Source: Homework 6, Prof. McLeod, Penn State
Difficulty: Intermediate
Prerequisites: Basic supply and demand curves, solving linear equations, concept of consumer and producer surplus.
Big picture: This topic sits at the intersection of two core microeconomics themes: how markets reach equilibrium, and what happens when the government intervenes with a per-unit tax. You should already be comfortable solving for equilibrium by setting supply equal to demand. The new layer here is tax incidence, which asks who bears the economic burden of a tax regardless of who writes the cheque. This matters because tax policy debates hinge on it, and it is tested heavily in intermediate micro.
When a per-unit tax is levied on consumers, the market price adjusts so that both buyers and sellers share the burden. The split depends on the relative elasticities of supply and demand, not on who the tax is formally imposed on. The tax also reduces the quantity traded and creates a deadweight loss, representing value that neither buyers, sellers, nor the government captures.
Equilibrium price (P*)
The price at which quantity supplied equals quantity demanded. At this price, the market clears with no surplus or shortage.
In simple terms, this is the price where buyers and sellers agree, and every unit produced finds a buyer.
Equilibrium quantity (Q*)
The number of units bought and sold at the equilibrium price.
Think of it as the volume of trade the market settles on when left alone.
Tax incidence
The division of the economic burden of a tax between buyers and sellers, which depends on the relative elasticities of supply and demand rather than on who is legally required to pay the tax.
In simple terms, this means the person who writes the cheque to the government is not necessarily the person who bears the cost.
Consumer tax burden
The portion of the tax that causes consumers to pay more than they did before the tax. Measured as the difference between what consumers pay after the tax and the original equilibrium price.
Producer tax burden
The portion of the tax that causes producers to receive less than they did before the tax. Measured as the difference between the original equilibrium price and the price producers receive after the tax.
Deadweight loss (DWL)
The loss in total surplus (consumer surplus + producer surplus + tax revenue) caused by the tax. It represents transactions that would have been mutually beneficial but no longer occur.
Think of it as the economic value that simply vanishes, captured by nobody.
Per-unit tax (excise tax)
A fixed dollar amount levied on each unit of a good bought or sold. It drives a wedge between the price consumers pay and the price producers receive.
Set quantity supplied equal to quantity demanded and solve for P.
Supply: Q = -60 + 3P
Demand: Q = 540 – 5P
Setting equal: -60 + 3P = 540 – 5P
8P = 600
P* = 75
Plug P* back into either equation to find Q*.
Q* = -60 + 3(75) = 165
A $24 tax on consumers shifts the demand curve down by $24.
New demand: Q = 540 – 5(P + 24) = 540 – 5P – 120 = 420 – 5P
Equivalently, consumers now face a total cost of P + 24 for each unit, so their willingness to pay the market price falls by $24.
New equilibrium: set new demand equal to supply.
420 – 5P = -60 + 3P
8P = 480
New market price (what producers receive): Ps = 60
Price consumers pay: Pc = 60 + 24 = 84
Consumer burden: Pc – P* = 84 – 75 = $9 per unit. Consumers pay $9 more than before.
Producer burden: P* – Ps = 75 – 60 = $15 per unit. Producers receive $15 less than before.
The total ($9 + $15 = $24) equals the tax.
Producer share of the tax: 15/24 = 5/8 = 62.5%.
Consumer share of the tax: 9/24 = 3/8 = 37.5%.
The side of the market that is more inelastic bears a larger share of the tax.
Here, supply is relatively more inelastic than demand (slope of supply in Q-P space is 3; slope of demand is 5 in absolute value), so producers bear the larger share.
Q after tax = -60 + 3(60) = 120 units (or equivalently, 420 – 5(60) = 120).
The tax reduced quantity traded from 165 to 120, a drop of 45 units.
DWL is the triangle between the supply and demand curves, from the post-tax quantity to the pre-tax quantity.
DWL = 0.5 x tax x (change in quantity) = 0.5 x 24 x 45 = $540.
Equilibrium condition:
Qs = Qd, then solve for P.
Tax wedge (tax on consumers):
Pc = Ps + tax, where Pc is the price consumers pay and Ps is the price producers receive.
