over quantity:
PED = (ΔQ ÷ ΔP) × (P ÷ Q)
On a straight line the first bracket never changes: a €1 price cut always brings the same extra number of units. The second bracket changes constantly. At the top of the curve the price is high and the quantity is small, so P ÷ Q is large and PED is large. At the bottom the price is low and the quantity is large, so P ÷ Q is small and PED is small. Figure 7 marks what follows.
Take a concrete line. A coach company's demand curve runs from €10, where nobody travels, down to a price of zero, where 1,000 seats a week would go. Each €1 off the fare brings 100 more passengers, so ΔQ ÷ ΔP is −100 at every point.
| Fare | Passengers | P ÷ Q | PED = −100 × (P ÷ Q) | Total revenue |
|---|---|---|---|---|
| €8 | 200 | 0.040 | −4.0 elastic | €1,600 |
| €5 | 500 | 0.010 | −1.0 unitary | €2,500 |
| €2 | 800 | 0.0025 | −0.25 inelastic | €1,600 |
Three results to carry into the exam. PED falls steadily as you move down the curve, from infinity where the curve meets the price axis to zero where it meets the quantity axis. The midpoint of the line is where PED equals 1. And the half above the midpoint is elastic while the half below it is inelastic.
Now put section 5 next to it. Cutting the fare raises revenue while demand is elastic, leaves it unchanged for an instant at the midpoint, and lowers it once demand is inelastic. So total revenue is at its highest at the midpoint of a straight-line demand curve, which is what the third column of the table shows and what Figure 8 draws.
A firm sitting on the inelastic half of its demand curve is leaving money on the table: it should raise the price, since revenue rises and it sells fewer units while doing it.
8HLWhy primary commodities are less price elastic than manufactured products
Primary commodities are the raw output of farming, fishing, forestry and mining: wheat, coffee beans, crude oil, copper, timber. Manufactured products are goods that have been processed or assembled: a jar of coffee, a car, a phone. As a group, primary commodities have a lower PED. Four reasons, and a good answer gives at least two of them with an example.
They tend to be necessities, or the inputs to necessities. People need to eat and to heat their homes. A household cannot respond to a rise in the price of wheat by giving up food.
They have few close substitutes. Wheat is wheat. Copper wire in a cable can be replaced only by redesigning the product, which takes years. A manufactured product almost always sits on a shelf beside a rival that does the same job, so buyers switch easily and its PED is higher.
Each one takes a small proportion of the buyer's income. The wheat inside a loaf is a few cents of a €2 loaf. The price of wheat can double without the shopper changing what they buy. The manufactured good is bought whole, at its full price, out of a budget the buyer is watching.
They are mostly bought by firms as inputs, in fixed proportions, in the short run. A mill that is set up to process wheat cannot switch to something else this season. Its demand for wheat follows its own output, not the wheat price.
The consequence matters more than the reasons. When demand is inelastic, a shift in supply — a drought, a good harvest, a mine reopening — produces a very large change in price. That is why the prices of primary commodities swing far more than the prices of manufactured goods, and why the incomes of the producers who depend on them are unstable.
9Income elasticity of demand
The second number measures a different cause. Income elasticity of demand (YED) measures how much the quantity demanded of a good responds to a change in consumers' income.
YED = percentage change in quantity demanded ÷ percentage change in income
The price of the good is held still here. YED is not measured along a demand curve at all: a change in income shifts the whole curve, which is exactly the shift you learned in 2.1.
Work one household through a pay rise, from €40,000 to €44,000 a year. That is +€4,000 on €40,000, so income rose by +10%.
| Good | Before | After | % change in quantity | YED | What it is |
|---|---|---|---|---|---|
| Restaurant meals | 20 a year | 26 a year | +30% | +30 ÷ +10 = +3.0 | normal, income elastic |
| Bread | 150 loaves | 153 loaves | +2% | +2 ÷ +10 = +0.2 | normal, income inelastic |
| Intercity coach trips | 10 a year | 9 a year | −10% | −10 ÷ +10 = −1.0 | inferior |
Read the answer in two steps, in this order.
Read the sign first. It tells you what kind of good this is.
- Positive YED: income up, quantity up. A normal good.
- Negative YED: income up, quantity down. An inferior good, one the buyer moves away from as they can afford better. The coach trips are replaced by the train or by a car. "Inferior" describes the response to income and says nothing about the quality of the good.
Then read the size against 1. It tells you how strongly income pulls.
- YED between 0 and 1: income inelastic demand. Quantity rises, but by proportionately less than income. These are the necessities. Bread is the example above, and food as a whole behaves the same way.
- YED greater than 1: income elastic demand. Quantity rises by proportionately more than income. These are services and luxury goods: restaurant meals, holidays, private tuition, insurance.
