Why a percentage tax such as VAT pivots supply, with the gap widening as price rises, and how to work VAT out in both directions.
At the pump, fuel duty is a fixed 52.95p a litre. Then VAT at 20% is charged on the whole price, duty included. So when fuel is dearer, the government collects more VAT on every litre, even though duty has not changed. And any rise in duty costs drivers 20% more than the rise itself: a 1p rise in duty adds 1.2p at the pump.
Two taxes on one litre: one fixed, one a percentage. Why do they look different on a diagram?
Sources: HMRC, Fuel duty rates 2026 to 2027; HMRC, VAT rates.
An ad valorem tax is a percentage of the price. In the UK, VAT is the main one: 20% on most goods and services, 5% on some, such as household energy, and 0% on others, such as most food and children’s clothes.
Compare a specific tax: a fixed amount per unit, such as fuel duty or the sugar levy.
The model keeps the same assumptions as before: a competitive market, normal supply and demand, and only the tax changes. One more: the percentage is charged on the price before tax, the price firms need.
VAT is 20% of the price.
A £10 T-shirt has £2 of VAT added. A £100 coat has £20 added.
On a supply diagram, how will the gap between supply before and after VAT look?
A percentage tax adds more to an expensive item than a cheap one. So the supply curve does not shift in parallel: it pivots up, and the gap widens as the price rises.
The market before the tax: P1 and Q1. Supply shows the price firms need to supply each quantity.
Now a 25% ad valorem tax. At every quantity, firms now need 25% more than before. Where supply is low, at a low price, 25% is a small amount. Where supply is high, at a high price, 25% is a big amount. So S + tax starts close to S and moves further away: it pivots up.
Check: A 25% tax is added to a price of £4 and to a price of £12. What is the tax on each?
25% of £4 is £1 and 25% of £12 is £3. The higher the price, the more tax per unit.
The gap between S and S + tax is the tax per unit. It is small at low prices and large at high prices. That widening gap is the one thing to get right when you draw it: never draw an ad valorem tax as a parallel shift.
Check: Supply pivots up to S + tax. What happens at the new equilibrium?
At the old price, firms now supply less than buyers want. The excess demand pushes the price up, and as it rises demand contracts, so quantity falls.
Everything else works as before. The new equilibrium is where S + tax crosses demand. The price rises from £9 to P2, £10, and the quantity falls from Q1 to Q2.
Firms keep the price before tax, read off the original supply curve straight below the new equilibrium: £8. The tax per unit is £10 minus £8, which is £2. Check: 25% of £8 is £2.
Check: Consumers pay £10, which includes 25% tax on the price firms keep. What do firms keep?
The tax is 25% of the price firms keep, so £10 is 125% of it. £10 ÷ 1.25 = £8. Taking 25% off £10 gives £7.50, which is the classic mistake.
Revenue is the tax per unit times Q2: £2 × 8 = £16. As before, split it at P1 to see the incidence: consumers pay £1 more, firms keep £1 less. And the trades between Q2 and Q1 are lost: the deadweight loss.
Now suppose prices rise across the economy.
Check: Inflation raises the pre-tax price of every good by 10%. The VAT rate stays at 20%. What happens to the VAT paid on each unit?
VAT is 20% of the price. If the price is 10% higher, 20% of it is 10% higher too, with no change in the rate.
Why use a percentage tax at all? Revenue rises automatically with prices: when inflation pushes prices up, VAT revenue rises too, without the government changing the rate. A specific tax such as fuel duty raises nothing extra unless the rate is raised.
They drew S + VAT parallel to S, which is a specific tax. VAT is a percentage of the price, so the tax per unit grows as the price rises: S + VAT should pivot up, the gap widening.
Distinguish between a specific tax and an ad valorem tax, and show the difference on a diagram.
A specific tax is a fixed amount charged on each unit, whatever its price, such as fuel duty at 52.95p a litre. An ad valorem tax is a percentage of the price, such as VAT at 20%.
[Diagram: two panels. Left: S and a parallel S + tax. Right: S and an S + tax that starts just above S and gets steeper, with the gap widening.]
Both raise firms’ costs, so supply shifts up. With a specific tax the gap between S and S + tax is the same at every quantity, so the shift is parallel. With an ad valorem tax the tax per unit is bigger when the price is higher, so S + tax pivots up and the gap widens as price rises.
In both cases the price consumers pay rises, the quantity falls, the government raises the tax per unit times the new quantity and there is a deadweight loss. An ad valorem tax also raises more revenue automatically when prices rise.
However, VAT is regressive: poorer households spend a larger share of their income, so they pay a larger share of it in VAT, which is why most food and children’s clothes are zero-rated. How much of either tax falls on consumers depends on the price elasticities of demand and supply.
VAT rates: HM Revenue and Customs (gov.uk). Fuel duty: HMRC, Fuel duty rates 2026 to 2027. Diagrams drawn with Rough.js and perfect-freehand, both MIT licensed. Your answers are saved only on this device.