Governments tax the seller, but the seller rarely pays. Who actually carries a tax is decided by elasticity, not by the wording of the law — and that gap between who is charged and who bears the cost is one of the first genuinely counter-intuitive results an economics tutor in London will hand you. Get elasticity and tax incidence clear once and a large slice of first-year microeconomics falls into place with it.
1 · Elasticity, in one idea
Elasticity measures how much a quantity responds to a price change. The price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price. If a 10% price rise cuts quantity by 20%, elasticity is −2, and demand is elastic. If the same rise cuts quantity by just 5%, elasticity is −0.5, and demand is inelastic.
The sign is almost always negative for demand, so we talk about its size: above one in magnitude is elastic, below one is inelastic. The same idea applies to supply — the price elasticity of supply says how strongly sellers expand output when the price rises.
What makes something inelastic? Few substitutes, a small share of your budget, habit, and a short time horizon. Fuel and cigarettes are the classic inelastic goods — buyers keep buying even when the price climbs.
2 · Who really pays a tax
Suppose the government adds a fixed duty per unit and makes the seller hand it over. That is the statutory side of the tax — the legal question of who writes the cheque. It is not the interesting question.
The interesting question is economic incidence: after prices adjust, whose wallet is lighter? A per-unit tax drives a wedge between the price buyers pay and the price sellers keep. The size of that wedge is the tax. How it splits between the two prices is what elasticity decides — and, remarkably, it makes no difference at all whether the law names the buyer or the seller. The split comes out the same either way.
Here is the rule that does all the work:
The more inelastic side of the market bears the larger share of the tax.
The intuition is clean. Whoever can walk away most easily escapes the tax; whoever is stuck with the good pays it. Inelastic means stuck.
3 · Elasticity fixes the split
At one extreme, if supply is perfectly elastic, the whole tax lands on buyers. At the other, if demand is perfectly inelastic, buyers again bear all of it. Most real markets sit between, and the burden splits in proportion to how inelastic each side is.
There is a second cost, quite separate from who pays. The tax shrinks the quantity traded, and some mutually beneficial trades simply stop happening. Nobody collects the value of those lost trades — not the buyer, not the seller, not the government. That lost value is the deadweight loss, the true economic cost of the tax over and above the revenue it raises.
Worked example — a duty on wine
Take the market for a mid-range bottle of wine. Inverse demand is P = 14 − 2Q and inverse supply is P = 2 + Q, with P in pounds and Q in thousands of bottles a week. A specific duty of £3 a bottle is imposed on sellers.
Step 1 — The pre-tax equilibrium. Set demand equal to supply: 14 − 2Q = 2 + Q, so 3Q = 12 and Q = 4. The price is P = 2 + 4 = £6. Call this point E₀ = (4, 6).
Step 2 — Read the slopes. Demand falls by £2 for each extra thousand bottles; supply rises by £1. Demand is the steeper curve, which is the first sign that buyers will bear more.
Step 3 — Confirm with elasticities. At E₀ the price elasticity of demand is (−½)(6/4) = −0.75, inelastic; the elasticity of supply is (1)(6/4) = +1.5, elastic. The inelastic side is demand, so buyers should carry the larger share.
Step 4 — Impose the duty. Sellers now need £3 more for every bottle, so the price buyers pay must exceed the price sellers keep by exactly £3. The traded quantity is where that gap fits between the two curves: (14 − 2Q) − (2 + Q) = 3, giving 12 − 3Q = 3 and Q = 3.
Step 5 — The two prices. Buyers pay the demand price at Q = 3: Pᵦ = 14 − 6 = £8. Sellers keep £3 less: Pₛ = 8 − 3 = £5.
Step 6 — Split the burden. Buyers were paying £6 and now pay £8 — up £2. Sellers were getting £6 and now keep £5 — down £1. The £2 and £1 add to the £3 duty, and buyers carry two-thirds of it. That two-thirds is exactly what the slopes predicted: 2 ⁄ (2 + 1).
