Tax Revenue and Deadweight Loss

Why do taxes exist? What are the effects of taxes? We discuss how taxes affect consumer surplus and producer surplus and discuss the concept of deadweight loss at length. We’ll also look at a real-world example of deadweight loss: taxing luxury yachts in the 1990s.

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- So far in our videos, we've looked at
the effect of taxes on market prices, but

we haven't said much about why government
levies taxes in the first place, namely to

get revenues. So let's look at that and
also the cost of raising revenues, which

is deadweight loss.

We can show pretty much
everything we need to show with a

single diagram. So here is our initial
equilibrium. The price with no tax is $2

and the quantity exchanged with no tax is
700 units. Now, let's recall that consumer

surplus is the consumer's gain from
exchange, and it's this green area here,

the area underneath the demand curve and
above the price, up to the quantity

exchanged. So it's the area above the
price of $2 and up to the quantity

exchange of 700 below the demand curve,
this area right here. Producer surplus is

the producer's gain from exchange, and is
the area above the supply curve, up to the

quantity exchanged and below the price,
below the producer's price. Now, you may

also recall that a free market maximizes
consumer plus producer surplus. What we're

going to show is that when we have a tax,
this is no longer true. The intervention

into the free market means that consumer
and producer surplus are not maximized.

Let's take a look. So suppose we have tax
of $1, and using our wedge method, we can

find what the new price is going to be for
the buyers. It's going to be here. So the

new price for the buyer is say, $2.50.
Notice now, the consumer surplus is not

this large green area since the price is
now higher and the quantity exchanged has

fallen.
The quantity exchanged falls from 700

units to 500 units. So the consumer
surplus with the tax is this smaller green

area here. Again, it's the area above the
buyer's price, up to the quantity

exchanged, and below the demand. So
exactly the definition hasn't changed, but

because of the tax, the price of the buyer
changes, and the quantity demanded

exchanges, so the consumer surplus changes
as well. In this case, it gets a lot

smaller. What about producer surplus?
Well, again, the price which the sellers

receive falls. So producer surplus is no
longer this large blue area, but is now

just this much smaller blue area. So the
tax reduces consumer surplus and it

reduces producer surplus. Now, what about
this area in the middle? Well,

fortunately, that's not wasted. That, in
fact, is tax revenues. So notice that the

tax, the height of the tax here is $1 and
there are 500 units exchanged, so the

government gets $1 for each of those 500
units. So this revenue, tax revenue is the

area. It's the height of this box times
the width, and the height is the tax, the

width is the quantity exchanged. So this
is tax revenue. Now, what about this final

bit over here? That used to be consumer
and producer surplus, but now it's

deadweight loss. Nobody gets that. That is
lost gains from trade. So remember, people

used to trade 700 units, now they're only
trading 500 units. Those units were

benefiting people, but they're not anymore
because these trades are not occurring.

I'm going to explain that in a little bit
more detail in the next slide. For now,

just be sure that you understand how to
label these areas.

So this is the new consumer surplus, tax
revenues, the new producer surplus, and

this area is deadweight loss. Okay, let's
explain deadweight loss in a little bit

more detail. Here's the way to think about
deadweight loss. Suppose that you're

planning a trip to New York and you're
going to take the bus. The benefit of the

trip to you, the value of seeing the
sights in New York is $50, the cost of the

bus ticket is $40.

So do you take the trip?
Is it a value? Yes, you take the trip. The

total value of the trip is $10, it's a
positive, so you decide to take the trip.

Trips is equal to one. You make the trip.
Okay, no problem. Now, suppose there's a

tax of $20 on bus fares and let's suppose
that raises the cost of the trip from $40

to $60. It doesn't have to raise it by
exactly that amount, by exactly the $20,

but let's suppose it does. Okay, so the
cost of the trip is now $60. The benefit

is still $50. So do you take the trip? No.
The benefit is less than the cost. So now,

no trip. Trips are equal to zero. Does the
government raise any revenue from you? No.

