Deadweight Loss Calculator

The trades that never happened

Put a tax on something and two things follow. The obvious one is that money moves from buyers and sellers to the government, and everyone can see that happening. The less obvious one is that some sales simply stop occurring. There were people willing to pay slightly more than it cost to produce the thing, and once the tax opens a gap between what the buyer pays and what the seller receives, those deals no longer make sense to either side.

Nobody gets that value. The buyer does not get the product, the seller does not get the sale, and the government collects no tax on a transaction that never took place. It is not moved from one pocket to another, it just stops existing. That is deadweight loss, and this calculator measures it.

Before and after, in four numbers

Original price and original quantity describe the market as it was, before whatever intervention or distortion you are measuring. New price and new quantity describe it afterwards.

The word tax is the obvious case, but the same measurement applies far more widely than that. A price ceiling such as rent control, a price floor such as a minimum price, a tariff on imports, a subsidy pushing quantity above what the market would choose, or a monopolist restricting output to hold prices up. In every one of them, a wedge opens between price and quantity, some trades stop, and the arithmetic below applies unchanged.

A triangle worth 100

Say a market cleared at 10 a unit with 1,000 units sold. A tax of 2 per unit pushes the price buyers pay to 12, and at that price only 900 units change hands.

The deadweight loss is 100: half of the 2 price wedge, multiplied by the 100 units that no longer trade.

It is worth being clear about what that 100 is and is not. The government collects tax on the 900 units that still sell, and that revenue is a transfer, taken from buyers and sellers and handed to the state, unpleasant for them perhaps but not destroyed. The 100 is different. It is the value that used to be created by those last 100 sales and now is not created by anyone. That is the part economists mean when they call this a loss rather than a cost.

Why it comes out as a triangle

The formula multiplies the price change by the quantity change and halves it, which is the area of a triangle. The halving is not a fudge, and understanding where it comes from makes the result far easier to trust.

Think about which sales disappear. They are not a random hundred. They are the marginal ones, the deals that were only just worth doing. The very last unit that used to sell was worth barely more to its buyer than it cost to produce, so almost nothing is lost when it stops. Move back through the disappearing sales and each one was worth a little more than the one after it, so a little more is lost each time.

Line that up and you get a shape that starts at nothing and grows steadily to the full size of the wedge. That is a triangle, and the area of a triangle is half the base times the height. Here the base is the drop in quantity and the height is the gap in price.

The shape has a name in economics, the Harberger triangle, after Arnold Harberger, who in the 1950s and 60s did the work of actually measuring these things rather than only describing them. His finding on monopoly distortion in the United States was famously modest, somewhere around a tenth of a percent of national income, which was considerably smaller than people had assumed and changed the debate accordingly.

Double the wedge, quadruple the loss

Here is the property that makes this measurement genuinely important for policy, and the numbers show it cleanly.

In our example a wedge of 2 cost 100. Now double the wedge to 4. Quantity falls further, to 800, and the deadweight loss becomes 400, four times as much. Triple the wedge to 6, quantity falls to 700, and the loss is 900, nine times the original.

The reason is geometric. Raising the wedge stretches both sides of the triangle at once, the height directly and the base because more trades collapse. Area grows with the product of the two, so the loss grows roughly with the square of the distortion. Doubling gives four times, tripling gives nine.

That is the formal argument behind a rule of thumb you will hear from tax economists across the political spectrum: broad bases and low rates. Spreading a modest rate across many things does far less damage than concentrating a heavy rate on a few, because the harm from a heavy rate rises faster than the rate does. It also explains why the last increment of an already high tax is the most costly part of it.

The easier it is to walk away, the more is lost

The other thing driving the size of the triangle is not in the formula at all, but sits behind the quantity figure you enter.

Keep the wedge at 2 and change only how sharply people respond. If quantity falls from 1,000 to 950, the loss is 50. If it falls to 900, the loss is 100. If it falls to 800, the loss is 200. Same tax, four times the damage, purely because buyers and sellers had somewhere else to go.

Which gives you the practical intuition. Tax something people cannot easily give up and quantity barely moves, so the triangle is thin and most of what you take is a transfer rather than a loss. Tax something with close substitutes, or something people can postpone, and demand collapses, the triangle stretches out, and a great deal of value evaporates for a relatively modest amount of revenue collected.

If you want to measure how easily your customers can move to something else, that is exactly what the Cross Price Elasticity Calculator is for.

A deadweight loss is not automatically an argument

It is tempting to treat any deadweight loss as proof that a policy is a mistake. That is a step too far, and the honest position is more interesting.

Sometimes the trades being prevented were causing harm that nobody was paying for. A tax on pollution reduces the quantity of a polluting activity, and the triangle measures the value of the production that stopped. But the point of the tax was to stop it, because those sales were imposing costs on people outside the transaction. Here the deadweight loss in the narrow market is the intended effect, and it can be more than offset by the harm avoided elsewhere. The same logic applies to taxes designed to discourage genuinely harmful consumption.

There is also the simple fact that governments have to raise money somehow, and every method of doing it creates some version of this triangle. The realistic question is rarely whether a tax causes deadweight loss, since they all do. It is which tax causes the least for the revenue raised, which is precisely what this measurement is for.

A last note on the arithmetic. This calculation assumes supply and demand behave in a straight line over the range you are looking at, which is a fair approximation for modest changes and gets shakier for large ones. Treat the result as a well-founded estimate of scale rather than a precise figure, which is how the economists who invented it treated it too.

Questions people ask

How do you calculate deadweight loss?

Multiply the change in price by the change in quantity and halve it. A 2 price wedge that reduces quantity by 100 units gives a deadweight loss of 100.

Is deadweight loss the same as the tax collected?

No, and the distinction is the whole point. Tax revenue is a transfer from buyers and sellers to the government. Deadweight loss is value that nobody receives, because the transactions that would have created it no longer happen.

What causes deadweight loss besides taxes?

Anything that pushes quantity away from what the market would freely trade: price ceilings such as rent control, price floors, tariffs, subsidies, monopoly pricing, and unpriced external costs.

Can deadweight loss be zero?

Yes, if quantity does not change. If buyers and sellers keep trading exactly the same amount despite the price wedge, no trades are lost and the whole effect is a transfer. In practice quantity almost always moves at least a little.

References

The triangle method and its use in measuring welfare cost come from the sources below.

1. Harberger, A. C. (1964). The Measurement of Waste. American Economic Review, 54(3), 58–76. The paper that established the triangle method for estimating deadweight loss.
2. OpenStax. Principles of Economics (consumer and producer surplus, taxation, and the efficiency cost of market interventions). openstax.org