Every business that has ever cut a price has been asking the same question: will enough extra customers arrive to make up for the money lost on each sale? Price elasticity of demand is the tool economists use to answer it. It measures how strongly buyers react when a price changes.
Price elasticity of demand
A measure of the responsiveness of quantity demanded to a change in price.
PED = % change in quantity demanded ÷ % change in priceFormulae are not supplied in the exam. You must recall this.
Calculating PED
A café raises the price of a coffee from 10 to 12 riyals. Weekly sales fall from 500 cups to 400. Calculate PED.
Ignore the minus sign when judging the strength of the response, and read only the size of the number. A coefficient between 0 and 1 means demand is inelastic: buyers barely react, so quantity changes proportionately less than price. A coefficient greater than 1 means demand is elastic: buyers react sharply, and quantity changes proportionately more than price.
The negative sign is not an error. Demand curves slope downward, so price and quantity always move in opposite directions and PED is almost always negative. Show the sign in your working, then discuss the magnitude. Candidates who claim the negative sign means demand is inelastic lose the interpretation mark every time.
A 10% fall in the price of a good causes quantity demanded to rise by 25%. What is the PED?
Whether demand is elastic or inelastic depends mainly on how easily buyers can escape the price rise. Close substitutes make demand elastic, because customers simply switch. Necessities tend to be inelastic, since people buy them regardless. Goods taking a large share of income are more elastic, because the price change is felt more keenly. Habit-forming goods are inelastic. Time matters too: demand becomes more elastic in the long run as buyers find alternatives.
Sketch two demand curves through the same point, one elastic and one inelastic, and show how the same price rise affects quantity differently on each.
A steeper curve indicates more inelastic demand over that range. Label both axes and mark the quantity change on each.
Two extreme cases complete the picture. Perfectly inelastic demand has a PED of 0: quantity does not change at all when price changes, and the demand curve is vertical. Perfectly elastic demand has an infinite PED: at one price buyers will take any quantity, but at any higher price they buy none, and the demand curve is horizontal. Unitary elasticity, a PED of exactly 1, means quantity changes by the same percentage as price.
PED, spending and revenue
The amount consumers spend on a good and the revenue firms earn from it are the same number: price multiplied by quantity. PED tells you what happens to it when price changes. If demand is elastic, a price rise loses so many sales that total spending and revenue fall, and a price cut raises them. If demand is inelastic, a price rise loses few sales, so spending and revenue rise, and a price cut lowers them. If demand is unitary, revenue stays the same.
Whether a price change raises revenue
A cinema cuts its ticket price from $8 to $6 and weekly attendance rises from 1,000 to 1,500. A bus company raises its fare from $2.00 to $2.50 and weekly passengers fall from 10,000 to 9,000. For each, calculate PED and the change in revenue.
Draw two demand curves, one steep (inelastic) and one flat (elastic). On each, show the same price rise and shade the revenue gained from the higher price on units still sold and the revenue lost from units no longer sold.
Revenue rises when the gained rectangle is bigger than the lost one. On the inelastic curve it is; on the elastic curve it is not. The two rectangles are the whole argument in one picture.
PED matters for decisions across the economy. Consumers facing a price rise on a good with inelastic demand, such as fuel, end up spending more of their income on it. Firms use PED to set prices: they raise prices where demand is inelastic and cut them where it is elastic. Workers are affected because a firm whose demand is elastic may lose many sales, and so jobs, if its costs and prices rise. Governments tax goods with inelastic demand, such as tobacco and petrol, because consumption falls only a little, so the tax raises a lot of revenue, though for the same reason it does less to cut consumption.
PED and total revenue
This is where elasticity stops being an abstraction and starts making firms money. Total revenue is price multiplied by quantity, so a price change pulls those two terms in opposite directions. Which one wins is decided entirely by PED. Where demand is inelastic, the quantity effect is weak, so raising price raises revenue. Where demand is elastic, the quantity effect dominates, so raising price lowers revenue and cutting price raises it. At unit elasticity, revenue is at its maximum and a small price change leaves it unaltered.
Why a price cut can raise revenue
- A firm lowers price, so revenue per unit sold falls.
- The lower price attracts buyers who were previously priced out and encourages existing buyers to purchase more.
- Quantity demanded therefore rises.
- If PED is greater than 1, the percentage rise in quantity exceeds the percentage fall in price.
- The quantity gain outweighs the price loss.
- Total revenue rises, since TR = P × Q and Q has grown proportionately more than P has fallen.
- The reverse holds where PED is less than 1, so a firm facing inelastic demand raises revenue by raising price instead.
AO2 analysis is 40% of the marks. Examiners credit the linking between steps rather than the conclusion. Never jump from 'price fell' to 'revenue rose'.
Practise this chain →Revenue effect of a price rise
Return to the café. Did raising the price from 10 to 12 riyals increase revenue?
