Difficulty: Introductory to Intermediate | Prerequisites: Linear supply and demand curves, basic algebra.
This topic covers what happens when the government drops a per-unit tax into an otherwise competitive market. You already know how to find equilibrium where supply meets demand; now you are learning who actually pays that tax (spoiler: it depends on elasticities, not on which side the tax is legally imposed) and how much total surplus the economy loses in the process. This is foundational for policy analysis and appears in nearly every intermediate micro course. If you are comfortable solving two linear equations simultaneously, you have the maths you need.
Set demand equal to supply to find the no-tax equilibrium. A per-unit tax shifts the effective supply curve up by the tax amount, reducing quantity and raising the buyer's price while lowering the seller's net price. The side with the more inelastic curve bears the larger share of the tax burden. The lost surplus that neither buyers, sellers, nor the government captures is deadweight loss, calculated as the area of the triangle between the old and new quantities.
Market equilibrium
The price and quantity at which quantity demanded equals quantity supplied. Graphically, it is where the demand and supply curves cross.
In simple terms, it is the price the market settles on when nobody is interfering.
Per-unit tax (excise tax)
A fixed monetary amount charged on each unit of a good sold. It can be levied on buyers or sellers; the economic outcome is the same either way.
Think of it as a flat fee per item, like a fuel duty of 18p per litre.
Tax incidence
The division of the actual economic burden of a tax between buyers and sellers, regardless of which side the law says must pay it.
In simple terms, it answers the question "who really ends up worse off?"
Tax wedge
The gap between what the buyer pays and what the seller receives, equal to the per-unit tax. In our example: buyer pays 52, seller receives 34, tax wedge = 18.
Deadweight loss (DWL)
The reduction in total surplus caused by the tax. It represents transactions that would have happened without the tax but no longer do, so the gains from those trades are lost entirely.
Think of it as the cost of the tax that nobody collects: not the buyer, not the seller, not the government.
Tax revenue
The total amount the government collects: tax per unit multiplied by the quantity sold after the tax.
Consumer surplus
The difference between what buyers are willing to pay and what they actually pay, summed across all units purchased.
Producer surplus
The difference between what sellers receive and the minimum they would accept, summed across all units sold.
Given linear demand and supply curves:
Demand: P = 100 - 4Q
Supply: P = 10 + 2Q
Set demand equal to supply:
100 - 4Q = 10 + 2Q
90 = 6Q
Q = 15*
Substitute back to find price:
P = 100 - 4(15) = 40*
Equilibrium: Q = 15, P = 40.
Suppose the government levies a tax of t = 18 per unit on sellers. The supply curve shifts up by 18:
New supply: P = 10 + 2Q + 18 = 28 + 2Q
New equilibrium:
100 - 4Q = 28 + 2Q
72 = 6Q
Q_tax = 12
Buyer's price (what buyers pay):
P_buyer = 100 - 4(12) = 52
Seller's net price (what sellers keep after paying the tax):
P_seller = 52 - 18 = 34
The tax burden splits according to relative elasticities, not according to who writes the cheque.
Buyer's burden: price rose from 40 to 52, so buyers bear 12 of the 18 tax.
Seller's burden: net price fell from 40 to 34, so sellers bear 6 of the 18 tax.
Buyers bear more of the burden here because demand is more inelastic (steeper) than supply. The general rule: the more inelastic side bears the larger share.
Deadweight loss is the triangle formed by the tax wedge and the reduction in quantity:
DWL = 0.5 × tax × (Q* - Q_tax)
DWL = 0.5 × 18 × (15 - 12)
DWL = 0.5 × 18 × 3
DWL = 27
This is surplus that existed before the tax but is now lost: the trades between Q = 12 and Q = 15 no longer happen, and nobody captures the gains they would have generated.
Equilibrium condition: Q_d(P) = Q_s(P), or equivalently set the demand price equal to the supply price.
With tax on sellers: P_demand = P_supply + t. Equivalently, shift the supply curve up by t.
