In simple terms
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The Government's Two Price Levers
An indirect tax adds a cost to every unit sold, pushing supply up so consumers pay more and buy less. A subsidy does the opposite, lowering the effective cost so consumers pay less and buy more. Both move the market away from its free equilibrium, which is why both create a deadweight loss.
Picture the supply curve as a ramp that sellers must climb to bring goods to market. A specific tax nails a fixed-height step onto the whole ramp — every unit now starts higher by the same amount. An ad valorem tax instead tilts the ramp, so the higher the price, the bigger the step. A subsidy shaves the ramp down. In every case the meeting point with demand slides to a new price and quantity, and you can measure exactly who pays for the change.
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Find the free-market equilibrium where the original demand and supply meet.
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Shift supply: up by the tax (parallel for a specific tax, pivoting for ad valorem), or down by the subsidy.
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Read off the new quantity, the price consumers pay on demand, and the price producers keep on the original supply.
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Turn the diagram into money: revenue or government cost, the consumer and producer shares, and the deadweight-loss triangle.
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Full topic notes
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Indirect taxes: shifting supply upward
An indirect tax is levied on spending rather than on income or profit. Governments use them to raise revenue and to discourage consumption of goods with negative side-effects, such as tobacco or fuel. Because the tax is a cost the seller must cover, it shifts the supply curve upward. Two forms appear on Paper 3, and they shift supply in different shapes.
Tax revenue = tax per unit × post-tax quantity (Q2) — the rectangle between Pc and Pp up to Q2.
A specific (per-unit) tax is a fixed cash amount per unit — say $3 per bottle. It shifts supply vertically upward by that same $3 at every quantity, so the new supply curve is parallel to the old one.
An ad valorem tax is a percentage of the price — say 20%. Since 20% of a high price is more money than 20% of a low price, the curve pivots upward, opening a wider gap at higher prices.
After either tax the new quantity Q2 is lower and the price consumers pay, Pc, is higher, read off the demand curve at Q2.
The price producers actually keep, Pp, is lower than the old price P1, read off the original supply curve at Q2. The vertical gap Pc − Pp at Q2 equals the per-unit tax.
Who really pays? Incidence and elasticity
The seller hands the tax to the government, but that does not mean the seller bears it. How the burden splits between consumers and producers depends on the relative price elasticities of demand and supply — specifically, on which side is less willing to change its behaviour when the price moves.
The more inelastic side of the market carries the larger share of the tax.
If demand is more inelastic than supply (PED < PES), consumers bear more — they keep buying despite the higher price, so sellers can pass the tax on.
If supply is more inelastic than demand (PES < PED), producers bear more — they cannot easily cut output, so they absorb the tax.
The more elastic both curves are, the bigger the fall in quantity a tax causes, and so the larger the deadweight loss.
Subsidies: shifting supply downward
A subsidy is a per-unit payment from the government to producers, lowering their effective costs and encouraging output. Subsidies commonly target goods with positive externalities — renewable energy, public transport, vaccinations — or strategically important industries. A subsidy behaves like a negative tax: supply shifts vertically downward by the subsidy amount.
Government spending on a subsidy = subsidy per unit × post-subsidy quantity (Q2).
Supply shifts down by the per-unit subsidy, so the new quantity Q2 is higher.
Consumers pay a lower price Pc; producers receive a higher price Pp = Pc + subsidy. The vertical gap at Q2 equals the subsidy.
The government's total cost = subsidy per unit × the new quantity Q2 (not Q1).
Consumer and producer surplus both rise, but the government's outlay exceeds the combined gain, so a subsidy also produces a deadweight loss from over-provision.
Welfare: surplus, revenue and deadweight loss
Every tax and subsidy redistributes surplus and destroys some of it. A tax shrinks both consumer and producer surplus; part of the lost surplus becomes government revenue, but the surplus on the trades that no longer happen is lost to everyone — the deadweight loss. A subsidy raises consumer and producer surplus, but the government spends more than that combined gain, and the excess spent on the extra units beyond the efficient quantity is the deadweight loss. In both cases the market is pushed off its allocatively efficient quantity, and the size of the distortion grows with elasticity.
Tax: consumer surplus falls, producer surplus falls, government gains revenue (the rectangle), and the triangle beyond it is deadweight loss.
Subsidy: consumer surplus rises, producer surplus rises, government spending is the full rectangle to Q2, and the triangle by which spending exceeds the extra surplus is deadweight loss.
The more elastic demand and supply, the larger the quantity change and therefore the larger the deadweight loss for a given tax or subsidy.
Common mistakes examiners penalise
Confusing specific and ad valorem taxes — a specific tax shifts supply in PARALLEL; an ad valorem tax PIVOTS it. Drawing a parallel shift for a percentage tax loses marks.
Using the wrong quantity — revenue, subsidy cost and total incidence use the post-intervention quantity Q2; deadweight loss uses the CHANGE in quantity (Q1 − Q2). This mix-up is the single most common Paper 3 error.
Assuming the seller bears the tax — the burden splits by relative elasticity, not by who physically pays the government. With inelastic demand, consumers carry most of it.
Mislabelling Pc and Pp — the price consumers pay comes off DEMAND at Q2; the price producers keep comes off original SUPPLY at Q2. Swapping them makes every later figure wrong.
Forgetting units and follow-through — state units ($, thousands, etc.) and show each method line so that a single early slip still earns method and follow-through marks.
Worked examples
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A market has demand Qd = 120 − 10P and supply Qs = −30 + 20P, where P is in dollars and Q is in thousands. A specific tax of $1.50 per unit is imposed. Find (a) the original equilibrium, (b) the post-tax equilibrium, (c) tax revenue, (d) the consumer and producer burden, and (e) the deadweight loss.
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(a) Original equilibrium. Set Qd = Qs: 120 − 10P = −30 + 20P → 150 = 30P → P1 = $5. Then Q1 = 120 − 10(5) = 70 (i.e. 70,000 units).
The market for solar panels has demand Qd = 800 − 2P and supply Qs = −100 + 3P (P in euros). The government introduces a subsidy of €50 per panel. Find (a) the original equilibrium, (b) the post-subsidy equilibrium, (c) the total cost to the government, and (d) the deadweight loss.
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(a) Original equilibrium. 800 − 2P = −100 + 3P → 900 = 5P → P1 = €180. Q1 = 800 − 2(180) = 440 panels.
Paper 3 (HL) quantitative question: A specific tax of $3 per unit is imposed on a good. After the tax, equilibrium quantity is 800 units and consumers pay $2 more per unit than before. Calculate the total tax revenue, the consumer tax burden and the producer tax burden. [5]
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Indirect tax
A tax on spending rather than on income or profit. It is collected from the seller, who typically passes part of it on to buyers through a higher price. Examples: VAT/GST and excise duties on fuel, alcohol and tobacco.
Key takeaways
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- ✓
A specific (per-unit) tax is a fixed cash amount per unit — say $3 per bottle. It shifts supply vertically upward by that same $3 at every quantity, so the new supply curve is parallel to the old one.
- ✓
An ad valorem tax is a percentage of the price — say 20%. Since 20% of a high price is more money than 20% of a low price, the curve pivots upward, opening a wider gap at higher prices.
- ✓
After either tax the new quantity Q2 is lower and the price consumers pay, Pc, is higher, read off the demand curve at Q2.
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The price producers actually keep, Pp, is lower than the old price P1, read off the original supply curve at Q2. The vertical gap Pc − Pp at Q2 equals the per-unit tax.
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