506 section 9 Behind the Demand Curve: Consumer Choice
The area of the shaded rectangle is:Area=Height×Width=$40 per room×5,000 rooms=$200,000,orTax revenue=Area of shaded rectangleThis is a general principle: The revenue collected by an excise tax is equal to the area of a rec-
tangle with the height of the tax wedge between the supply price and the demand price and the width
of the quantity sold under the tax.The Costs of Taxation
What is the cost of a tax? You might be inclined to answer that it is the amount of
money taxpayers pay to the government—the tax revenue collected. But suppose the
government uses the tax revenue to provide services that taxpayers want. Or suppose
that the government simply hands the tax revenue back to taxpayers. Would we say in
those cases that the tax didn’t actually cost anything?
No—because a tax, like a quota, prevents mutually beneficial transactions from oc-
curring. Consider Figure 50.10 once more. Here, with a $40 tax on hotel rooms, guests
pay $100 per room but hotel owners receive only $60 per room. Because of the wedge
created by the tax, we know that some transactions didn’t occur that would have oc-
curred without the tax. More specifically, we know from the supply and demand curves
that there are some potential guests who would be willing to pay up to $90 per night
and some hotel owners who would be willing to supply rooms if they received at least
$70 per night. If these two sets of people were allowed to trade with each other without
the tax, they would engage in mutually beneficial transactions—hotel rooms would be
rented. But such deals would be illegal because the $40 tax would not be paid. In our
example, 5,000 potential hotel room rentals that would have occurred in the absence of
the tax, to the mutual benefit of guests and hotel owners, do not take place because of
the tax.
So an excise tax imposes costs over and above the tax revenue collected in the form of
inefficiency, which occurs because the tax discourages mutually beneficial transactions.
You may recall from Module 9 that the cost to society of this kind of inefficiency—the
value of the forgone mutually beneficial transactions—is called the deadweight loss.
While all real-world taxes impose some deadweight loss, a badly designed tax imposes a
larger deadweight loss than a well-designed one.
To measure the deadweight loss from a tax, we turn to the concepts of producer and
consumer surplus. Figure 50.11 shows the effects of an excise tax on consumer
and producer surplus. In the absence of the tax, the equilibrium is at Eand the equilib-
rium price and quantity are PEandQE, respectively. An excise tax drives a wedge equal to
the amount of the tax between the price received by producers and the price paid by con-
sumers, reducing the quantity sold. In this case, with a tax of Tdollars per unit, the quan-
tity sold falls to QT.The price paid by consumers rises to PC,the demand price of the
reduced quantity, QT,and the price received by producers falls to PP,the supply price of
that quantity. The difference between these prices, PC−PP,is equal to the excise tax, T.
Using the concepts of producer and consumer surplus, we can show exactly how
much surplus producers and consumers lose as a result of the tax. We learned previ-
ously that a fall in the price of a good generates a gain in consumer surplus that is
equal to the sum of the areas of a rectangle and a triangle. Similarly, a price increase
causes a loss to consumers that is represented by the sum of the areas of a rectangle and
a triangle. So it’s not surprising that in the case of an excise tax, the rise in the price
paid by consumers causes a loss equal to the sum of the areas of a rectangle and a trian-
gle: the dark blue rectangle labeled Aand the area of the light blue triangle labeled Bin
Figure 50.11.Thedeadweight loss (from a tax) is the
decrease in total surplus resulting from the
tax, minus the tax revenues generated.