How tax size changes the loss
Why doubling a tax quadruples its deadweight loss, why revenue first rises then falls, and the debate over the Laffer curve.
FinanceA company's marketAbout 5 min: 3 reading, 2 practiceUpdated
General education, not financial advice.
- Explain why deadweight loss grows with the square of the tax
- Describe how tax revenue changes as a tax grows
- Set out the Laffer curve and the debate about supply-side economics
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 8 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
Deadweight loss grows faster than the tax. On a supply-and-demand graph, the deadweight loss is a triangle whose height is the tax and whose base is the fall in quantity. Both grow in proportion to the tax, so the area grows with its square. Mankiw's rule:
- Double the tax: the deadweight loss rises 4 times.
- Triple the tax: it rises 9 times.
Revenue first rises, then falls. Revenue is the tax times the quantity sold. A small tax raises a little; a bigger one raises more. But as the tax keeps growing, the market shrinks so much that revenue starts to fall. A tax so high that nobody trades raises nothing.
Quick check
Tap an answer to check it.
A tax's deadweight loss is 50. The tax is doubled. Roughly what is the new deadweight loss, by Mankiw's rule?
- Deadweight loss grows with the square of the tax, not in proportion
Show answer
200. Doubling the tax multiplies the loss by 2² = 4.
Why it matters
The Laffer curve. The curve of revenue against the tax rate, rising and then falling, is called the Laffer curve. Mankiw tells the story: in 1974 the economist Arthur Laffer drew it on a napkin for journalists and politicians and suggested that US tax rates were so high that cutting them would raise revenue.
- Most economists were sceptical. The idea was right in theory, Mankiw writes, but there was little evidence that US rates were that high.
- Ronald Reagan took up the idea; cutting taxes to encourage work became known as supply-side economics.
- Economists still debate it. Many believe later history refuted the claim that the cuts would raise revenue; others read the 1980s as more favourable to the supply-siders. The experiment can't be rerun.
- Some take a middle view: an overall tax cut normally reduces revenue, but some taxpayers at some times may be on the wrong side of the curve. A cut is more likely to raise revenue for taxpayers facing the highest rates, and Laffer's argument is stronger in countries with much higher rates than the US; Mankiw mentions Sweden in the early 1980s, at about 80%.
The lesson for policy. The cost of a tax, and what it raises, depend not just on its rate but on how people's behaviour responds. A small tax has a small deadweight loss relative to its revenue; a large one has a large loss and may raise little extra.
Worked example
The market from the last lesson: demand price = 10 − Q, supply price = Q. With a tax t, the quantity sold is (10 − t) ÷ 2.
| Tax | Sold | Revenue | Loss |
|---|---|---|---|
| 0 | 5 | 0 | 0 |
| 2 | 4 | 8 | 1 |
| 4 | 3 | 12 | 4 |
| 6 | 2 | 12 | 9 |
| 8 | 1 | 8 | 16 |
- Revenue = tax × quantity. It rises from 0 to 12, then falls back to 8.
- Deadweight loss ("Loss") = ½ × tax × (5 − quantity). Doubling the tax from 2 to 4 multiplies it by 4 (1 to 4); tripling from 2 to 6 multiplies it by 9 (1 to 9).
- Going from a tax of 4 to 6 raises no extra revenue but more than doubles the deadweight loss.
Text description
Two curves for the market in the worked example, with the tax per unit across. Tax revenue (solid) rises from 0 to a peak of 12.5 at a tax of 5, then falls back to 0 at a tax of 10, when no one trades: the Laffer curve. The deadweight loss (dashed) is 1 at a tax of 2, 4 at 4, 9 at 6, 16 at 8 and 25 at 10: it grows with the square of the tax.
Common mistake
Assuming a higher tax rate always raises more revenue. Past some point the shrinking market outweighs the higher rate. But the opposite mistake is common too: as Mankiw reports, many economists hold that an overall tax cut normally lowers revenue, and that the Laffer effect applies only where rates are very high.
Key terms
- Laffer curve
- the relationship between the size of a tax and the revenue it raises: first rising, then falling
- supply-side economics
- the view that tax cuts encourage people to work and produce more
- deadweight loss
- the fall in total surplus caused by a tax
Practise the key terms
Tap a card to turn it over. 3 cards.
| Front | Back |
|---|---|
| Laffer curve | the relationship between the size of a tax and the revenue it raises: first rising, then falling |
| supply-side economics | the view that tax cuts encourage people to work and produce more |
| deadweight loss | the fall in total surplus caused by a tax |
Practice
Work it through
Using the worked example's market, set a tax of 3.
- (10 − 3) ÷ 2
- 3 × 3.5
- ½ × 3 × (5 − 3.5)
Quick quiz
Tap an answer to check it.
A tax is tripled. By how much does its deadweight loss rise, by Mankiw's rule?
- The loss grows with the square of the tax
- 3² = 9
Show answer
9 times. Both the height and the base of the triangle triple.
What did Laffer suggest in 1974?
- He argued the opposite for the US at the time
Show answer
That US tax rates were so high that cutting them would raise revenue. He thought the US was on the falling side of the curve.
What middle position do some economists take, as Mankiw describes it?
- Few economists hold this
Show answer
Overall tax cuts normally reduce revenue, but some taxpayers may be on the wrong side of the curve. A cut is more likely to raise revenue where rates are very high.
In short
- Deadweight loss grows with the square of the tax: double it, ×4; triple it, ×9.
- Revenue rises then falls as the tax grows: the Laffer curve.
- Laffer and Reagan's supply-side argument is still debated; Mankiw describes most economists as sceptical.
- Behaviour, not just the rate, decides a tax's cost and revenue.
Mastery check
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Check yourself
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In the worked example's table, at which tax rates is revenue highest?
Show answer
At 4 and 6, both raising 12. (Between the rows, the true peak is a tax of 5, raising 12.5.)
Why does deadweight loss grow with the square of the tax?
Show answer
It is a triangle whose height and base both grow in proportion to the tax.
What is supply-side economics?
Show answer
The view that tax cuts encourage people to work and produce more, possibly raising revenue.
Further reading
- N. Gregory Mankiw, Principles of Macroeconomics, 6th ed. (South-Western Cengage, 2012), chapter 8.
- On this site: Deadweight loss.
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