Tax wedge: P_buyer - P_seller = t
Buyer's burden: P_buyer(after tax) - P*(no tax)
Seller's burden: P*(no tax) - P_seller(after tax)
Deadweight loss (linear curves): DWL = 0.5 × t × (Q* - Q_tax)
Tax revenue: T_rev = t × Q_tax
Excise taxes on petrol, cigarettes, and alcohol work exactly this way. Governments choose to tax goods with inelastic demand (people buy roughly the same amount regardless of price) partly because it raises more revenue and partly because the deadweight loss is smaller. The insight that legal incidence (who writes the cheque) differs from economic incidence (who actually bears the cost) is one of the most practically important results in all of economics.
Students often believe that if the tax is legally imposed on sellers, then sellers pay all of it. They do not. The economic burden depends on relative elasticities, not on who hands the money to the government.
A common error is computing deadweight loss as a rectangle (tax × change in quantity) rather than a triangle (0.5 × tax × change in quantity). The triangle shape reflects the fact that the lost surplus is largest for the first foregone unit and tapers to zero.
Students sometimes forget that tax revenue is not a loss to society: it transfers surplus to the government. Only the deadweight loss triangle is surplus that vanishes entirely.
Confusing the buyer's price with the seller's net price is a frequent source of arithmetic errors. Always label both clearly.
⚠️ Expect a question that gives you linear supply and demand, imposes a tax, and asks for the new equilibrium, buyer/seller prices, tax revenue, and deadweight loss. This is a high-frequency exam question.
⚠️ Be prepared to explain who bears more of the burden and why (relative elasticities).
⚠️ Know that the deadweight loss formula uses 0.5, not 1. Getting this wrong halves or doubles your answer.
⚠️ If the question asks for a "per-unit welfare loss" or "public welfare loss," it is asking for deadweight loss.
True or false: If a tax is imposed on sellers, only sellers bear the economic burden.
False. The burden is shared; the split depends on relative elasticities.
Fill in the blank: Deadweight loss equals 0.5 × ____ × (Q_before - Q_after).
The per-unit tax, t.
True or false: Tax revenue is part of the deadweight loss.
False. Tax revenue is a transfer to the government. Deadweight loss is the surplus that nobody receives.
Q: Demand is P = 80 - 2Q and supply is P = 20 + Q. Find the equilibrium price and quantity.
A: 80 - 2Q = 20 + Q → 60 = 3Q → Q = 20. P = 80 - 2(20) = 40.
Q: A tax of t = 12 is imposed on sellers in the market above. Find the new quantity, the buyer's price, and the seller's net price.
A: 80 - 2Q = 20 + Q + 12 → 48 = 3Q → Q = 16. P_buyer = 80 - 2(16) = 48. P_seller = 48 - 12 = 36.
Q: Calculate the deadweight loss from the tax.
A: DWL = 0.5 × 12 × (20 - 16) = 0.5 × 12 × 4 = 24.
Q: How much of the tax burden falls on buyers vs sellers?
A: Buyer's burden = 48 - 40 = 8. Seller's burden = 40 - 36 = 4. Buyers bear twice as much because demand is steeper (more inelastic) than supply.
This connects directly to price elasticity of demand and supply: the elasticity values determine tax incidence, and understanding elasticity deeply makes the burden analysis intuitive rather than formulaic.
It also links to welfare economics and efficiency: deadweight loss is the central measure of how a policy distorts an otherwise efficient market outcome.
In later coursework, you will see how these ideas extend to monopoly pricing (where the firm acts as if it is imposing a tax on consumers) and international trade (where tariffs are per-unit taxes on imports).
Market equilibrium, supply and demand, per-unit tax, excise tax, tax incidence, tax burden, economic incidence vs legal incidence, tax wedge, deadweight loss, DWL, welfare loss, consumer surplus, producer surplus, tax revenue, elasticity and tax incidence, Harberger triangle, efficiency loss from taxation