Excise Tax Explained: Definition, Graph, Incidence and Deadweight Loss

Excise tax is a tax on the production or sale of one specific good or service, such as gasoline, cigarettes or alcohol, rather than on spending in general. Excise taxes are often set as a fixed dollar amount per unit, and that per-unit form is the one AP questions use. On a supply and demand graph, an excise tax collected from sellers shifts supply up by the amount of the tax, so buyers pay more, sellers keep less and fewer units are traded.

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Supply and demand at equilibrium, drawn by the interactive graph. Tap it to drag the curves, open the full version, or put it on your own site free, or turn it into a five-minute class activity.

Excise taxes are tested in AP Microeconomics topic 2.8, The Effects of Government Intervention in Markets, and they come back in topic 6.2, Externalities, when a tax is used to correct pollution or other spillover costs.

What makes a tax an excise tax

Three features mark an excise tax:

• It targets one product. A tax on gallons of fuel or packs of cigarettes is an excise tax.
• It is usually charged per unit. The tax is a set number of dollars per gallon, pack or bottle, not a percentage of the price.
• It is often collected before the register. The law usually names a producer, wholesaler or retailer as the payer, so the tax is built into the shelf price.

Governments use excise taxes to raise revenue and to discourage goods whose use harms other people.

Per-unit vs ad valorem excise taxes

A per-unit (or specific) tax is a fixed amount on each unit. An ad valorem tax is a percentage of the price. Both can be excise taxes as long as they apply to one product.

Excise tax formulas

Every excise tax question uses the same four relationships. Call the tax t, the original quantity Q0 and the after-tax quantity Qt.

• The wedge: price buyers pay - price sellers keep = t. This gap is the tax wedge.
• Tax revenue: t x Qt. Use the after-tax quantity, never Q0.
• Deadweight loss: 1/2 x t x (Q0 - Qt).
• Buyers' share of the tax: Es ÷ (Es + Ed), where Ed is the absolute value of the price elasticity of demand and both elasticities are measured at the original equilibrium. With straight-line curves this split is exact. The sellers' share is Ed ÷ (Es + Ed).

Excise tax on a supply and demand graph

Put price on the vertical axis and quantity on the horizontal axis. Draw downward-sloping demand and upward-sloping supply crossing at P0 and Q0.

1. Shift supply straight up by the tax. The new curve, often labeled S + tax, sits exactly t dollars above the old one at every quantity.

2. Find the new quantity, Qt, where S + tax crosses the original demand curve. Qt is smaller than Q0.

3. Go up from Qt to demand to read the buyer price, Pb, which is above P0.

4. Go down from Qt to the original supply curve to read the seller price, Ps, which is below P0.

5. The rectangle between Pb and Ps, running from zero to Qt, is tax revenue. The triangle between Qt and Q0, pointing at the old equilibrium, is deadweight loss.

A tax collected from buyers shifts demand down by t instead, with identical prices, quantity, revenue and deadweight loss. You can drag the supply curve up yourself in the supply and demand sandbox.

Worked example: a $6 excise tax

Take a hypothetical weekly market for cases of energy drinks with demand Qd = 400 - 10P and supply Qs = 20P - 80.

Step 1: equilibrium before the tax. Set 400 - 10P = 20P - 80. Then 480 = 30P, so P = $16. Quantity is 400 - 10(16) = 240 cases.

Step 2: add a $6 tax on sellers. Sellers keep P - 6, so supply becomes Qs = 20(P - 6) - 80 = 20P - 200.

Step 3: the new equilibrium. Set 400 - 10P = 20P - 200. Then 600 = 30P, so buyers pay Pb = $20. Quantity is 400 - 200 = 200 cases. Sellers keep Ps = 20 - 6 = $14. Check on the original supply curve: 20(14) - 80 = 200 cases.

Step 4: who pays. Buyers pay 20 - 16 = $4 more per case. Sellers keep 16 - 14 = $2 less. Buyers carry two thirds of the tax. The elasticity formula agrees: Ed = 10 x (16 ÷ 240) = 0.67 and Es = 20 x (16 ÷ 240) = 1.33, so the buyers' share is 1.33 ÷ 2.00 = 0.67.

