Price elasticity of demand and total revenue

Last time

Before we start: last time, in Market failure, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.

How much do buyers react?

When the price of salt goes up, people buy almost the same amount. When the price of one brand of soft drink goes up, many switch to another brand. The law of demand says quantity falls, but not by how much. Price elasticity of demand measures how much.

The definition

Price elasticity of demand, or PED, measures the responsiveness of quantity demanded to a change in price. If quantity demanded changes by a bigger percentage than price, demand is price elastic. If by a smaller percentage, it is price inelastic. Always use the word responsiveness, or sensitivity, in a definition. That is where the marks are.

The formula

PED equals the percentage change in quantity demanded divided by the percentage change in price. Example: the price of coffee rises by 10 per cent and quantity demanded falls by 3 per cent. PED is minus 3 divided by 10, which is minus 0.3. The examiner warned that some candidates turned the formula upside down and got 3.3. Quantity always goes on top.

Reading the number

PED is usually negative, because price and quantity move in opposite directions. Ignore the sign and read its size from this table.

A worked example

A price falls from 20 dollars to 16 dollars. The change is minus 4, and minus 4 over 20 is a fall of 20 per cent. Quantity demanded rises from 100 to 130. That is plus 30 over 100, a rise of 30 per cent. PED is 30 divided by minus 20, which is minus 1.5. Its size is more than 1, so demand is price elastic.

What makes demand elastic

Substitutes: the more close substitutes a product has, the more elastic its demand. One brand of soft drink has many substitutes. Share of income: a product that takes a large part of income, like a car, has more elastic demand than a cheap one, like a box of matches. Necessity and habit: necessities and addictive goods have inelastic demand. Time: demand becomes more elastic as people have longer to find alternatives.

Examples to use

Inelastic demand: salt, petrol, cigarettes, medicines, and basic food such as wheat flour. People still need them when the price rises. Elastic demand: one brand among many, foreign holidays, luxury goods, and anything with close substitutes. In an answer, never just give the example. Say why: no close substitutes, a necessity, or a large share of income.

PED and total revenue

Total revenue is price times quantity sold. What happens to it after a price change depends on PED. If demand is inelastic, a price rise increases total revenue, because quantity falls by a smaller percentage than price rises. If demand is elastic, a price rise decreases total revenue, because quantity falls by a bigger percentage.

Revenue, worked

A firm sells 100 units at 10 dollars, so revenue is 1,000 dollars. It raises the price to 12 dollars. If demand is inelastic, it still sells 95, and revenue rises to 1,140 dollars. If demand is elastic, sales fall to 70, and revenue falls to 840 dollars.

Why PED matters

Firms use PED to set prices. A firm with inelastic demand can raise its price and earn more revenue. One with elastic demand may cut its price to sell much more. Governments tax products with inelastic demand, such as petrol and cigarettes, because tax revenue stays high when people keep buying. But if the aim is to cut consumption, a tax works better when demand is elastic.

Making demand less elastic

The mark scheme lists ways a firm can make demand for its product more price inelastic. First, advertising and branding, to make the product seem special. Second, removing substitutes: merging with or taking over rivals, so customers have fewer alternatives. Third, building loyalty and habit, through quality, loyalty schemes and good service.

Mistakes that lose marks

Mistake one: putting price on top of the formula. Quantity demanded always goes on top. Mistake two: giving the answer as a percentage, such as 16 per cent. PED is a number with no units. Mistake three: saying a price rise always raises revenue. It depends on PED. The fix: quantity on top, a plain number, and revenue linked to PED.

The full-marks tip

The full-marks tip: use the word responsiveness in the definition, and put quantity demanded on top of the formula. When revenue is asked, say whether demand is elastic or inelastic, then which way revenue moves.

On one card

So, on one card: price elasticity of demand. Keep it for revision.