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- [Prof. Alex Tabarrok]
So far in our videos,

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we've looked at the effect
of taxes on market prices,

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but we haven't said much

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about why government levies taxes
in the first place,

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namely to get revenues.

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

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which is deadweight loss.

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We can show pretty much
everything we need to show

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with a single diagram.

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So here is our initial equilibrium.

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The price with no tax is $2

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and the quantity exchanged
with no tax is 700 units.

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Now, let's recall
that consumer surplus

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is the consumer's
gain from exchange,

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and it's this green area here,

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the area underneath the demand curve

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and above the price,

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up to the quantity exchanged.

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So it's the area
above the price of $2

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and up to the quantity exchanged
of 700 below the demand curve --

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this area right here.

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Producer surplus
is the producer's gain from exchange,

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and it’s the area
above the supply curve,

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up to the quantity exchanged
and below the price,

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below the producer's price.

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Now, you may also recall

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that a free market maximizes
consumer plus producer surplus.

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What we're going to show
is that when we have a tax,

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this is no longer true.

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The intervention
into the free market

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means that consumer
and producer surplus

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are not maximized.

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Let's take a look.

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So suppose we have tax of $1,

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and using our wedge method,

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we can find what the new price
is going to be for the buyers.

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It's going to be here.

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So the new price
for the buyers is say, $2.50.

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Notice now, the consumer surplus
is not this large green area

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since the price is now higher
and the quantity exchanged

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has fallen.

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The quantity exchanged
falls from 700 units to 500 units.

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So, the consumer surplus
with the tax

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is this smaller green area here.

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Again, it's the area
above the buyer's price,

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up to the quantity exchanged,
and below the demand.

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So exactly the definition
hasn't changed,

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but because of the tax
the price to the buyer changes,

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and the quantity demanded exchanges,

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so the consumer surplus
changes as well.

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In this case, it gets a lot smaller.

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What about producer surplus?

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Well, again, the price
which the sellers receive falls.

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So producer surplus is no longer
this large blue area,

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but is now just
this much smaller blue area.

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So the tax reduces consumer surplus
and it reduces producer surplus.

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Now, what about
this area in the middle?

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Well, fortunately,
that's not wasted.

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That, in fact, is tax revenues.

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So notice that the tax -- 
the height of the tax here -- is $1,

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and there are 500 units exchanged,

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so the government gets $1
for each of those 500 units.

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So this revenue,
tax revenue, is the area.

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It's the height
of this box times the width,

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and the height is the tax,
the width is the quantity exchanged.

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So this is tax revenue.

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Now, what about
this final bit over here?

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That used to be consumer
and producer surplus,

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but now it's deadweight loss.

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Nobody gets that.
That is lost gains from trade.

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So remember,
people used to trade 700 units.

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Now they're only trading 500 units.

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Those units
were benefitting people,

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but they're not anymore

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because these trades
are not occurring.

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I'm going to explain that
in a little bit more detail

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in the next slide.

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For now, just be sure
that you understand

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how to label these areas.

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So this is the new consumer surplus,

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tax revenues,
the new producer surplus,

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and this area is deadweight loss.

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Okay, let's explain deadweight loss
in a little bit more detail.

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Here's the way
to think about deadweight loss.

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Suppose that you're planning
a trip to New York

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and you're going to take the bus.

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The benefit of the trip to you,

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the value of seeing
the sights in New York is $50.

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The cost of the bus ticket is $40.

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So do you take the trip?
Is it a value?

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Yes, you take the trip.

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The total value of the trip is $10,
it's a positive,

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so you decide to take the trip.

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Trips is equal to one.
You make the trip.

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Okay, no problem.

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Now, suppose there's a tax
of $20 on bus fares

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and let's suppose
that raises the cost of the trip

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from $40 to $60.

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It doesn't have to raise it
by exactly that amount,

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by exactly the $20,
but let's suppose it does.

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Okay, so the cost
of the trip is now $60.

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The benefit is still $50.

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So do you take the trip? No.

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The benefit is less than the cost.

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So now, no trip.
Trips are equal to zero.

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Does the government
raise any revenue from you?

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No.

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

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Is there a deadweight loss?
Yes.

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You have lost
the value of the trip.

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You used to, when there was no tax,
you took the trip, it was worth $10,

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so the world was better off
by that $10 of value.