An Engel curve puts the same information on a diagram: income up the vertical axis, quantity of the good across the horizontal. Figure 9 draws the three cases.
The necessity in panel (a) is steep, because a large rise in income buys only a little more bread. The luxury in panel (b) is shallow and gets shallower, because quantity runs ahead of income. The inferior good in panel (c) rises at low incomes and then turns back on itself: past a certain income the household starts buying less of it. That turning point is where YED changes from positive to negative, and it is the reason a good can be normal for one group of buyers and inferior for another.
Figure 10 is the whole of YED on one line, and it is the fastest thing to revise from.
10HLWhy YED matters
SL students can stop at section 9.
For a firm, YED is a forecast. A firm selling income elastic goods — holidays, restaurant meals, new cars — knows its sales will rise faster than the economy when incomes are growing and fall faster when they are not. That firm needs to plan for both: capacity and stock for the good years, and enough cash to survive the bad ones. A firm selling income inelastic necessities has steadier sales but will never grow quickly on rising incomes alone, so it grows by taking market share or by entering new markets instead. A firm that sells across a range of YED values is steadier than one that does not, which is one reason large firms hold both discount and premium ranges.
For the structure of the economy, YED explains a pattern that shows up in every country as it grows richer. Income rises; spending on food and other primary output rises by proportionately less, because its YED is low; spending on manufactured goods rises roughly in step; spending on services rises by proportionately more, because their YED is above 1. Demand therefore moves across the three sectors, and output and employment follow it. The primary sector shrinks as a share of the economy, manufacturing grows and then shrinks in its turn, and services take the largest share. That is the sectoral structure of an economy changing, and differences in YED are one of the main reasons it changes.
Evaluate it, though. YED is one force among several. Technology, trade, relative prices and government policy all move resources between sectors too, and a YED estimated from one period of one country's data is a weak basis for predicting another. Use YED as an explanation of a direction, not as a forecast of a figure.
11Where marks are lost
Dropping the minus sign. PED is negative for a normal downward-sloping demand curve. Calculate it, write it with its sign, and only then compare sizes. A PED written as "0.5" when the working gives −0.5 loses the mark in a two-mark calculation.
Attaching units to an elasticity. PED is not in euros, in percent, or in units. It is a pure number. "PED = −0.5" is right; "PED = −0.5%" is wrong.
Comparing PED with zero instead of with 1. "PED is 0.8, which is greater than zero, so demand is elastic" is a common and fatal sentence. The dividing line is 1.
Taking the percentage change from the wrong base. Percentages are measured from the starting value. Going from 800 to 760 is a fall of 5%, not 5.3%.
Confusing slope with elasticity. A straight-line demand curve has one slope and a different PED at every point. Saying "the curve is steep, so PED is constant" throws away the whole of section 7.
Assuming a price rise always raises revenue. It raises revenue only if demand is price inelastic. If demand is elastic, the same price rise lowers revenue.
Using "inferior" to mean low quality. Inferior means negative YED. A good can be well made and still be inferior for a household whose income has risen.
Dividing by the wrong percentage. In PED the denominator is the percentage change in price; in YED it is the percentage change in income. Write the formula down before you divide, every time, and you will not mix them.
12Draw it right
An elasticity diagram is marked on the same things as any demand diagram, plus two more that are specific to this subtopic.
- Axes labelled P (price, with units) and Q (quantity, with units and a time period), price vertical.
- The curve labelled D. In a two-panel answer, label the panels as well.
- For a relatively elastic and a relatively inelastic comparison, draw the same price change in both panels. If the price change is different, the diagram shows nothing.
- Both prices and both quantities marked, P₁ P₂ Q₁ Q₂, with dotted lines to the axes.
- A perfectly elastic curve is horizontal; a perfectly inelastic curve is vertical. Students reverse these under pressure. The one that looks like a wall is the one nothing gets through: vertical, PED = 0.
- For a revenue question, shade the rectangle gained and the rectangle lost in different shades and label them. The answer is which is bigger, so the marker must be able to see both.
- Unitary elastic demand is drawn as a bend, not a straight line, and a straight line is never labelled "constant elasticity".
- Refer to the diagram in your writing by number: "as Figure 5 shows, the area gained exceeds the area lost, so total revenue rises".
13Try it
Marks in brackets. Answers and marker's notes are at the end. Show your working on every calculation: method earns marks even when the arithmetic slips.
