Efficiency of an Excise Tax (I)
Politicians may not
be fascinated with the efficiency effects of taxes, but
economists are. This section looks at how one can examine
the efficiency implications of a simple tax, the
excise tax.
An excise tax is a sales tax on a specific item. An
excise tax can be a per unit tax or an ad
valorem tax. The first is a fixed amount of tax per
item, whereas the second is a percentage of the value of the
item. Excise taxes are a relatively minor source of revenue
for most governments, but they can be examined with simple
diagrams and they illustrate problems that all taxes
have.
The picture below shows supply and demand diagrams for a
competitive market with constant marginal costs. With
constant marginal costs, the supply curve will be a
horizontal line. Before any tax is imposed, q1 is the
quantity sold and P1 is the price. A per unit excise
tax imposes a wedge between the price that the
sellers see and the price that the buyers see. In the graph
the existence of this wedge is indicated by shifting up the
supply curve to "Supply with Tax." The "Supply" line shows
how sellers react to the prices they see, and the
"Supply-with-Tax" line shows how the sellers react to the
prices that the buyers see.1
As a result of the tax, the equilibrium quantity is
q2. Buyers pay a price of P2, but sellers
receive only a price of P1. The amount of revenue
that the government collects is the tax (P2-P1) times
q2, or the wavy rectangle.
This figure illustrates two important results. First,
consumers totally bear this particular tax because the price
rises by the full amount of the tax. This is true whether
buyers or sellers actually write the check that is sent to
the government. If the sellers are legally responsible for
paying the check, the tax is totally shifted. This extreme
result occurs because of the peculiar way in which the
supply curve is drawn--it is not a general result of excise
taxes.
Second, the tax causes a welfare loss or economic
inefficiency because it prevents some exchanges that could
benefit both buyers and sellers. There are several ways to
show this cost. One is to use the concept of consumers'
surplus. The loss of value to consumers is the loss of
consumers' surplus, the area a-c-d-b. The tax
revenue, or area a-c-b-e, represents that part of
lost value government captures. The triangle c-d-e is
a loss to the consumers but it is not a gain to anyone
else.
Another way of indicating that there is a welfare loss is
to ask what happens to consumers' costs and benefits if
another unit beyond q2 in the graph above is
produced. The extra value of another unit is the distance
from the demand curve to the horizontal axis. The extra cost
in terms of the value of resources that must be used is the
distance from the "supply" curve to the horizontal axis.
Because this latter distance is less than the former,
consumers as a whole would benefit by greater production of
the taxed item. But this will not happen because the
perceived marginal costs--which include the tax--are greater
than the actual marginal costs that include only the value
of resources.
The efficiency loss of an excise tax can also be
illustrated in terms of a production-possibilities
frontier.
1Alternatively, the demand curve
could be moved downward by the amount of the tax. With this
interpretation, the prices along the axis would represent
the price excluding the tax. The original demand curve would
remain the line showing how buyers react to the price
including the tax, and the new demand curve would indicate
how buyers would react to the price ignoring the tax. The
supply curve would show how sellers react to price excluding
the tax, and the intersection of the supply and demand
curves would show the equilibrium price excluding
tax.
Copyright
Robert Schenk
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