Price elasticity of demand

Price elasticity of demand, or PED, answers one question: when the price changes, how much does the quantity people buy change? A firm deciding whether to cut its price and a government deciding what to tax both need that answer, which is why PED turns up so often in the exam.

The formula

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

Say the price of a bus ticket rises by 10 per cent and the number of tickets sold falls by 5 per cent. PED is 5 divided by 10, which is 0.5.

Work out each percentage change as the change divided by the original figure, then multiply by 100. Show your working. In a calculation question the method usually carries a mark of its own, so you can still score even if the final number is wrong.

The minus sign

For almost every good, price and quantity move in opposite directions, so the answer comes out negative. Most mark schemes accept the number on its own, but the safest thing is to write the value and then say what it means. Write 0.5, and then write that demand is price inelastic. The words are what earn the mark.

Reading the number

• Below 1. Demand is price inelastic. Quantity changes by proportionally less than price. The curve is steep.
• Above 1. Demand is price elastic. Quantity changes by proportionally more than price. The curve is flatter.
• Exactly 1. Unit elastic. The two percentage changes match.
• Zero. Perfectly inelastic. Quantity does not change at all, so the curve is vertical.
• Infinity. Perfectly elastic. The curve is horizontal. This one is rare in real markets.

What makes demand inelastic

• Few substitutes. If there is nothing else that does the job, buyers have to pay.
• The good is a necessity, such as basic food, medicine or fuel for getting to work.
• It takes up a small share of income. Nobody stops buying salt because it went up by two rupees.
• The good is addictive or habit forming.
• There is little time to react. Demand is usually more elastic in the long run, because people find alternatives eventually.

Turn each of those around and you get the reasons demand is elastic: many close substitutes, a luxury rather than a necessity, a large share of income, and plenty of time to switch.

Why firms care: total revenue

Total revenue is price times quantity. It is the money coming in from sales, before any costs are taken off.

• If demand is inelastic and the firm raises the price, revenue rises. The price is up a lot and quantity is down only a little.
• If demand is inelastic and the firm cuts the price, revenue falls.
• If demand is elastic and the firm raises the price, revenue falls. It loses more in sales than it gains on each unit.
• If demand is elastic and the firm cuts the price, revenue rises. This is why a sale works for clothes but not for electricity.

Be careful with the word profit. Revenue is not profit. Profit is revenue minus costs, and a question about revenue is not asking you about costs.

Where else it shows up

Governments use PED when they choose what to tax. An indirect tax on a good with inelastic demand, such as petrol or cigarettes, raises a lot of money, because people keep buying it. The same tax on a good with elastic demand raises less, because people simply buy less of it. That is also why a tax meant to change behaviour works better when demand is elastic, and a tax meant to raise money works better when demand is inelastic.

Farmers meet PED too. Food usually has inelastic demand, so a very good harvest can push the price down so far that farmers earn less than they did in a normal year.

Drawing it

The 2281 and 9708 syllabuses both ask you to draw demand curves showing different PED. You do not need to write numbers on the axes. A steep curve for inelastic demand and a flat curve for elastic demand is enough, as long as both axes are labelled and the curve is labelled D.

A good way to show it is to draw the same size price change against each curve, then drop lines down to the quantity axis. The flat curve gives the much bigger change in quantity, and the picture makes the point for you.

The mistakes to avoid

• Saying demand is elastic without saying what makes it elastic. Always give the reason.
• Confusing PED with income elasticity or cross elasticity. PED is about the price of the good itself.
• Writing that demand is elastic because the good is expensive. Price level is not the point. What matters is whether buyers have somewhere else to go.