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Now with the tax,
you don't take the trip,

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so that $10 is a deadweight loss.

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It's gone.

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And notice that it's
not made up for by revenue.

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There's no revenue.

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So deadweight loss
is the value of the trips not made

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because of the tax,

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

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Government only makes revenue

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on the trips
which continue to occur.

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So deadweight loss

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is the value of the trips
not made because of the tax.

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Now, to return this
to a more general case,

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instead of trips,
let's just replace that with trades.

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Deadweight loss

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is the value of the trades not made
because of the tax.

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Very quickly,
here's our diagram again.

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Before the tax,
there were 700 trades.

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After the tax,
there were 500 trades.

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So these are the 200 trades
which are not made

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because of the tax.

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And the value
of those 200 trades occurs

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because for these trades,

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the demanders value them

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more than it costs the suppliers
to provide those trades.

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So the demanders value the trades
as given by the demand curve,

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the height of the demand curve.

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The suppliers are willing
to supply those trades --

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the cost to them is given
by the height of the supply curve.

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So the value, the value
minus the costs, if you like,

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is given by this triangle.

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Because those trades
no longer occur,

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that value is no longer produced --
that's deadweight loss,

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the value of the trades
which don't occur because of the tax.

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Here's one more important point
about deadweight loss.

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Deadweight losses are larger

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the more elastic the demand curve
holding revenues constant.

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So for example, which of these
goods would we more like to tax --

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the one on the left
where the demand curve is elastic

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or the one on the right

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where the demand curve
is more inelastic?

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Notice that tax revenues
are the same.

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So if we have a choice,
which good do we want to tax?

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Well, pretty clearly, we want to tax
the good with the inelastic demand

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because the deadweight losses,
the lost gains from trade,

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are much smaller over here
than they are over here.

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So the tax on the good
with the elastic demand --

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it's creating a lot of waste
in order to get this revenue.

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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.

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The intuition here is pretty simple.

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

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And that's what we don't want.

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We don't want
to deter a lot of trades,

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because it's the lost gains
from trade

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which create the problem.

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We don't get any tax revenue
when we deter a trade.

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

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So we want to make sure

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that we deter
as few exchanges as possible

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and that will maximize our revenue
compared to our loss.

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Now, sometimes economists
are laughed at or derided

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

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a good with a very inelastic demand.

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Now, there are many reasons

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for taxing some goods
and not other goods,

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depending upon
who uses the insulin,

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whether it's poor people
or rich people

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or how important
health is and so forth.

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Nevertheless, as a general rule,

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it is better to tax goods
with an inelastic demand

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than goods with an elastic demand.

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That's important,

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and let me give you
an illustration of that.

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Here's something

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which you might think
would be a good idea to tax ---

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luxury yachts.

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They're only bought by the rich,

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so you're not really
harming people very much, right?

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Well, maybe so.

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However, in 1990,

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the federal government
actually applied a 10% luxury tax

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to many luxury goods,
including pleasure boats or yachts

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with a sales price above $100,000.

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They expected tax revenue
of $31 million.

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The reality, however,
was quite different.

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The tax revenues
were only $16.6 million.

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That was because sales of yachts
fell tremendously.

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Perhaps the yacht buyers decided,

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well, they could wait a year or two
before buying their yacht --

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see what happens.

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Or maybe they decided

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they could buy their yachts
in other countries.

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Yachts are pretty easy
to move around the world.

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After all, that's what they're for.

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The net result, in fact,

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was a loss of 7,000 jobs
in the yacht industry.

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Indeed, the federal government
ended up paying out more

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in unemployment benefits
to unemployed yacht workers

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than it collected
in tax revenues from yachts.

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Because of this, the federal tax
was repealed in 1993.

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The lesson here --

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don't tax goods
which have really elastic demands.

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You're not going to get
a lot of revenue,

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you're going to deter
a lot of trades,

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and that will create
a lot of deadweight loss,

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and perhaps,
secondary losses for other people,

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such as the workers.

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That's it actually for taxes.

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The only thing
we have left to do is subsidies.

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We can actually do that
in the next lecture pretty quickly

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because subsidies
are just negative taxes.

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So everything
we've said about taxes,

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with just a few changes
to our language,

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we'll go through
with subsidies as well.

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Thanks.

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- [Narrator]
If you want to test yourself,

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click “Practice Questions.”

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

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♪ [music] ♪