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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- [Prof. Alex Tabarrok]
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
at 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 exchanged
of 700 below the demand curve --

this area right here.

Producer surplus
is the producer's gain from exchange,

and it’s 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 buyers 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 to 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 benefitting 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 costs,

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 want to tax?

Well, pretty clearly, we want to 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.

They 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.

- [Narrator]
If you want to test yourself,

click “Practice Questions.”

Or, if you're ready to move on,
just click “Next Video.”

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