What you'll learn
Demand and supply tell you the direction in which quantity responds to a change. Elasticity tells you by how much, and that is what makes the model useful for a decision. A firm considering a price cut, a government considering a tax, a farmer deciding what to plant — all of them need the magnitude, not just the sign.
Elasticity is always a responsiveness ratio: the percentage change in the variable responding, divided by the percentage change in the variable causing it. Four versions are examined. Price elasticity of demand (PED) measures the response of quantity demanded to the good's own price. Income elasticity (YED) measures the response to income. Cross elasticity (XED) measures the response to the price of another good. Price elasticity of supply (PES) measures the response of quantity supplied to price.
The single most useful result in the topic is the link between PED and total revenue: cutting price raises revenue where demand is elastic and lowers it where demand is inelastic. That converts an abstract number into advice a business can act on.
By the end you should be able to calculate all four elasticities, interpret the sign as well as the magnitude, apply PED to revenue and tax decisions, and explain what determines each.
Key terms and definitions
Price elasticity of demand (PED) — percentage change in quantity demanded ÷ percentage change in price. Normally negative.
Elastic demand — PED greater than 1 in magnitude; quantity responds more than proportionately.
Inelastic demand — PED less than 1 in magnitude; quantity responds less than proportionately.
Unit elastic — PED exactly 1; quantity changes in the same proportion as price.
Income elasticity of demand (YED) — percentage change in quantity demanded ÷ percentage change in income.
Normal good — positive YED: demand rises with income. A luxury has YED above 1; a necessity has YED between 0 and 1.
Inferior good — negative YED: demand falls as income rises.
Cross elasticity of demand (XED) — percentage change in demand for one good ÷ percentage change in the price of another. Positive for substitutes, negative for complements.
Price elasticity of supply (PES) — percentage change in quantity supplied ÷ percentage change in price. Normally positive.
Midpoint (arc) method — using the average of the two prices and quantities as the base, so the answer is the same in both directions.
Core concepts
Reading the sign and the magnitude separately
The sign tells you the direction of the relationship; the magnitude tells you the strength. Both carry marks.
PED is negative because price and quantity move in opposite directions, and it is conventional to discuss its magnitude while noting the sign. YED and XED are different: there the sign is the answer. A negative YED identifies an inferior good; a positive XED identifies substitutes. Reporting the magnitude and omitting the sign loses the point of the calculation.
Why the base matters, and the midpoint method
Elasticity calculated from a starting price differs depending on which end you start from, because the percentage changes are measured against different bases.
Take demand falling from 1,200 units at $8 to 800 units at $12. Measured from $12, the fall in price to $8 gives a 50% rise in quantity against a 33.3% fall in price — a PED of 1.5. Measured from $8, the rise in price to $12 gives a 33.3% fall in quantity against a 50% rise in price — a PED of 0.67.
Same two points, two different answers. The midpoint method resolves this by using the average of the two prices and quantities as the base, giving the same result in either direction. Where an examiner supplies two price–quantity pairs rather than a single starting point, the midpoint method is usually what is wanted — and stating which method you used protects the mark either way.
PED and total revenue
This is the result worth knowing cold.
Where demand is elastic, a price cut raises total revenue: quantity rises proportionately more than price falls. Where demand is inelastic, a price cut lowers total revenue: the quantity gain is too small to offset the lower price. Where demand is unit elastic, total revenue is unchanged by a price change.
That last case gives a useful check. If total revenue is identical at two prices, PED across that range is exactly 1.
What determines each elasticity
PED depends on the availability of close substitutes (more substitutes, more elastic), whether the good is a necessity or a luxury, the proportion of income it absorbs, whether it is habit-forming, and the time allowed to adjust. Demand is almost always more elastic in the long run, because buyers need time to find alternatives.
YED depends on the nature of the good. Staples have low positive YED; restaurant meals and foreign travel have high positive YED; the cheapest staples can have negative YED as incomes rise and buyers trade up.
XED depends on how closely two goods substitute or complement each other. The closer the relationship, the larger the magnitude.
PES depends on how easily producers can change output: the availability of spare capacity, whether the good can be stored, the mobility of factors, and above all time. Agricultural supply is highly inelastic within a growing season and far more elastic over several seasons. That is a central fact for Caribbean agriculture and a ready example in any answer.
Why elasticity matters for policy
A tax on a good with inelastic demand raises substantial revenue and changes behaviour little — which is why tobacco, fuel and alcohol are taxed heavily. A tax intended to discourage consumption works poorly on such a good, so a government cannot usually maximise both revenue and behaviour change with the same tax.
The incidence of a tax also follows from elasticity: the more inelastic side of the market bears more of it. Where demand is inelastic and supply elastic, consumers pay most of a tax through a higher price.
Worked examples
Example 1 — PED by the midpoint method (6 marks)
In the bottled water market, quantity demanded is 800 at $12 and 1,200 at $8.
Change in quantity = 400; average quantity = (800 + 1,200) ÷ 2 = 1,000, so %ΔQ = 40%. Change in price = −$4; average price = ($12 + $8) ÷ 2 = $10, so %ΔP = −40%.
PED = 40 ÷ −40 = −1.0, that is, unit elastic.
Confirm it with revenue: at $12, total revenue is 12 × 800 = $9,600; at $8, it is 8 × 1,200 = $9,600. Revenue is unchanged, which is exactly what unit elasticity means. The two results agreeing is a strong check.