PED is not a fixed property of a good. Along a straight-line demand curve it falls continuously as you move down the curve. Near the top, price is high and quantity is low, so a given absolute change is a large percentage of quantity and a small percentage of price, making demand elastic. Near the bottom the reverse holds and demand is inelastic. Unit elasticity sits at the midpoint. This is why a firm cannot simply describe its product as elastic; it must specify the price range.
Draw a straight-line demand curve with the corresponding total revenue curve beneath it. Mark the elastic range, the unit elastic point and the inelastic range.
Total revenue peaks exactly where PED equals −1, at the midpoint of the demand curve. Line the two diagrams up vertically so the quantity axes match.
When a question asks you to explain a revenue outcome, always route your answer through PED explicitly. State what the coefficient implies about relative percentage changes, then say which effect dominates, then give the revenue conclusion. Answers that leap from 'price rose' to 'revenue rose' skip the analysis marks entirely.
Two related measures complete the picture. Income elasticity of demand compares the percentage change in quantity demanded with the percentage change in income, and its sign classifies the good: positive for normal goods, negative for inferior goods. Cross elasticity of demand compares the percentage change in quantity demanded of one good with the percentage change in the price of another, and its sign reveals the relationship: positive for substitutes, negative for complements.
Income and cross elasticity
Income elasticity of demand (YED)
A measure of the responsiveness of quantity demanded to a change in income.
Cross elasticity of demand (XED)
A measure of the responsiveness of quantity demanded of one good to a change in the price of another good.
YED = % change in quantity demanded / % change in income. XED = % change in quantity demanded of good A / % change in price of good BFor PED only the size matters and the sign is almost always negative. For YED and XED the sign is the first thing to read, because it tells you what kind of good or relationship you are looking at. Formulae are not printed in any 9708 paper, so recall both.
The sign and size of YED classify a good. A negative YED means an inferior good: as incomes rise, people buy less of it and switch to something they prefer, as with the cheapest own-brand foods or long-distance bus travel. A positive YED means a normal good, and normal goods divide further. A YED between 0 and 1 means a necessity: demand rises with income, but proportionately less, as with basic food and utilities. A YED above 1 means a luxury, sometimes called income elastic: demand rises proportionately more than income, as with foreign holidays, restaurant meals and designer clothing. The same good can change category as a country gets richer, since what counts as a luxury at one income level becomes a necessity at another.
Calculating and classifying YED and XED
Average household income rises from $40,000 to $44,000. Over the same period, weekly sales of good A rise from 200 to 230, of good B from 500 to 520, and of good C fall from 300 to 270. Separately, the price of coffee rises by 20%, after which demand for tea rises by 10% and demand for sugar falls by 6%. Calculate YED for A, B and C and XED for tea and sugar, and classify each.
XED is read the same way. A positive value means the goods are substitutes, and the larger it is, the closer the substitutes: two brands of the same petrol might have a very high XED, tea and coffee a modest one. A negative value means complements, goods used together, such as printers and ink cartridges or cars and fuel, and the larger its size, the more tightly they are linked. A value close to zero means the goods are unrelated. What determines YED is mainly whether the good is seen as a necessity or a luxury, the income level of the buyers, and the share of income spent on it. What determines XED is how closely the goods can replace or accompany each other, which depends on the product, on brand loyalty and on time, since substitution is easier once buyers have had time to find alternatives.
Both measures are used in decisions. A firm selling luxuries knows its sales will rise strongly in a boom and fall sharply in a recession, so it plans capacity and stock accordingly, while a firm selling inferior goods may do well in a downturn; firms often hold a mix of products to spread that risk. A firm watching a rival's price uses XED to judge how many customers it will lose or gain, and one selling complements, such as games consoles and games, may price the first low to sell more of the second. Governments use YED to forecast demand for services such as healthcare as incomes grow, and to judge which taxes will raise more revenue over time, and competition authorities use XED to decide whether two firms' products are close enough substitutes for a merger between them to reduce competition.
A good has an income elasticity of demand of -0.6. If incomes rise by 5%, what happens to quantity demanded?
YED and XED questions are marked on the sign as much as on the number. Say what the sign shows before anything else: negative YED means inferior, positive means normal, above 1 means luxury; positive XED means substitutes, negative means complements. Then use the size. Candidates who compute the value correctly and never interpret it lose half the marks.
Applied context
Airlines split a single flight into fare classes precisely because PED differs across passengers. A business traveller flying on Tuesday for a Wednesday meeting has almost no substitute and faces highly inelastic demand. A family booking a holiday six months ahead can move dates, airports or destinations, so their demand is elastic. Same aircraft, same route, prices differing by a factor of five. Fuel duty works on the same principle from the other direction: governments tax petrol heavily because demand is inelastic in the short run, so revenue holds up even as the tax rises.
One example understood properly beats four mentioned in passing. Be ready to say why demand is inelastic in your example, not merely that it is.