Price Elasticity of Demand (PED)
Allocation of Resources
Total revenue (TR) = Price × Quantity.
The same Price × Quantity figure can be read from two directions. To the firm it is (the money it takes in); to consumers it is their total expenditure (the money they spend on the good). The two are always equal, so everything that follows about a firm's revenue applies in mirror image to consumer spending: when a price change raises a firm's revenue, it raises consumer expenditure by exactly the same amount.
When a firm changes its price, two things happen at once:
- Price goes up (or down): that pushes TR up (or down).
- Quantity demanded goes down (or up): that pulls TR in the opposite direction.
Whether total revenue ends up higher or lower depends on which of the two effects is bigger, and that is exactly what PED measures.
The PED-TR rule
| If demand is... | A price rise does what to TR? | A price fall does what to TR? |
|---|---|---|
Inelastic (|PED| < 1) | TR rises (Qd falls only a little) | TR falls (Qd rises only a little) |
Unitary elastic (|PED| = 1) | TR unchanged | TR unchanged |
Elastic (|PED| > 1) | TR falls (Qd falls a lot) | TR rises (Qd rises a lot) |
The rule can also be shown as a calculation, which is how a question usually asks for it. Take a chocolate bar selling 1,000 bars a day at $2.00 each. The price rises to $2.20 and daily sales fall to 950.
- Before: TR = $2.00 × 1,000 = $2,000 a day
- After: TR = $2.20 × 950 = $2,090 a day
- PED = −5% ÷ +10% = −0.5, so demand is inelastic and total revenue rises by $90. Consumers now spend $2,090 a day instead of $2,000, which is the same $2,090 the firm receives as total revenue.
Now take a designer handbag selling 1,500 units a month at $200. The price rises to $240 and monthly sales fall to 900.
- Before: TR = $200 × 1,500 = $300,000 a month
- After: TR = $240 × 900 = $216,000 a month
- PED = −40% ÷ +20% = −2.0, so demand is elastic and total revenue falls by $84,000. Consumers spend $84,000 a month less on handbags, which is exactly the revenue the firm has lost.
The simplest way to memorise it: price and TR move in the same direction when demand is inelastic; in opposite directions when demand is elastic.
Common exam question
How a price change affects total revenue
Question: Explain an advantage and a disadvantage to a producer of price-inelastic demand, or analyse how a price rise affects producers' revenue (4–6 marks).
Asked in 2 of the 11 structured papers. With inelastic demand a price rise cuts quantity demanded less than proportionately, so revenue rises (the advantage); a price cut raises it less than proportionately, so revenue falls (the disadvantage). Each effect earns a mark and its explanation another. For the 6-mark analysis, say demand contracts and revenue depends on PED, then take both cases; producers of a substitute gain revenue as buyers switch.
Set in 4 of the 13 multiple-choice papers. A price rise with PED between 0 and 1 raises revenue; a PED of 1 leaves it unchanged. If the price doubles, a PED of 0 gains most: sales do not fall, so revenue doubles. Options pairing a price fall with inelastic demand, or a rise with elastic demand, cut revenue.
What firms should do
A firm that knows its PED can pick its pricing strategy.
- Selling an inelastic good? Raise the price. The fall in quantity sold is smaller than the rise in price, so TR rises.
- Selling an elastic good? Cut the price. The rise in quantity sold is larger than the fall in price, so TR rises.
The same rule explains why some firms charge different customer groups different prices for a similar service. A train operator can charge more at peak times, when commuters have few alternatives and demand is inelastic, and less off-peak, when demand is elastic and a lower fare attracts many extra passengers. In each case the firm is applying the PED-revenue rule to the group in front of it.