Price Elasticity of Demand (PED)

2. The PED formula

$\text{PED} = \dfrac{\%\,\Delta\,Q_d}{\%\,\Delta\,P}$

That is, PED is the percentage change in quantity demanded divided by the percentage change in price. Both numbers are percentages, not raw unit changes.

To work out either percentage change:

$\% \,\text{change} = \dfrac{\text{new value} - \text{old value}}{\text{old value}} \times 100$

A short illustration before the full template. The price of a takeaway pizza rises from £8 to £10, and quantity demanded falls from 200 to 150 per evening.

• %ΔP = (10 − 8) ÷ 8 × 100 = +25 %
• %ΔQd = (150 − 200) ÷ 200 × 100 = −25 %
• PED = −25 ÷ 25 = −1

The PED value is negative for a downward-sloping demand curve (price and quantity move in opposite directions). The papers print PED both with and without the minus sign, and a mark scheme has accepted a calculated PED either way, so this set of notes classifies PED by its absolute value.

3. The five categories of PED

Demand can be sorted into five categories based on |PED|. All five are named in the 2027-2029 syllabus (2.6.2), so you need to be able to interpret a PED value in each category and draw the matching demand curve. The two extremes are limiting cases rather than everyday examples, but they are examinable.

Each category can be drawn as a demand curve; the steeper the curve, the more inelastic demand is.

The full interpretation ladder, which is what a question means when it asks what a PED value tells you:

• |PED| = 0: perfectly inelastic, drawn as a vertical demand curve.
• 0 < |PED| < 1: inelastic, so quantity demanded responds less than proportionately to the price change.
• |PED| = 1: unitary elastic, so total revenue is unchanged when price changes.
• |PED| > 1: elastic, so quantity demanded responds more than proportionately.
• |PED| = ∞: perfectly elastic, drawn as a horizontal demand curve.

Most calculation questions land in the inelastic and elastic bands, so the quickest check is whether the value is below or above 1, but you are expected to recognise and use all five.

4. Calculating PED step by step

On the papers a PED calculation is a one-mark item scored on the answer alone, so follow these steps in order: the wrong options come from skipping or swapping them.

Step 1. Calculate the percentage change in quantity demanded.

Step 2. Calculate the percentage change in price.

Step 3. Divide: PED = %ΔQd ÷ %ΔP.

Step 4. Interpret the result: say whether demand is elastic (|PED| > 1) or inelastic (|PED| < 1), and what that means for total revenue.

5. The determinants of PED: SPLAT

The PED of a good depends on several non-price factors. The mnemonic SPLAT groups the five main ones and is the one most commonly used.

Two similar-sounding ideas to keep apart:

• A change in the price of substitutes shifts the demand curve (topic 4). What determines PED is the number and closeness of substitutes, although rivals becoming cheaper or better does make them closer substitutes, so demand becomes more elastic.
• A change in income shifts the demand curve. What determines PED is the proportion of income the good takes, although a fall in income raises that proportion and so can make demand more elastic.

6. PED, consumer expenditure and firms' revenue: the central application

Total revenue (TR) = Price × Quantity.

The same Price × Quantity figure can be read from two directions. To the firm it is total revenue (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

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.

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.

7. The significance of PED: who it matters for

PED is not only a firm's tool. It shapes the decisions of four groups: consumers, workers, producers and the government.

Consumers

PED describes consumers' own responsiveness, so it decides which price rises a household absorbs and which it reacts to. For a necessity with no close substitute, demand is inelastic: the household keeps buying much the same quantity, its total expenditure on that good rises, and less of the budget is left for everything else. For an elastic good, the consumer has real choices: switch to a rival brand, postpone the purchase until prices fall, or go without. Knowing which of your purchases are elastic tells you where cutting back actually protects your budget.

Workers

Demand for labour is derived from demand for the product, so the PED of what a worker helps produce affects that worker's job. Where the product has price-inelastic demand, a price rise barely dents sales, so output and revenue are stable, employment is more secure, and workers are in a stronger position when bargaining for higher pay because the firm can pass the extra cost on to customers. Where the product is price-elastic, sales and output swing sharply with price, so hiring and hours are volatile and pay demands are more likely to be resisted or met with job losses, since the firm cannot raise its price without losing customers.

Producers and firms

Beyond setting the price (the rule above), PED tells a firm how much risk any price change carries. If demand is inelastic the firm can pass a cost increase or a new tax on to its customers with little loss of sales; if demand is elastic it has to absorb most of that cost itself. A firm whose products all have elastic demand also faces far less predictable revenue, so it will be more cautious about committing to extra capacity.

Government

The government uses PED when deciding what to tax and what to subsidise.

• Taxes on inelastic goods raise large tax revenue with a small fall in quantity sold. This is why "sin taxes" on cigarettes, alcohol and fuel are so common: these goods are inelastic, so the tax raises revenue without wiping out the market.
• Taxes on elastic goods raise less revenue and shrink the market a lot. A high tax on a luxury good would push consumers to substitutes, and tax revenue would fall.
• Subsidies on elastic goods produce a large rise in quantity demanded for each pound of subsidy spent. This is why subsidies for renewable-energy products like solar panels are designed to be substantial: demand responds strongly.

Be careful: for an inelastic good, quantity demanded does fall when its price rises, just by a smaller percentage than the price rise; only perfectly inelastic demand (PED = 0) does not fall at all. When cigarette duty rises, smoking really does fall a little, but by less than the price has risen.