What is deadweight loss?

Deadweight loss is the lost gain from trades that would have been worth making but do not happen. It appears when taxes, price controls, monopoly pricing or other distortions push the quantity traded below the efficient level. It matters because the loss is not transferred to anyone else: it is simply gone.

How it works

Each possible trade has a buyer who values the good at some amount and a seller whose cost is some lower amount. The gap between them is the gain from the trade. A distortion stops the trades with the smallest gaps first, because those are the ones the distorted price makes unattractive.

The lost value is the sum of the gaps on the trades that no longer occur. It grows faster than the size of the distortion, because each additional unit of distortion removes trades with larger gaps. For a simple linear case, the loss is roughly half of the price distortion times the quantity lost.

Example

Say a good would sell 100 units a week at 10 each, with buyers valuing the last unit at 10 and sellers' cost on it also at 10. A tax of 4 per unit is added and the quantity falls to 80. The 20 trades that disappeared each had a gain that ranged from 0 up to 4. Their average gain is about 2, so the total loss is about 20 times 2, which is 40 per week. The tax collected on the 80 remaining units is 320, but the 40 is lost to everyone. All figures are illustrative.

How to model it in Machinations

Model buyers and sellers with two Sources feeding a Trader, with a Register that computes the quantity traded from the price and a tax Lever. Add a Pool called Gains from trade that collects the gap between value and cost for each unit traded, and a second Pool for tax revenue. Play with the tax at 0 and at 4, and chart the gains Pool against the baseline to see how much value the tax removed.