Commodity Taxes

In this video we cover taxes and tax revenue and subsidies on goods. We discuss commodity taxes, including who pays the tax and lost gains from trade, also called deadweight loss. We’ll take a look at the tax wedge and apply what we learn to the example of Social Security taxes.

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- [Tyler] Today we begin the first of
several talks on taxes and subsidies.

We're not going to be talking about income
taxes and income subsidies. Those are

typically topics for macroeconomics.
Instead, we'll be talking about taxes and

subsidies on goods, like a sales tax or a
subsidy for wheat. These are also called

commodity taxes and subsidies. So let's
get going.

We're going to be emphasizing

three important ideas about commodity
taxation. First, who pays the tax does not

depend on who writes the check to the
government. For example, suppose the

government is taxing apples. The
government could make the buyer of apples

pay for each apple that they buy. Or they
could require the sellers of the apples

pay for each apple that they sell. What
we're going to show is that, from the

point of view of the buyers or sellers, it
actually doesn't matter how the tax is

placed. The actual outcomes are going to
be identical. Another way of putting this

is that the economic incidence of the tax,
who actually pays the tax, does not depend

on the legal incidence, who is in law
required to write the check to the

government. This will become a little bit
clearer as we go along. Don't worry about

it if it's not clear yet. The second key
point, who pays the tax does depend on the

relative elasticities of demand and
supply. In fact, we can summarize point

one and point two by saying, who pays the
tax depends not on the laws of congress

but rather on the laws of supply and
demand. The third point is that commodity

taxation raises revenue, but it also takes
away some gains from trade, that is, it

creates deadweight loss. We're going to be
looking at point one in this talk, and

then we'll move on to point two, and point
three in later talks. So, let's start with

point one.
Let's begin our analysis of commodity

taxation by assuming the suppliers are the
one who have to send the check to the

government. That is the legal incidence of
the tax falls on the suppliers. What does

a tax on the suppliers do? We can think
about a tax on suppliers as increasing

their costs. This is going to shift the
supply curve up by the amount of the tax,

so the supply curve shifts up like this.
Another way of thinking about this, is to

remember that the supply curve tells us
the minimum amount which suppliers require

to offer a given quantity in the
marketplace. The tax, that is going to

increase the minimum amount that suppliers
are requiring to offer that quantity in

the marketplace. It shifts up that minimum
amount required by just the amount of the

tax. With the new supply curve we find the
new equilibrium. The market equilibrium

moves from point A to point B. What we see
is that of course, the quantity which is

exchanged goes down, in addition, the
price paid by the buyers goes up. How much

do the suppliers get? The suppliers
collect this amount, the price paid by the

buyers, but now they have to give a
certain amount of that, the tax to the

government. The suppliers end up receiving
this amount after tax, right here. In

other words, what the tax does, it means
that the buyers pay more than before, and

the sellers receive less than before.
Without any tax, the price the buyers pay

is the same as the price the supplier
receives. With the tax the buyers pay a

certain price, but the sellers get less
than that. They get whatever the buyers

pay minus of course, the tax. That's the
situation when the suppliers pay the tax,

or the suppliers have to send the check to
the government. Let's now look at what

happens when it's the buyers who must send
the check to the government. Now, we look

at the situation when the legal incidence
is on the buyers. We begin just as before

with the equilibrium with no taxes.
No taxes on sellers or buyers. Again, that

equilibrium is at point A. I've also
included this supply curve here. This is

the supply curve when the tax is on the
suppliers. It's the supply curve from the

previous problem. It's not relevant for
this problem. I've included it rather to

remind us of where the equilibrium on the
previous problem was. You can think of

this as a kind of ghost supply curve. It's
a supply curve from the previous problem

coming back to haunt us. So what's the
effect of a tax on the demanders? Think

about it this way. Suppose the most you
were willing to pay for an apple is one

dollar. Again, most you're willing to pay
for that apple, a dollar, no more. Now,

suppose you learned that the government
has instituted a new tax. For every apple

you buy, you must now pay 25 cents to the
government. Now, how much are you willing

to pay to suppliers for that apple?
You're only willing to pay the maximum

amount that you're going to be willing to
pay suppliers is now 75 cents. The maximum

amount that apple was worth to you is a
dollar. If you know you're going to be

taxed 25 cents if you buy that apple, then
the most you're going to be willing to pay

the supplier is 75 cents, because 75 cents
plus the 25 cent tax to the government,

that's one dollar. That's the most you're
willing to pay to get the apple. In other

words, what a tax on demanders does is it
reduces their willingness to pay, and that

means the demand curve shifts. Which way?
The demand curve shifts down by the amount

of the tax. So let's shift. The tax is
exactly the same amount that was before.