Step 5: revenue. 6 x 200 = $1,200 per week. The excise tax revenue calculator runs the same step.

Step 6: deadweight loss. 1/2 x 6 x (240 - 200) = 1/2 x 6 x 40 = $120.

Step 7: check with surplus. Demand reaches zero at P = $40 and supply starts at P = $4.

Buyers and sellers lose $1,320 together. The government collects $1,200, and the missing $120 is the deadweight loss. For more on the two triangles, see consumer and producer surplus explained.

Who pays an excise tax?

The party the law names is the statutory payer. The party that actually loses money once prices adjust is the economic payer, and tax incidence is the study of that split. The rule: the more inelastic side of the market pays more.

• If demand is more inelastic than supply, buyers carry most of the tax, as in the energy drink example.
• If supply is more inelastic, sellers carry most of it.
• With perfectly inelastic (vertical) demand, buyers pay the whole tax and quantity does not fall.
• With perfectly elastic (horizontal) demand, sellers pay the whole tax.

The tax incidence guide works through these cases on graphs, and the tax incidence calculator splits any tax for you. If the elasticity labels feel shaky, review elastic vs inelastic demand.

Why elasticity also decides revenue and deadweight loss

When demand or supply is inelastic, quantity barely falls. Revenue stays high because t is multiplied by a large Qt, and deadweight loss stays small because few trades disappear. That is why an excise tax on a good with inelastic demand raises a lot of revenue with little deadweight loss.

Raise the tax in the example to $12. Supply becomes 20(P - 12) - 80 = 20P - 320, so 400 - 10P = 20P - 320 gives P = $24 and Q = 160. Revenue is 12 x 160 = $1,920, up 60%. Deadweight loss is 1/2 x 12 x 80 = $480, four times the old $120. With straight-line curves, doubling the tax quadruples the deadweight loss. The deadweight loss guide explains the triangle, and the Laffer curve shows where rising rates eventually cut revenue.

Excise tax vs sales tax vs tariff

A sales tax is broad and shows up at checkout. A tariff applies only at the border and protects domestic producers, which tariffs, quotas and trade barriers covers in AP Micro topic 2.9. The excise tax vs sales tax comparison puts the first two side by side. Excise taxes on everyday goods tend to be regressive, because those goods take a bigger share of a low-income budget, which progressive vs regressive taxes explains.

Excise taxes as Pigouvian taxes

An excise tax that corrects a negative externality is called a Pigouvian tax, after the economist Arthur Pigou.

Go back to the energy drink market and suppose, hypothetically, that every case creates $6 of litter cleanup cost for the town. Marginal social cost is then supply plus $6, which is exactly the S + tax curve from the worked example. The socially optimal quantity is where demand meets marginal social cost: 200 cases.

Without a tax, the market makes 240 cases. On the 40 extra cases, social cost runs above what buyers are willing to pay, a gap that grows from $0 to $6. The loss is 1/2 x 40 x 6 = $120. A $6 tax moves the market to 200 cases and removes that loss.

So the same $6 tax creates a $120 deadweight loss in a market with no externality and removes a $120 deadweight loss in a market with a $6 external cost. The Pigouvian tax guide works a full example, and the externality sandbox shows the MSC curve.

How excise taxes show up on the AP exam

Questions usually ask you to shift supply up by the tax, label Pb, Ps and Qt, shade revenue and deadweight loss, calculate both, and use elasticity to say who carries more of the tax. Common mistakes:

• Using the original quantity for revenue. Revenue is t x Qt.
• Shifting supply right or down. A tax on sellers moves supply up and to the left.
• Shifting both curves. Shift supply for a tax on sellers or demand for a tax on buyers, never both.
• Letting the law decide incidence. Elasticity decides who pays.
• Calling revenue deadweight loss. Revenue is the rectangle; deadweight loss is the triangle.

For practice problems, work through the supply and demand module.