Step 7 — Revenue and deadweight loss. The government collects £3 on each of 3,000 bottles: £9,000 a week. Trade has fallen from 4,000 to 3,000 bottles, and the value of those lost trades is the triangle between the curves — ½ × £3 × 1,000 = £1,500 of deadweight loss.
Confident you could split a tax by elasticity under exam pressure? The wedge, the two prices and the burden shares trip up more first-years than any other part of this topic — one sign slip and the whole split inverts. It is exactly what a one-on-one economics tutor drills with you until the diagram and the algebra move together. Book a trial session.
Practice
Q1. Inverse demand is P = 20 − Q and inverse supply is P = 2 + 2Q. A specific tax of £6 is imposed. Find the new quantity, the two prices, the burden on each side, the revenue, and the deadweight loss.
Q2. Inverse demand is P = 10 − Q, and supply is perfectly elastic at P = £4. A £2 tax is imposed. How is the burden split, and why?
Q3. At a market’s equilibrium the price elasticity of demand is −0.25 and the price elasticity of supply is 0.75. A £4 specific tax is imposed. What share falls on consumers, and how much per unit?
Answers. Q1: pre-tax Q = 6, P = 14; with the tax Q = 4, buyers pay £16, sellers keep £10. Buyers bear £2 and sellers £4 — here supply is the steeper, more inelastic side, so sellers carry more. Revenue £24; deadweight loss ½ × 6 × 2 = £6. Q2: buyers bear the entire £2, because perfectly elastic supply will not absorb a penny; quantity falls from 6 to 4, revenue £8, deadweight loss £2. Q3: the consumer share is eₛ ⁄ (eₛ + |e_d|) = 0.75 ⁄ (0.75 + 0.25) = 0.75, so consumers bear £3 and producers £1.
Key takeaways
- Elasticity is responsiveness — the percentage change in quantity over the percentage change in price. Above one is elastic, below one is inelastic.
- A tax opens a wedge between the price buyers pay and the price sellers keep, equal to the tax. Which side the law charges is irrelevant to the outcome.
- The more inelastic side bears more. The party that cannot easily walk away pays the larger share.
- A tax also causes deadweight loss — the value of the trades it prevents — which is a cost on top of the revenue collected.
Why London students choose our economics tutoring
- Exam-shaped practice: whether your first year sits at LSE, UCL or King’s, sessions rehearse the exact wedge-and-incidence calculation examiners set, so the diagram and the algebra are automatic under time pressure.
- Diagram fluency: our tutors get you moving between the graph, the elasticities and the numbers in one motion — the skill that separates a first from a 2:1 on this topic.
- One-on-one pace: a private economics tutor works at your speed, catching the sign slips and split errors that cost easy marks.
FAQ
Q: What is the difference between elastic and inelastic demand?
A: Elastic demand responds strongly to price — a small price change causes a larger percentage change in quantity, so elasticity exceeds one in magnitude. Inelastic demand barely responds, so elasticity is below one. Necessities with few substitutes tend to be inelastic; luxuries with close substitutes tend to be elastic.
Q: Does it matter whether a tax is levied on the buyer or the seller?
A: No. The economic burden is identical either way. The law decides who physically pays the government, but prices adjust so that the real cost is shared according to the relative elasticities of supply and demand.
Q: Who bears more of a tax?
A: The more inelastic side of the market. If demand is less elastic than supply, buyers bear more; if supply is less elastic, sellers bear more. Whoever finds it harder to change their behaviour ends up carrying the tax.
Q: What is deadweight loss?
A: It is the value of the trades that no longer happen because the tax raises the price to buyers and lowers it to sellers. Those trades would have benefited both sides, so the surplus they would have created is simply lost.
Q: How do I calculate tax incidence in an exam?
A: Find the pre-tax equilibrium, then impose the wedge: the buyer price minus the seller price must equal the tax. Solve for the new quantity, read the two prices off the demand and supply curves, and compare each to the original price to get the split.
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