Since you don't take the trip, the
government makes no revenue. Is there a

deadweight loss? Yes. You have lost the
value of the trip. You used to, when there

was no tax, you took the trip, it was
worth $10, so the world was better off by

that $10 of value. Now with the tax, you
don't take the trip, so that $10 is a

deadweight loss. It's gone. And notice
that it's not made up for by revenue.

There's no revenue. So deadweight loss is
the value of the trips not made because of

the tax, and there's no revenue on trips
which aren't made.

Government only makes revenue on the trips
which continue to occur. So deadweight

loss is the value of the trips not made
because of the tax. Now, to return this to

a more general case, instead of trips,
let's just replace that with trades.

Deadweight loss is the value of the trades
not made because of the tax. Very quickly,

here's our diagram again. Before the tax,
there were 700 trades. After the tax,

there were 500 trades. So these are the
200 trades which are not made because of

the tax. And the value of those 200 trades
occurs because for these trades, the

demanders value them more than it costs
the suppliers to provide those trades. So

the demanders value the trades as given by
the demand curve, the height of the demand

curve, the suppliers are willing to supply
those trades, the cost to them is given by

the height of the supply curve, so the
value, the value minus the cost, if you

like, is given by this triangle. Because
those trades no longer occur, that value

is no longer produced, that's deadweight
loss, the value of the trades which don't

occur because of the tax. Here's one more
important point about deadweight loss.

Deadweight losses are larger the more
elastic the demand curve holding revenues

constant. So for example, which of these
goods would we more like to tax, the one

on the left where the demand curve is
elastic or the one on the right where the

demand curve is more inelastic? Notice
that tax revenues are the same. So if we

have a choice, which good do we wanna tax?
Well, pretty clearly, we wanna tax the

good with the inelastic demand because the
deadweight losses, the lost gains from

trade, are much smaller over here than
they are over here.

So the tax on the good with the elastic
demand, it's creating a lot of waste in

order to get this revenue. Over here, the
tax on the good with the inelastic demand,

there's only a little bit of waste for the
same amount of revenue. The intuition here

is pretty simple. If the demand curve is
inelastic, then a tax won't deter many

trades. And that's what we don't want. We
don't want to deter a lot of trades

because it's the lost gains from trade
which create the problem. We don't get any

tax revenue when we deter a trade. There's
no tax revenue when you deter an exchange.

So we want to make sure that we deter as
few exchanges as possible and that will

maximize our revenue compared to our loss.
Now, sometimes economists are laughed at

or derided because this implies, for
example, that you ought to tax insulin, a

good with a very inelastic demand. Now,
there are many reasons for taxing some

goods and not other goods, depending upon
who uses the insulin, whether it's poor

people or rich people or how important
health is and so forth. Nevertheless, as a

general rule, it is better to tax goods
with an inelastic demand than goods with

an elastic demand. That's important, and
let me give you an illustration of that.

Here's something which you might think
would be a good idea to tax, luxury

yachts. They're only bought by the rich,
so you're not really harming people very

much, right? Well, maybe so. However, in
1990, the federal government actually

applied a 10% luxury tax to many luxury
goods, including pleasure boats or yachts

with a sales price above $100,000, the
expected tax revenue of $31 million. The

reality, however, was quite different. The
tax revenues were only $16.6 million.

That was because sales of yachts fell
tremendously. Perhaps the yacht buyers

decided, well, they could wait a year or
two before buying their yacht, see what

happens, or maybe they decided they could
buy their yachts in other countries.

Yachts are pretty easy to move around the
world. After all, that's what they're for.

The net result, in fact, was a loss of
7,000 jobs in the yacht industry. Indeed,

the federal government ended up paying
out more in unemployment benefits to

unemployed yacht workers than it collected
in tax revenues from yachts. Because of

this, the federal tax was repealed in
1993. The lesson here, don't tax goods

which have really elastic demands.
You're not going to get a lot of revenue,

you're going to deter a lot of trades, and
that will create a lot of deadweight loss,

and perhaps, secondary losses for other
people, such as the workers. That's it

actually for taxes. The only thing we have
left to do is subsidies. We can actually

do that in the next lecture pretty quickly
because subsidies are just negative taxes.

So everything we've said about taxes, with
just a few changes to our language, will

go through with subsidies as well. Thanks.

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