Price elasticity of demand, explained simply

Two cafés raise the price of a coffee from $3 to $3.60. The café inside a train station loses 12 customers a day. The café on a street with five other cafés loses 120. Same price rise, very different reaction. Elasticity is the number that measures that reaction.

Two cafés, one price rise

At $3 both cafés sell 200 cups a day. Then both go to $3.60, a rise of 20%. The station café sells 188 cups: a fall of 6%. The café street sells 80 cups: a fall of 60%. Someone with a train to catch in six minutes has nowhere else to go; a customer on the street just walks next door.

The formula: turn the reaction into one number

Divide the % change in cups by the % change in price. A % change is (new − old) ÷ old, times 100.

Quantity falls when price rises, so the ratio is really negative; economists drop the minus sign. Read the number like this: every 1% added to the price costs the station 0.3% of its sales and the street 3%.

Elastic or inelastic: compare with 1

The dividing line is 1, not 0. Above 1, sales fall by a bigger % than the price rises: demand is elastic, like the café street at 3. Below 1, sales fall by a smaller % than the price rises: demand is inelastic, like the station at 0.3. Exactly 1 is unit elastic: sales move by the same % as the price.

Try one: bus fares rise by 10% and trips fall by 4%. Elasticity is 4 ÷ 10 = 0.4, below 1: inelastic. Most people still need to get to work.

Why it matters: the revenue rule

What a café cares about is takings, also called total revenue: price × cups sold. Here elasticity decides everything.

The café street took in $3 × 200 = $600 a day. At $3.60 it takes in $3.60 × 80 = $288: each coffee earns more, but far fewer are sold. The station café at $3.60 takes in $3.60 × 188 = $676.80, more than before: few customers leave, and each pays more.

This is the revenue rule: with elastic demand a price rise lowers takings, with inelastic demand it raises them. Backwards it is the total revenue test: price and takings moving the same way means inelastic, opposite ways means elastic. On a straight demand line takings peak in the middle, where elasticity is exactly 1: for the café street, $2 and 400 cups, $800 a day.

What makes demand elastic?

• Substitutes. The more alternatives, the more elastic. Gasoline at one particular station is elastic (drivers fill up down the road); gasoline in general is not.
• Need or treat. Needs, like a medicine, are inelastic; treats, like a movie night, are elastic.
• Share of budget. A big expense makes people look harder. Salt is a tiny share of anyone's budget, so nobody reacts to its price.
• Time. Over months, people find other options, so demand gets more elastic.

The trap on tests

The first trap is to confuse elasticity with slope. The café street's line has the same slope everywhere, yet elasticity is 3 at $3 and 1 at $2: a % change depends on where you start, and 20 fewer cups is a lot out of 100 but little out of 400. So compare two curves from the same point, as the first graph does at $3.

The second trap is the formula itself. The AP exam (the Advanced Placement economics exam taken by many US high-school students) and many textbooks use the midpoint method: each change is divided by the average of the old and new values, so the answer is the same going up or down. Take a 1,000-seat hall where every seat sells at $20 and only 600 would come at $25. The simple method gives 40% ÷ 25% = 1.6; the midpoint method gives 50% ÷ 22.2% = 2.25. Different number, same verdict: elastic, and the higher price loses money ($25 × 600 = $15,000 instead of $20,000). Use the method your course asks for.

Quick check