To solve, substitute the demand curve with P replaced by (P + tax), then set equal to supply and solve for the new market price Ps.
Deadweight loss triangle:
DWL = 0.5 x (tax per unit) x (reduction in quantity)
Tax burden shares (using slopes in Q-P space):
Producer share = |slope of demand| / (|slope of demand| + slope of supply)
Consumer share = slope of supply / (|slope of demand| + slope of supply)
With demand slope = 5 and supply slope = 3: producer share = 5/8, consumer share = 3/8.
Sin taxes on cigarettes and alcohol work exactly this way: the government levies a per-unit tax, and the burden falls more heavily on whichever side of the market is more inelastic. Because smokers tend to be addicted (inelastic demand), they bear most of the tax on cigarettes.
Sales taxes, fuel excise duties, and sugar taxes all create the same wedge between buyer and seller prices. The deadweight loss formula is used by policy analysts to estimate the efficiency cost of any proposed tax.
Students often think that if the tax is levied on consumers, consumers pay the whole tax. They do not. The economic burden is shared regardless of the legal incidence.
Students sometimes confuse the new market price with the price consumers pay. When a tax is on consumers, the market price falls (producers receive less), and consumers pay the market price plus the tax.
A common error is computing deadweight loss as 0.5 x tax x original quantity. The correct formula uses the change in quantity, not the original quantity.
Students often forget that the tax burden split depends on relative elasticities. A steeper (more inelastic) curve bears more of the tax, not less.
Expect to be asked to compute equilibrium, post-tax prices for both sides, quantity after tax, and deadweight loss. These are standard problem-set questions.
Be ready to explain why the tax burden split does not depend on who the tax is formally levied on. This is the most commonly tested conceptual point.
The DWL triangle formula (half x base x height) is quick marks if you remember to use the change in quantity as the base.
If the exam gives you different supply and demand slopes, the producer-share and consumer-share formulas let you answer the incidence question in seconds.
True or false: If a tax is imposed on consumers, producers do not bear any of the tax burden. (False.)
Fill in the blank: Deadweight loss equals 0.5 x ______ x ______. (Tax per unit; reduction in quantity.)
True or false: The more inelastic side of the market bears the larger share of the tax. (True.)
Fill in the blank: A $24 tax creates a $24 ______ between the price consumers pay and the price producers receive. (Wedge.)
Q: Given Supply: Q = -60 + 3P and Demand: Q = 540 – 5P, what are the equilibrium price and quantity?
A: P* = 75, Q* = 165.
Q: A $24 per-unit tax is levied on consumers. What price do consumers pay and what price do producers receive?
A: Consumers pay $84. Producers receive $60.
Q: What proportion of the $24 tax is borne by producers?
A: Producers bear $15 of the $24, which is 5/8 or 62.5%.
Q: What is the quantity traded after the tax?
A: 120 units.
Q: What is the deadweight loss from the tax?
A: DWL = 0.5 x 24 x (165 – 120) = 0.5 x 24 x 45 = $540.
Q: Would the answers change if the $24 tax were levied on producers instead of consumers?
A: No. The economic incidence (who bears the burden) and the deadweight loss are identical regardless of which side the tax is formally imposed on. The equilibrium prices paid and received, the quantity, and the DWL would all be the same.
This connects directly to consumer and producer surplus, which you need to visualise the areas gained and lost when a tax is introduced. If you are shaky on surplus calculations, revisit those notes first.
The concept of elasticity and tax incidence reappears in public finance and welfare economics. The same logic applies to subsidies (a negative tax), where the subsidy benefit is split by the same elasticity rule.
Deadweight loss is the foundation for understanding why economists generally prefer lump-sum taxes to per-unit taxes, a point that comes up in discussions of optimal taxation.
Supply and demand equilibrium, per-unit tax, excise tax, tax incidence, consumer burden, producer burden, tax wedge, deadweight loss, DWL, welfare loss, Harberger triangle, elastic vs inelastic tax burden, who bears the tax, tax on buyers vs tax on sellers, ECON 102, intermediate microeconomics, Penn State, McLeod