Tax revenue is a rectangle

Use the after-tax quantity.

The rectangle must use the number of units that still trade after the tax. Using the original quantity overstates revenue.

Revenue equals tax per unit times units still traded. If a $4 tax reduces quantity to 800, revenue is $3,200. Using the original pre-tax quantity overstates revenue because some trades disappear. The revenue rectangle has the tax wedge as height and after-tax quantity as width.

The rectangle’s height is P_b-P_s, not the buyer burden alone or seller burden alone. Its width is the common post-tax quantity, since that is how many taxable units remain. Label both dimensions before multiplying: tax revenue=t× Q_tax. If the graph shows a wedge of $6 and 420 trades, revenue is $2,520 regardless of how the $6 is split.

Consumer and producer surplus shrink. Part becomes government revenue, a transfer within the measured economy. The remainder disappears as deadweight loss. With linear curves, the deadweight-loss triangle is one-half the tax wedge times the reduction in quantity.

Deadweight loss measures the gains from trades between Q_tax and the old efficient quantity Q_e. For these marginal units, willingness to pay exceeded seller cost before tax, but the wedge prevents exchange. With straight curves, the lost area is DWL=1/2 t (Q_e-Q_tax). The original quantity enters only through the reduction, not as the width of the revenue rectangle.

Revenue and deadweight loss

A $6 tax reduces weekly trades from 500 to 420. Revenue is $6×420=$2,520. If demand and supply are linear, deadweight loss is 1/2(6)(80)=$240. The $2,520 is not added to deadweight loss.

The example contains three different quantities: 500 before tax, 420 after tax, and 80 eliminated. Match them to their roles. Revenue uses 420. Deadweight loss uses 80. The reduction in trades is not the amount purchased, and the original amount is not the taxed base after behavior changes.

Government revenue is a transfer in the basic surplus accounting, but spending or raising it can have additional benefits and costs. The diagram isolates the tax market itself. Do not call the entire rectangle a social benefit or loss without information about how funds are used.

If a tax corrects a negative externality, reducing quantity can recover rather than destroy social surplus. The ordinary deadweight-loss triangle assumes the pre-tax competitive quantity was efficient. When private supply omits an external cost, a corrective tax can move quantity toward MSB=MSC. Always identify which curves represent social values.

For a subsidy, the corresponding government expenditure is subsidy per unit times the post-subsidy quantity. A subsidy wedge usually expands quantity and may create overproduction when the untaxed market was efficient. The same rectangle logic applies, but the direction of payment and the potential distortion differ from a tax.

In either case, a rectangle uses the units that remain subject to the policy after behavior adjusts.