Let's shift the demand curve down by the
amount of the tax. We find now that the

new equilibrium is at point B. Notice
first of all, that the quantity has

declined. The quantity exchange has
declined by exactly the same amount as

before in the previous problem. What about
the price received by the sellers? The

sellers now receive this price.
Low and behold, that's exactly the same

price as it was before. How about the
price paid by the buyers? The buyers now

pay what they paid to the suppliers, plus
they must pay the tax to the government.

This distance is the tax. Low and behold,
the price after tax paid by the buyers is

once again exactly what it was when the
tax was on the suppliers. When the tax is

on the buyers, the buyers pay more than
before. The sellers receive less than

before by exactly the same amounts. The
quantity declines by the same amount, too.

The net price, or the total price paid by
the buyers is the same. The total price

received by the sellers is the same. Now
that you know the idea, I'm going to show

you a simpler way of demonstrating this.
What we just showed is that it doesn't

matter whether the suppliers must write
the check to the government or the

demanders must write the check to the
government in order to pay the tax. In

other words, we can analyze the tax by
shifting the supply curve up, or by

shifting the demand curve down. As long as
we analyze the same size tax, we're going

to get equivalent outcomes. It's going to
come out the same whichever choice of tax

we make. There's actually a simpler way of
thinking about this. What we can think

about such a tax is doing, is driving a
wedge between what the buyer is paying and

what the sellers receive. When there's no
tax, what the buyers pay is what the

sellers receive, but when there's a tax,
the buyers pay more than what the sellers

receive. The difference is what the
government gets. The difference is the

amount of the tax. So let's think about
this as a tax wedge. Let's say this tax

wedge, this side is, let's say a dollar.
Another way of analyzing the tax is to

drive this wedge into the diagram until
the top of the wedge hits the demand

curve, and the bottom of the wedge just
touches the supply curve. Let's take a

look. I'm going to drive the wedge in.
What this tells us is that the price the

buyer pays will be here, point B.
The price the suppliers receive will be

point D. The difference is the tax. For
instance, if the buyers end up paying

$2.65, then the sellers must receive $1.65
if the tax is a dollar. Similarly, if the

suppliers receive a $1.65 and the tax is a
dollar, the buyers must be paying $2.65.

With this wedge, we could read off the
diagram the price the buyer pays, the

price the seller receives, and the
quantity exchanged. We don't even have to

shift any curves. We just drive the wedge
into this diagram. Let's do an

application. In the United States, under
the Federal Insurance Contributions Act,

FICA, 12.4% of earned income up to an
annual limit must be paid into social

security, and 2.9%, an additional 2.9%
must be paid into Medicare. Half of this

amount comes directly from the employee.
You can see it on your own paychecks. This

is the FICA tax, and half the amount comes
from the employer. The question is, does

the fact that it's a 50/50 split, does
this make a difference? Does this mean for

example, that since the employer is paying
half that this is necessarily a good deal

for the employee? No it doesn't mean that.
What we now know is that we could have

100% of this tax paid by the employee, or
we could have 100% of this tax paid by the

employer. This wouldn't make a difference,
not to wages, not to prices, not to

anything. It would change the legal
incidence of the tax, but it would not

change the final economic incidence. I
haven't said here who actually pays the

tax. That's what we're going to be talking
about in the next lecture. What I've said

here is that it doesn't matter who pays
the tax from a legal point-of-view of who

is obliged to deliver that money. So the
legal incidence again, does not have a

bearing on the economic incidence of the
tax.

What we're going to talk about in the next
lecture is what does determine the

economic incidence of a tax. It turns out
to be elasticities of supply and demand,

and that's what we'll take up in the next
lecture. Thanks again for listening.

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