Example 2 — How the base changes the answer (5 marks)
Using the same two points but the point method:
From $12 falling to $8: %ΔQ = 400 ÷ 800 = +50%; %ΔP = −4 ÷ 12 = −33.3%; PED = 1.5, elastic.
From $8 rising to $12: %ΔQ = −400 ÷ 1,200 = −33.3%; %ΔP = 4 ÷ 8 = +50%; PED = 0.67, inelastic.
The same pair of points yields 1.5, 0.67 or 1.0 depending on the method and direction. That is not a flaw to be hidden but the reason the midpoint method exists, and saying so explicitly is worth a mark in an evaluation question.
Example 3 — Price elasticity of supply (5 marks)
Quantity supplied is 1,000 at $8 and 1,400 at $12. Calculate PES from the $8 base.
%ΔQ = 400 ÷ 1,000 = +40%. %ΔP = 4 ÷ 8 = +50%. PES = 40 ÷ 50 = 0.8, which is inelastic.
Interpretation: producers cannot expand output proportionately to the price rise in the time available, which is typical of a short-run agricultural or bottling operation with limited spare capacity. Over a longer period, with time to add capacity, PES would rise.
Example 4 — Income and cross elasticity (6 marks)
Incomes rise by 10%. Demand for imported cheese rises by 18%; demand for cassava falls by 6%.
Cheese: YED = 18 ÷ 10 = +1.8. Positive and above 1, so a normal luxury — demand grows faster than income. Cassava: YED = −6 ÷ 10 = −0.6. Negative, so an inferior good — buyers trade up as incomes rise.
Separately, the price of brand A juice rises 20% and demand for brand B rises 10%. XED = 10 ÷ 20 = +0.5. Positive, so the two are substitutes, though not especially close ones.
In each case the sign carries the classification and the magnitude carries the strength. An answer giving only the number has done half the work.
Example 5 — Advising on a price cut (5 marks)
A firm with inelastic demand for its product proposes a price cut to raise revenue.
The advice is that it will not work. With inelastic demand, the proportionate rise in quantity is smaller than the proportionate fall in price, so total revenue falls. To raise revenue the firm should consider raising price instead.
The qualification worth adding: this holds only within the range over which demand is inelastic, and only if rivals do not respond. A price rise that provokes competitors to hold their prices may shift demand away from the firm altogether, which the elasticity figure alone does not capture.
Common mistakes and how to avoid them
Reporting YED or XED without the sign. For those two, the sign is the classification.
Using absolute changes instead of percentages. Elasticity is a ratio of percentage changes throughout.
Mixing the midpoint and point methods within one answer. Choose one and state which.
Saying a price cut always raises revenue. It does so only where demand is elastic.
Confusing elastic supply with elastic demand. They have different determinants; time matters most for supply.
Assuming elasticity is constant along a curve. On a straight-line demand curve it varies from elastic at the top to inelastic at the bottom.
Treating a good as inelastic because it is expensive. What matters is the availability of substitutes and the share of income, not the price level.
How this links to your Internal Assessment
Elasticity turns a descriptive Internal Assessment into an analytical one, because it produces a number that supports a recommendation.
If you can obtain price and quantity data for a real good over time — a shop's own sales records are ideal — calculate PED and use it to advise on pricing. State the method you used and acknowledge that other things were not equal over the period, which is the honest limitation of any elasticity estimated from real data.
Survey data can support YED and XED estimates. Asking respondents how their purchases changed when incomes or a rival's price changed gives a rough figure, and being explicit that it is a stated rather than an observed response is better analysis than presenting it as precise.
Where you cannot obtain data, you can still reason qualitatively: identify the determinants that apply to your good and conclude whether demand is likely to be elastic or inelastic. A reasoned judgement with the determinants named earns well.
Exam technique for elasticity
Show the formula, the substitution and the answer, and then interpret it. A bare number earns a fraction of the available marks; the interpretation — elastic or inelastic, normal or inferior, substitutes or complements — is what the question is really testing.
State the sign for every elasticity and say what it means. For PED, note that it is negative and discuss the magnitude; for YED and XED, lead with the sign.
For revenue questions, set out the rule before applying it: elastic means a price cut raises revenue, inelastic means it lowers it. Then apply it to the figures given.
Command words are consistent. Calculate wants the working. Interpret or comment on wants the classification and what it means for the firm. Explain the determinants wants three or four developed, not eight listed. Discuss the usefulness of elasticity wants the limitations too — data is historical, other things rarely stay equal, and estimates assume rivals do not respond.
Quick revision summary
- Elasticity = percentage change in the responding variable ÷ percentage change in the causing variable.
- PED: elastic above 1, inelastic below 1, unit elastic at exactly 1 (in magnitude).
- Elastic demand: a price cut raises total revenue. Inelastic: a price cut lowers it. Unit elastic: revenue unchanged.
- Identical total revenue at two prices means PED over that range is 1.
- The point method gives different answers from each base; the midpoint method gives one answer — state which you used.
- YED: positive is normal (above 1 luxury, 0 to 1 necessity), negative is inferior. The sign is the classification.
- XED: positive means substitutes, negative means complements.
- PES: determined mainly by time, spare capacity, storability and factor mobility. Agricultural supply is very inelastic within a season.
- Demand is more elastic in the long run, because buyers need time to find substitutes.
- Taxes raise most revenue on inelastic goods, and change behaviour least on exactly those goods.
- Tax incidence falls more heavily on the more inelastic side of the market.
- Elasticity varies along a straight-line demand curve — elastic at the top, inelastic at the bottom.