What this lesson teaches
I can show how each intervention changes price, quantity, spending, revenue, consumer surplus and producer surplus.
Syllabus 9570, 2.1.3(b). Government Intervention in Markets: Government intervention in markets can affect the equilibrium price and quantity, consumer expenditure and producer revenue, consumer surplus and producer surplus
Make a guess
A tax cuts sales of a good from 80 to 60 units. Does all the surplus that buyers and sellers lose go to the government as tax revenue?
- Yes. Every dollar buyers and sellers lose becomes revenue.
- No. The government gets more than buyers and sellers lose.
- No. Some is lost to everyone as deadweight loss.
Show the answer
No. Some is lost to everyone as deadweight loss.
The 20 units no longer traded were worth more to buyers than they cost to make. That lost gain goes to nobody.
A tax shrinks consumer and producer surplus, raises revenue and creates a deadweight loss.
With a tax, consumer surplus is the area below demand and above the price buyers pay (P1). Producer surplus is the area above supply and below the price sellers keep (P2).
Both areas shrink. Part of what they lose becomes tax revenue for the government. The rest is lost to everyone: the deadweight loss.
The deadweight loss comes from the units between Q1 and Q0 that are no longer traded, even though buyers valued them more than they cost to make.
A subsidy works the other way: consumer and producer surplus rise, but the subsidy costs more than they gain, so there is also a deadweight loss.
- Tax
- CS and PS fall; tax revenue; deadweight loss.
- Subsidy
- CS and PS rise, but cost more than they gain.
Worked example: Surplus before and after a $2 tax
Before the tax: 80 units at $6. After: 60 units, buyers pay $7, sellers keep $5. Demand starts at $10 and supply at $2.
- Before: CS = 1/2 x 80 x ($10 - $6) = $160; PS = 1/2 x 80 x ($6 - $2) = $160.
- After: CS = 1/2 x 60 x ($10 - $7) = $90; PS = 1/2 x 60 x ($5 - $2) = $90.
- Tax revenue = $2 x 60 = $120.
- Deadweight loss = $320 - ($90 + $90 + $120) = $20.
Watch out for this
With a tax, producer surplus goes up to the price buyers pay.
Sellers do not keep the tax. Producer surplus stops at the price sellers keep (P2).
Check your understanding
Why does a tax create a deadweight loss?
- Some units that buyers value above their cost are no longer traded.
- Sellers receive a lower price, so producer surplus is lost to the government.
- The government spends the tax revenue less wisely than buyers would have.
Show the answer
Some units that buyers value above their cost are no longer traded.
Right. Those lost trades are a loss to buyers and sellers that no one gains back.