Deadweight loss
Why a tax costs buyers and sellers more than it raises, and what makes that extra loss large or small.
FinanceA company's marketAbout 5 min: 3 reading, 2 practiceUpdated
General education, not financial advice.
- Explain how a tax changes consumer surplus, producer surplus and tax revenue
- Define deadweight loss and show it with lost trades
- Explain why elasticity determines its size
Builds toward: Judge a company. Read a company's accounts, apply Graham's tests, and make a rough valuation.
A company's market: pricing power, taxes and trade: lesson 7 of 15
- A company's market
- Price elasticity of demand 6 min
- Elasticity and total revenue 5 min
- Consumer and producer surplus 4 min
- Market efficiency 5 min
- Price ceilings and floors 6 min
- Who really pays a tax 5 min
- Deadweight loss 5 min
- How tax size changes the loss 5 min
- Absolute and comparative advantage 5 min
- Why trade helps both sides 5 min
- Winners and losers from trade 5 min
- Tariffs and quotas 5 min
- What makes productivity grow 5 min
- Growth policy 5 min
- Why unemployment exists 6 min
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Pairs with any introductory economics textbook; for example N. Gregory Mankiw, Principles of Macroeconomics (6th ed.), chapter 8
What it is
A tax drives a wedge between what buyers pay and what sellers receive, so the quantity sold falls. To judge the tax's effect on welfare, Mankiw counts three groups:
- Buyers lose consumer surplus (they pay more).
- Sellers lose producer surplus (they receive less).
- The government gains tax revenue = tax per unit × quantity sold. This counts as a benefit, since it pays for roads, police, schools or help for the needy.
The losses to buyers and sellers are larger than the revenue raised. The difference, the fall in total surplus, is the deadweight loss of the tax.
Why the extra loss? Mankiw's example: Joe cleans Jane's house each week for 100. Joe's time is worth 80 to him, and a clean house is worth 120 to Jane, so each gains 20: total surplus 40. Now a tax of 50 is put on cleaners. Jane would pay at most 120, which would leave Joe 70 after tax, below his 80. Joe would need 130 from Jane, more than her 120. So they cancel the arrangement. Both lose 20, and the government collects nothing. The whole 40 is deadweight loss.
Quick check
Tap an answer to check it.
A seller's cost is 30 and a buyer values the good at 45. A tax of 10 is imposed. Will they still trade?
- The trade survives as long as value minus cost exceeds the tax
Show answer
Yes: the 15 of gains from trade is more than the 10 tax. 45 − 30 = 15, which is larger than 10, so a price exists that leaves both better off after tax.
Why it matters
Taxes distort incentives. By raising the price to buyers and lowering it to sellers, a tax stops some trades in which the buyer valued the good more than it cost to make. Those lost gains from trade are the deadweight loss.
Elasticity decides how big it is. The more buyers and sellers respond to the price, the more trades the tax prevents:
- The more elastic supply is, the larger the deadweight loss.
- The more elastic demand is, the larger the deadweight loss.
With very inelastic supply and demand, people keep trading despite the tax, so the quantity barely falls and the deadweight loss is small.
The labour-tax debate. Mankiw reports that, adding all labour taxes together, the marginal tax rate on a typical worker's last dollar of earnings is about 40%. Economists disagree about its deadweight loss because they disagree about the elasticity of labour supply:
- Some think most people would work full time whatever the wage, so labour supply is inelastic and the loss is small.
- Others point to people who can change their hours, second earners deciding whether to take paid work, older people choosing when to retire, and work in the untaxed "underground" economy, and conclude that the loss is large.
Worked example
A market with demand price = 10 − Q and supply price = Q (Q in thousands). Without a tax: Q = 5, price 5.
A tax of 2 a unit: buyers' price minus sellers' price must equal 2, so 10 − Q − Q = 2, giving Q = 4. Buyers pay 6; sellers receive 4.
- Tax revenue = 2 × 4 = 8.
- Lost trades: 1 (from 5 to 4).
- Deadweight loss = ½ × tax × lost quantity = ½ × 2 × 1 = 1.
The tax raises 8 but costs buyers and sellers 9 in lost surplus.
Text description
Demand (price = 10 minus quantity) and supply (price = quantity) cross at 5 thousand units and a price of 5. A tax of 2 drives a wedge: 4 thousand units are sold, buyers pay 6 and sellers keep 4. The shaded rectangle between 4 and 6, across 4 thousand units, is the tax revenue: 8. The small triangle between 4 and 5 thousand units, between the curves, is the deadweight loss: 1, the gains from trades that no longer happen.
Common mistake
Thinking a tax only moves money from buyers and sellers to the government. That transfer is the revenue. The deadweight loss is extra: it comes from trades that no longer happen, so nobody, including the government, receives it.
Key terms
- deadweight loss
- the fall in total surplus that results from a market distortion such as a tax
- tax revenue
- tax per unit × quantity sold
- tax wedge
- the gap between the price buyers pay and the price sellers receive
- gains from trade
- the surplus buyers and sellers get from trades that take place
- marginal tax rate
- the tax on the last unit of income
Practise the key terms
Tap a card to turn it over. 5 cards.
| Front | Back |
|---|---|
| deadweight loss | the fall in total surplus that results from a market distortion such as a tax |
| tax revenue | tax per unit × quantity sold |
| tax wedge | the gap between the price buyers pay and the price sellers receive |
| gains from trade | the surplus buyers and sellers get from trades that take place |
| marginal tax rate | the tax on the last unit of income |
Practice
Work it through
Joe's time is worth 60 a week; Jane values the cleaning at 100. A tax of 30 is put on cleaners.
- 100 − 60
- 40 − 30
- The gains (40) exceed the tax, so the trade still happens and the 30 is collected
Quick quiz
Tap an answer to check it.
Why does a tax cause a deadweight loss?
- That transfer is the revenue, not the deadweight loss
Show answer
It prevents trades in which the buyer valued the good more than it cost to make. The lost gains from those trades go to nobody.
Which market would a tax distort most?
- Then the quantity barely changes
Show answer
One where supply and demand are both very elastic. The more people respond, the more trades the tax stops.
Why do economists disagree about the deadweight loss of labour taxes?
- Mankiw puts the combined marginal rate at about 40%
Show answer
They hold different views of how elastic labour supply is. Elastic labour supply means a large loss; inelastic, a small one.
In short
- A tax lowers consumer and producer surplus by more than the revenue it raises.
- The difference, the deadweight loss, comes from trades that no longer happen.
- More elastic supply or demand means a larger deadweight loss.
- The size of the labour-tax loss depends on how elastic labour supply is.
Mastery check
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Check yourself
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In Mankiw's Joe-and-Jane example, how much revenue does the 50 tax raise?
Show answer
None: they cancel the arrangement, so the 40 of surplus is pure deadweight loss.
Supply is very inelastic. Is the deadweight loss of a tax large or small?
Show answer
Small.
In the worked example, what are the revenue and the deadweight loss of the tax of 2?
Show answer
Revenue 8, deadweight loss 1.
Further reading
- N. Gregory Mankiw, Principles of Macroeconomics, 6th ed. (South-Western Cengage, 2012), chapter 8.
- On this site: Who really pays a tax and How tax size changes the loss.
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