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Deadweight loss measures surplus loss from market distortions (monopoly, taxes, externalities). For small changes, deadweight loss is approximately half the distortion squared times quantity. Advanced welfare analysis uses compensating or equivalent variation to account for income effects, essential when income effects are large or distributional impacts matter. Distributional effects are equally important to efficiency effects in policy evaluation.
You already know that consumer and producer surplus measure the gains from trade in a market. Deadweight loss is what happens when a policy or market failure prevents some of those gains from being realized — it is surplus that simply vanishes, captured by no one. When a tax is imposed on a good, transactions that would have occurred at the free-market price no longer happen because the tax drives a wedge between what buyers pay and what sellers receive. The lost surplus from those missing transactions is the deadweight loss, represented by the familiar triangle between the supply and demand curves.
For small taxes or distortions, deadweight loss follows a useful approximation: it is roughly one-half times the tax (or distortion) squared times the quantity affected. The squared term is critical — it means deadweight loss grows more than proportionally with the size of the distortion. Doubling a tax roughly quadruples the deadweight loss. This is why economists generally prefer broad-based taxes at low rates over narrow taxes at high rates, and why large market distortions (like monopoly pricing far above marginal cost) are more damaging than small ones.
Standard surplus analysis assumes that a dollar is worth the same to every consumer, but this is clearly wrong when income effects matter. A dollar lost by a poor household is more consequential than a dollar lost by a wealthy one. Compensating variation asks: how much money would we need to give (or take from) a consumer after a price change to restore their original utility level? Equivalent variation asks: how much money would the consumer pay (or accept) to avoid the price change altogether? These measures, which you encountered in consumer theory, give more precise welfare assessments than simple surplus calculations because they account for how purchasing power changes affect different consumers differently.
The deeper lesson of advanced welfare analysis is that efficiency and distribution are inseparable in policy evaluation. A policy that increases total surplus but concentrates the gains among the wealthy while imposing costs on the poor may reduce social welfare under any reasonable welfare criterion. Conversely, a policy with modest deadweight loss might be worth adopting if it substantially improves the position of the worst-off. Complete policy evaluation requires measuring both the size of the pie (efficiency) and how the slices change (distribution) — and then making a value judgment about the tradeoff between them.