PED on a diagram

Elastic, inelastic, perfectly elastic, perfectly inelastic and unitary demand curves, and why PED changes along a straight line.

You can see elasticity on a diagram.

Five demand curves to know, each with a PED value:

• Elastic: relatively flat. PED bigger than 1 (ignoring the sign).
• Inelastic: relatively steep. PED between 0 and 1.
• Perfectly inelastic: vertical. PED = 0.
• Perfectly elastic: horizontal. PED = infinity.
• Unitary elastic: a curve, a rectangular hyperbola. PED = −1 all the way along.

One warning: steepness only tells you about elasticity when you compare curves through the same point, on the same axes. Along one straight line, PED changes, as you will see.

Think first

Petrol goes up 10p a litre at every station in town.

Then, separately, just one station puts its price up by 10p while the others do not.

In which case do drivers cut the petrol they buy from that station by more?

If only one station is dearer, drivers simply go to another: demand for one station’s petrol is very elastic. If every station is dearer, there is nowhere else to go: demand for petrol as a whole is inelastic. On a diagram, the first is a flat demand curve and the second a steep one.

Step by step

1. Two demand curves through the same point. The flat one is relatively elastic: a small change in price causes a big change in quantity. The steep one is relatively inelastic: even a big change in price barely changes quantity. Relatively means compared with each other: the flatter curve is more elastic, but that does not on its own tell you whether PED is above or below 1.

2. The two extremes. Vertical: perfectly inelastic, PED = 0. Quantity is the same at every price, like a drug a patient must have. Horizontal: perfectly elastic, PED = infinity. Raise the price at all and you sell nothing, like one wheat farmer selling at the market price.

   Check: A good has a vertical demand curve. What is its PED?

   Vertical: quantity demanded does not change at all whatever the price, so the % change in quantity is 0 and PED = 0.

3. Unitary elastic demand is a curve, not a straight line. Every percentage change in price is matched by the same percentage change in quantity, so spending, price times quantity, is the same at every point: here £100. The two rectangles have the same area.

4. Now one straight-line demand curve. Its slope is the same everywhere: each £2 cut in price adds 2 to quantity.

   Check: The slope of this line is the same all the way along. As you move down the line, what happens to PED, ignoring the sign?

   PED uses percentage changes, not the slope. Lower down, price is low and quantity is high, so the same change is a bigger percentage of price and a smaller percentage of quantity.

5. Near the top, price is high and quantity is low. A change of 2 in quantity is a big percentage of 4: +50%. A change of £2 in price is a small percentage of £16: −12.5%. PED = −4: very elastic.

   Check: Near the top of the line, the price falls from £16 to £14 and quantity rises from 4 to 6. What is the PED?

   Quantity +50% (2 on 4). Price −12.5% (2 on 16). PED = 50 ÷ −12.5 = −4: very elastic.

6. Near the bottom it flips. A change of 2 in quantity is a small percentage of 14: about +14%. A change of £2 is a big percentage of £6: about −33%. PED is about −0.43: inelastic. Same slope, very different PED.

7. At the top PED is −4, near the bottom about −0.43.

   Check: Where on a straight-line demand curve is PED exactly −1?

   PED falls steadily from elastic at the top to inelastic at the bottom, so it passes through −1 halfway along.

8. Halfway along, PED is exactly −1. Above the midpoint demand is elastic, below it inelastic. So a straight line is not "an elastic curve" or "an inelastic curve": it is both, depending on where you are.

What your diagram must show

• A straight, downward-sloping demand curve meeting both axes
• The midpoint marked
• PED = −1 labelled at the midpoint
• Elastic labelled above the midpoint
• Inelastic labelled below the midpoint

A common mistake

A vertical demand curve is perfectly inelastic, PED = 0: quantity demanded never changes, whatever the price. Perfectly elastic is horizontal.

Exam question

Using calculations, outline how PED changes along a straight-line demand curve.

Model answer

A straight-line demand curve has the same slope all the way along, but PED is the ratio of percentage changes, and these vary along the line.

Near the top of the curve, price is high and quantity is low. If the price falls from £16 to £14, quantity rises from 4 to 6. That is a +50% change in quantity but only a −12.5% change in price, so PED = 50 ÷ −12.5 = −4: demand is price elastic.

Near the bottom, price is low and quantity is high. If the price falls from £6 to £4, quantity rises from 14 to 16: +14% in quantity but −33% in price, so PED ≈ −0.43: demand is price inelastic.

So PED falls, ignoring the sign, as we move down the line. It is exactly −1 at the midpoint, elastic above it and inelastic below it.

Elasticity: exam-style questions