Business Economics · Government intervention in a market

Taxes and Subsidies: Incidence, Equilibrium and Deadweight Loss

Updated 11 October 2026 · Fact-checked

An indirect tax raises firms' costs, shifting supply left; a subsidy lowers costs, shifting supply right. Find the new equilibrium, then compare the price buyers pay and the price sellers keep. The side with the less elastic response bears more of a tax. A tax creates deadweight loss; a subsidy can too.

Understand Taxes and Subsidies

An indirect tax is charged on a good or service, such as GST or an excise duty. The seller pays it to the government, but that does not mean the seller bears it. Who bears it is called tax incidence.

A tax per unit acts like a rise in cost. At every quantity, sellers need a higher price to supply the same amount. So the supply curve shifts up (left) by the amount of the tax. The demand curve does not move. The new equilibrium has a higher price and a lower quantity.

The price buyers pay (Pc) rises. The price sellers keep after paying the tax (Pp = Pc − tax) falls. The gap between them is the tax per unit. The consumer bears the rise in Pc. The producer bears the fall in Pp. The less elastic side bears more of the burden, because it cannot easily walk away from the market.

A subsidy is the reverse. It is a payment per unit from the government to producers (or consumers). Supply shifts down (right) by the subsidy. Price falls, quantity rises. Buyers pay less, sellers receive more, and the benefit is shared. Again, the less elastic side gains more.

A specific tax is a fixed amount per unit, such as ₹5 per litre. An ad valorem tax is a percentage of the price, such as 18%. On a diagram, a specific tax gives a parallel shift of supply. An ad valorem tax gives a pivot, because the tax per unit grows as price rises.

Taxes and subsidies change welfare. A tax raises government revenue but reduces consumer and producer surplus by more than the revenue. The extra loss is the deadweight loss. It arises because trades that were worth making no longer happen. A subsidy costs the government more than the gains to buyers and sellers, so it also creates a deadweight loss when it pushes output beyond the efficient level, assuming no externalities.

Key rules to remember

Per-unit tax wedge: Pc − Pp = t; Pc is the price buyers pay, Pp is the price sellers keep, t is the tax per unit. Holds for a specific tax.
Ad valorem tax per unit: t = r × Pp (rate on the pre-tax seller price, equivalent to r ÷ (1 + r) × Pc), or t = r × Pc (if the rate is applied to the tax-inclusive price the buyer pays); Check how the question defines the rate. Per-unit tax changes with price.
Consumer share of tax burden: Consumer burden = (Pc_new − P_old) × Q_new; Use the new quantity traded.
Producer share of tax burden: Producer burden = (P_old − Pp_new) × Q_new; Consumer burden + producer burden = tax revenue = t × Q_new.
Tax revenue: Revenue = t × Q_new; Q_new is the quantity traded after the tax.
Deadweight loss of a tax (linear curves): DWL = ½ × t × (Q_old − Q_new); Area of the triangle between the curves, from the new quantity to the old one.
Subsidy per unit: Pc = Pp − s; Buyers pay Pc, sellers receive Pp, s is the subsidy per unit. Cost to government = s × Q_new.
Incidence and elasticity: Consumer share ÷ Producer share = PES ÷ |PED| (approximately, for small taxes); The more elastic side bears less. This is a guide, not an exact rule for large taxes on non-linear curves.

How to solve Taxes and Subsidies questions

Use this method for any numerical or diagram question on taxes and subsidies.

1Write down the demand and supply equations or the starting equilibrium price and quantity.
2Identify the instrument: tax or subsidy, specific or ad valorem, and who it is paid by.
3Use the wedge. Set the price buyers pay minus the price sellers receive equal to t for a tax. Set sellers' price minus buyers' price equal to s for a subsidy.
4Solve for the new quantity first by setting demand at Pc equal to supply at Pp. Then find Pc and Pp.
5Work out incidence: compare Pc and Pp with the old price. Consumer share is the rise in Pc (fall in Pc for a subsidy). Producer share is the fall in Pp (rise in Pp for a subsidy).
6Compute government revenue (t × Q_new) or cost (s × Q_new).
7Find the deadweight loss as ½ × t × change in quantity, or ½ × s × change in quantity for a subsidy.
8State the result in words, and link incidence to elasticity.

Quickest way: Wedge and triangle shortcut for linear curves

When to use it: Use when demand and supply are straight lines and the tax or subsidy is a fixed amount per unit.

Write demand as P = a − bQ and supply as P = c + dQ.
With a per-unit tax t, set a − bQ = c + dQ + t. Solve Q_new = (a − c − t) ÷ (b + d).
Original Q_old = (a − c) ÷ (b + d), so the fall in quantity is t ÷ (b + d).
Consumer share of t = b ÷ (b + d). Producer share of t = d ÷ (b + d).
DWL = ½ × t × t ÷ (b + d) = t² ÷ (2 × (b + d)).
For a subsidy, swap the sign of t. Quantity rises by s ÷ (b + d), and DWL = s² ÷ (2 × (b + d)).

