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

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

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

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is deadweight loss.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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fallen.
The quantity exchanged falls from 700

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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bus ticket is $40.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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go through with subsidies as well. Thanks.

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- If you want to test yourself, click
Practice Questions. Or if you're ready

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to move on, just click Next Video.

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♪ [music] ♪