What it means
Imagine a product that sells for $20 and a buyer who values it at $22 and a seller who can make it for $18. That trade creates $4 of value, but if a tax of $5 is added, the trade no longer makes sense and neither side gains.
The $4 of lost value goes to nobody, because the government does not collect any tax from a sale that never happens. The size of the loss depends on how much the tax changes behaviour.
When buyers and sellers cannot easily change what they do, such as with essential goods, few trades are lost and the welfare loss is small. When they can easily switch or walk away, the loss is much bigger.
Economists use a simple rule of thumb. The loss grows with the square of the tax rate, so doubling a tax roughly quadruples the welfare loss while only doubling the revenue.
This is why many tax experts prefer broad taxes with low rates over narrow taxes with high rates. For businesses, the concept explains why a tax on a product or input can cut volumes by more than managers first expect.
It also explains why firms lobby for tax measures that apply equally to all competitors, since a tax that falls on one product and not its substitute can move customers sharply. The welfare loss is only one side of the picture.
Taxes also pay for public services and may correct harmful behaviour, such as pollution, in which case the tax can improve overall welfare. A fair assessment weighs the loss against the benefits the tax revenue buys.
In practice, the size of the loss is estimated from price elasticity, which measures how strongly sales respond to a price change. A product with elastic demand, such as a branded snack with many alternatives, loses many trades when taxed.
A product with inelastic demand, such as a prescription medicine, loses very few.
In practice
Real-world examples.
Example
A beverage maker faces a new tax of $0.50 per bottle on sugary drinks. Sales volume drops by 15%, and the finance team estimates the welfare loss by combining the tax per bottle with the drop in volume to show the board what the levy really costs the market.
Example
A property economist studies a transaction tax on home sales. She finds that people delay moving house because of the tax, so fewer homes change hands and the loss is greater than the revenue figures alone suggest.
Example
A trade association for online retailers argues against a narrow tax on digital downloads. It points out that customers can easily switch to physical copies, so a large share of sales would simply disappear without bringing in much revenue. The association asks the government to consider a broader measure with a lower rate.
Formula
Calculation
Welfare loss (triangle approximation) = 1/2 x tax per unit x fall in quantity sold
Suppose a government adds a tax of $4 per unit to a product, and sales fall from 50,000 units to 40,000 units. The fall in quantity is 50,000 - 40,000 = 10,000 units. Welfare loss = 0.5 x 4 x 10,000 = $20,000. The tax revenue collected is 4 x 40,000 = $160,000, so the welfare loss equals 20,000 / 160,000 = 12.5% of the revenue raised.Case study
Seen in the real world.
Brightwater Cycles is an illustrative, fictional bicycle importer. When a new import levy of $40 per bicycle was announced, the finance director estimated that sales would fall from 25,000 to 20,000 units a year.
She calculated that the government would collect 40 x 20,000 = $800,000, while the triangle of lost trades equalled 0.5 x 40 x 5,000 = $100,000. The second figure would not show up in any government account, but it represented real lost sales and lost customer benefit.
Brightwater used the calculation in its submission to the consultation and asked for the levy to be phased in. The illustrative lesson is that a tax has a hidden cost beyond the revenue it raises, and that cost is largest where customers have easy alternatives.
Watch out
Common mistakes.
- Confusing the welfare loss with the tax revenue, when the revenue is transferred to the government and the loss is value that vanishes.
- Assuming a tax that raises a lot of money must have a large welfare loss, when a tax on goods with no easy substitutes can raise plenty with little loss.
- Forgetting that the loss rises faster than the tax rate, so a small increase on an already high tax costs more than the same increase on a low one.
Questions
People also ask.
Who bears the welfare loss?
It is shared between buyers and sellers, depending on how easily each side can change its behaviour.
Can a tax have no welfare loss?
Only if behaviour does not change at all, which is rare, although a tax that corrects a harmful side effect can improve welfare overall.
Is it the same as deadweight loss?
Yes, welfare loss of taxation is the deadweight loss caused specifically by a tax.
From the founder's library
Take it further with the book.
Build your financial confidence beyond this definition. Shihan's full-length guide, Accounting Fundamentals, takes the same plain-English approach and turns it into a complete, practical playbook for non-finance managers, business owners and students - with chapter-end quiz answers and presentation slides included.
25% off with code MMHQ25, applied at checkout. Priced in USD - checkout may show the equivalent in your local currency.
View the book and save 25%Related