Common mistakes in Taxes and Subsidies

Assuming the party who pays the tax to the government bears it.
Legal liability and economic burden sound like the same thing.
Fix: Always find the new Pc and Pp and compare with the old price. The burden depends on elasticity, not on who sends the cheque.
Shifting the wrong curve, or shifting demand for a tax on sellers.
Students think of the tax as hitting buyers.
Fix: A tax on sellers shifts supply. A tax on buyers shifts demand down by the tax. The result for Pc and Pp is the same either way.
Using the old quantity to calculate revenue or incidence in money terms.
The old equilibrium is the number already on the page.
Fix: Use Q_new. The tax is only paid on units that are still traded.
Drawing a parallel shift for an ad valorem tax.
Specific tax diagrams are the ones practised most.
Fix: An ad valorem tax pivots the supply curve, because the tax per unit rises with price. Use a parallel shift only for a specific tax.
Calculating deadweight loss as the whole tax revenue or using the wrong base.
The triangle and rectangle are confused.
Fix: The rectangle is revenue. The triangle is DWL. DWL = ½ × t × (Q_old − Q_new).
Saying a subsidy always helps society.
Lower prices look like a pure gain.
Fix: The government pays s × Q_new. With no externality, that exceeds the gain to buyers and sellers, so there is a deadweight loss. Mention that a subsidy can be justified if there is a positive externality.

Worked examples

Example 1

Demand is P = 100 − 2Q and supply is P = 10 + Q, with P in ₹ and Q in thousands of units. The government imposes a tax of ₹15 per unit on sellers. Find the new quantity, the prices buyers pay and sellers keep, the share of the tax borne by each side, tax revenue and the deadweight loss.

Show the solution

Original equilibrium: 100 − 2Q = 10 + Q gives 3Q = 90, so Q = 30 thousand and P = ₹40.
With the tax, sellers' supply is P_c = 10 + Q + 15 = 25 + Q.
Set 100 − 2Q = 25 + Q. Then 3Q = 75, so Q_new = 25 thousand.
Buyers pay Pc = 100 − 2 × 25 = ₹50.
Sellers keep Pp = 50 − 15 = ₹35. Check with supply: 10 + 25 = 35. Correct.
Consumer burden per unit = 50 − 40 = ₹10. Producer burden per unit = 40 − 35 = ₹5. These add to ₹15.
Tax revenue = 15 × 25,000 = ₹3,75,000.
DWL = ½ × 15 × (30,000 − 25,000) = ½ × 15 × 5,000 = ₹37,500.

Answer: New quantity 25 thousand units; buyers pay ₹50; sellers keep ₹35. Consumers bear ₹10 of the ₹15 tax and producers bear ₹5. Revenue is ₹3,75,000 and deadweight loss is ₹37,500.

Example 2

Using the same market (demand P = 100 − 2Q, supply P = 10 + Q, Q in thousands), the government instead gives a subsidy of ₹9 per unit to sellers. Find the new quantity, the price buyers pay, the price sellers receive, the cost to the government and the deadweight loss.

Show the solution

Original equilibrium: Q = 30 thousand and P = ₹40.
With the subsidy, sellers' marginal cost net of subsidy is P_c = 10 + Q − 9 = 1 + Q.
Set 100 − 2Q = 1 + Q. Then 3Q = 99, so Q_new = 33 thousand.
Buyers pay Pc = 100 − 2 × 33 = ₹34.
Sellers receive Pp = 34 + 9 = ₹43. Check with supply: 10 + 33 = 43. Correct.
Buyers gain ₹40 − ₹34 = ₹6 per unit. Sellers gain ₹43 − ₹40 = ₹3 per unit. These add to ₹9.
Cost to government = 9 × 33,000 = ₹2,97,000.
DWL = ½ × 9 × (33,000 − 30,000) = ½ × 9 × 3,000 = ₹13,500.

Answer: New quantity 33 thousand units; buyers pay ₹34; sellers receive ₹43. Buyers gain ₹6 per unit and sellers ₹3. The subsidy costs ₹2,97,000 and the deadweight loss is ₹13,500, assuming no externality.

Exam tips

In MCQs, first decide the direction: tax means price up and quantity down; subsidy means price down and quantity up.
For incidence questions, look for elasticity clues. The more inelastic side bears more of a tax and gains more from a subsidy.
In written answers, label Pc, Pp, the tax wedge, the revenue rectangle and the DWL triangle on the diagram. Marks are often given for labels.
Show a check: Pc − Pp must equal t for a tax, and Pp − Pc must equal s for a subsidy.
If asked to evaluate, mention the trade-off between revenue or equity goals and efficiency loss, and note that the result depends on elasticities.

Practice questions from Government intervention in a market

Taxes and Subsidies: frequently asked questions

What is the difference between a specific tax and an ad valorem tax?

A specific tax is a fixed amount per unit, such as ₹5 per litre, so supply shifts in parallel. An ad valorem tax is a percentage of price, such as 18%, so the tax per unit rises with price and the supply curve pivots.

Who bears more of a tax, buyers or sellers?

The side that is less responsive to price bears more. If demand is more inelastic than supply, buyers bear more. If supply is more inelastic, sellers bear more.

How do I calculate the effect of a subsidy on equilibrium price?

Shift supply down by the subsidy, or equivalently set the price sellers receive equal to the price buyers pay plus the subsidy. Solve for the new quantity, then find the buyers' price. The price buyers pay falls by less than the full subsidy when supply is not perfectly elastic.

Why does a tax create deadweight loss?

It reduces the quantity traded, so some trades where buyers valued the good more than the cost of supply no longer happen. The lost surplus on those trades is not collected by anyone. It is the triangle between the old and new quantities.

Is the deadweight loss larger when demand and supply are more elastic?

Yes, for a given tax. More elastic curves mean a larger fall in quantity, so the triangle is larger. This is why taxing inelastic goods is less distorting.