Q1. Define price elasticity of demand and state the formula used to calculate it. 2 marks
Q2. A cinema lowers its ticket price from €10 to €8. Weekly admissions rise from 1,200 to 1,680. Calculate the PED, and calculate the change in the cinema's total revenue. 4 marks
Q3. Explain, using examples, two determinants of the price elasticity of demand for a good. 4 marks
Q4. A household's annual income rises from €40,000 to €44,000. Its cinema trips rise from 15 to 21 a year, and its trips by intercity coach fall from 10 to 9. Calculate the YED for each good and identify what type of good each one is. 4 marks
Q5 (HL). Explain why the price elasticity of demand falls as you move down a straight-line downward-sloping demand curve. 4 marks
14In one breath
Elasticity is a percentage change divided by a percentage change, so it is a plain number with no units. PED is the percentage change in quantity demanded over the percentage change in price, it is negative, and it is compared with 1: below 1 is inelastic, above 1 is elastic, 0 is perfectly inelastic and vertical, infinity is perfectly elastic and horizontal, 1 is unitary. It depends on substitutes, necessity, the share of income, and time. If demand is inelastic, a price rise raises total revenue; if elastic, a price rise lowers it. HL: a straight line has a constant slope but a falling PED, elastic above the midpoint and inelastic below, with revenue highest at the midpoint, and primary commodities are less elastic than manufactures because they are necessities with few substitutes taking a small share of income. YED is the percentage change in quantity demanded over the percentage change in income: positive means normal, negative means inferior, below 1 means a necessity, above 1 means a service or luxury. HL: firms use YED to forecast, and differing YEDs move an economy from primary output towards services as it grows richer.
Answers
Q1. Price elasticity of demand measures the responsiveness of the quantity demanded of a good to a change in its own price. PED = percentage change in quantity demanded ÷ percentage change in price. 1 for responsiveness of quantity demanded to a change in the good's own price, 1 for the formula the right way up. "How much demand changes" scores 0, because demand is the whole curve and this is quantity demanded.
Q2. Percentage change in quantity demanded = (1,680 − 1,200) ÷ 1,200 = +40%. Percentage change in price = (8 − 10) ÷ 10 = −20%. PED = +40 ÷ −20 = −2, so demand is price elastic. Total revenue before = €10 × 1,200 = €12,000. Total revenue after = €8 × 1,680 = €13,440. Revenue rises by €1,440. This is what elastic demand predicts: the 40% rise in quantity outweighs the 20% cut in price. 1 for both percentage changes from the correct base, 1 for PED = −2 with the sign and the word elastic, 1 for both revenue figures, 1 for the change and a sentence linking it to the elastic value. An answer of "2" without the minus sign loses the sign mark but keeps the rest.
Q3. Any two of the four, each named, explained and exemplified. Number and closeness of substitutes: the more close substitutes a good has, the easier it is for buyers to switch when its price rises, so demand is more elastic. Demand for one brand of biscuit is elastic because the next brand sits on the same shelf; demand for insulin is inelastic because nothing else does the job. Degree of necessity: a necessity is bought whatever the price, so its demand is inelastic, such as the bus fare to work; a luxury such as a weekend away can be postponed, so its demand is elastic. 1 for naming each determinant, 1 for a correct explanation with an example of each. A list of four determinants with no explanation is capped at 2.
Q4. Percentage change in income = (44,000 − 40,000) ÷ 40,000 = +10%. Cinema trips: (21 − 15) ÷ 15 = +40%, so YED = +40 ÷ +10 = +4. Positive and greater than 1, so cinema trips are a normal, income elastic good — a service or luxury. Coach trips: (9 − 10) ÷ 10 = −10%, so YED = −10 ÷ +10 = −1. Negative, so intercity coach travel is an inferior good for this household. 1 for the percentage change in income, 1 for each correct YED with its sign, 1 for both classifications. Naming the sign rule without a calculated value scores 0 for that good; a correct value with no interpretation is capped at 2.
Q5 (HL). PED can be written as (ΔQ ÷ ΔP) × (P ÷ Q). On a straight line the slope is constant, so ΔQ ÷ ΔP is the same at every point. Moving down the curve, however, the price falls and the quantity rises, so the ratio P ÷ Q falls continuously. PED is therefore largest at the top, where price is high relative to quantity, and smallest at the bottom. It falls from infinity where the curve meets the price axis to zero where it meets the quantity axis, passing through 1 at the midpoint, so the upper half is elastic and the lower half inelastic. 1 for the formula in the ΔQ/ΔP × P/Q form, 1 for the slope term being constant, 1 for P ÷ Q falling as you move down, 1 for the conclusion with the midpoint and the two halves. An answer that only states "elastic at the top, inelastic at the bottom" with no reason is capped at 1.
Educerie · written from the published IB Diploma Programme Economics guide, first assessment 2022, section 2.5 Elasticities of demand. Original text, examples and questions. Diagrams drawn by Educerie. Last reviewed 11 September 2026.