How to Calculate Tax Revenue from a Per-Unit Tax
Tax revenue from a per-unit tax equals the tax per unit times the quantity sold after the tax, the rectangle between demand and supply on the graph.
The Tax Revenue formula
Calculator
Enter linear demand and supply (quantity in thousands) and a per-unit tax on sellers to get the after-tax quantity and revenue.
Quantity demanded, in thousands, if the price were zero.
Tax per unit times the quantity actually traded after the tax.
- Pre-tax equilibrium price
- $11
- Pre-tax quantity (thousands)
- 9
- Buyer price after tax
- $13
- Quantity after tax (thousands)
- 7
- Naive estimate (tax × pre-tax quantity)
- $36,000
Sellers keep this price minus the tax.
Too high, because the tax shrinks the quantity sold.
How to calculate Tax Revenue, step by step
- 1Find the pre-tax equilibrium. Read the original demand and supply schedule for the price and quantity where quantity demanded equals quantity supplied, before any tax exists.
- 2Shift supply by the tax. A per-unit tax collected from sellers means sellers need the tax amount extra at every quantity, so a seller who used to supply a given quantity at price P now needs price P plus the tax to supply that same quantity.
- 3Find the new, after-tax equilibrium. Solve where the demand schedule meets the shifted supply schedule. This gives the buyer price, the seller price, and the smaller quantity that actually trades once the tax is in place.
- 4Multiply the tax by the after-tax quantity. Tax revenue = tax per unit × the new, smaller quantity. On the graph this is the rectangle whose height is the tax per unit and whose width is the after-tax quantity, sitting between the buyer price on top and the seller price on the bottom.
Worked example: Tax Revenue
A market has this demand and supply schedule, quantity in thousands of units: at $5, quantity demanded is 15 and quantity supplied is 3; at $7, demanded 13 and supplied 5; at $9, demanded 11 and supplied 7; at $11, demanded 9 and supplied 9; at $13, demanded 7 and supplied 11; at $15, demanded 5 and supplied 13. Before any tax, the market clears at $11 with 9,000 units traded, the only row where the two quantities match. The government now places a $4 per-unit tax on sellers. A $4 tax means a seller only supplies a given quantity if the buyer price is $4 above what that row used to require, so match each supply row to a buyer price $4 higher: the 7,000-unit row, originally priced at $9, now needs a buyer price of $13 to bring the same 7,000 units to market. At $13, demanders also want exactly 7,000 units, so the after-tax market clears at a buyer price of $13 and a quantity of 7,000 units. Sellers keep $13 minus the $4 tax, or $9 per unit, which is exactly what row shows they were willing to supply 7,000 units for anyway. Tax revenue = $4 × 7,000 = $28,000.
Why the rectangle is never the naive tax times the original quantity
The mistake is treating quantity as fixed while only the tax changes. It is not fixed. A per-unit tax on sellers raises the price buyers face and lowers the price sellers keep, and both of those push quantity down from wherever it started.
In the worked example, quantity fell from 9,000 units to 7,000 units once the $4 tax was in place. The revenue rectangle is built on the smaller number: $4 × 7,000 = $28,000, not $4 × 9,000 = $36,000. The $8,000 gap is not money the government somehow lost. It was never collectable, because the 2,000 units it would have applied to no longer trade at all.
Those 2,000 units no longer trade. The deadweight loss of the tax is not the units themselves. It is the surplus those trades would have created: the triangle between the demand and supply curves over that quantity range. That value vanishes entirely because trades that made both a buyer and a seller better off before the tax are priced out once the tax exists. Deadweight loss and tax revenue divide the same lost consumer and producer surplus between them, so a bigger tax trades a bigger deadweight loss for more revenue only up to a point: a tax large enough shrinks the market so much that revenue starts to fall even as deadweight loss keeps growing, the same logic covered in the Laffer curve question below.
How much quantity falls for a given tax depends on how flat or steep the demand and supply schedules are. Flatter schedules (quantity swings a lot for a small price change) lose more quantity per dollar of tax, so their revenue rectangle sits further below the naive number. Steeper schedules (quantity barely moves) lose less quantity, so their actual revenue sits close to tax per unit times the original quantity. This is why governments tend to place per-unit taxes on goods with steep, unresponsive demand, like cigarettes or gasoline: the tax collects close to its full naive revenue instead of mostly shrinking the market.
Tax Revenue questions
How do you calculate tax revenue from a per-unit tax?
Find the quantity that actually trades after the tax shifts the supply schedule, then multiply the tax per unit by that after-tax quantity. Tax revenue = tax per unit × after-tax quantity. In the worked example, a $4 tax that leaves 7,000 units trading collects $4 × 7,000 = $28,000.
Why is tax revenue smaller than the tax times the original quantity?
Because the tax itself changes the quantity traded. Raising the buyer price and lowering the amount sellers keep makes some units no longer worth trading, so quantity falls from the pre-tax level to a smaller after-tax level. Multiplying the tax by the old, larger quantity counts units that stop trading once the tax exists. In the example, the naive figure of $4 × 9,000 = $36,000 overstates actual revenue of $28,000 by $8,000, because quantity fell from 9,000 to 7,000 units.
Who actually pays a per-unit tax, buyers or sellers?
Both usually do, split according to the buyer price rising and the seller price falling from the original equilibrium price. In the example the price buyers pay rose from $11 to $13, a $2 increase, and the price sellers keep fell from $11 to $9, a $2 decrease, splitting the $4 tax evenly here because demand and supply had matching slopes. A steeper (less responsive) side of the market bears a larger share.
Does tax revenue keep rising if the tax per unit keeps rising?
No. A larger tax per unit collects more on each unit but shrinks the quantity traded further, so revenue rises, reaches a maximum, and then falls as the tax gets large enough to shut down most of the market. This tradeoff is the same logic behind the Laffer curve.
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