Taxes and perfectly inelastic demand | Microeconomics | Khan Academy

Who bears the burden for the taxes when demand is inelastic

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Let's think about who bears the burden

of a tax in different situations.

In this video, we're
going to focus on insulin.

Insulin is interesting.

It's what's needed by Diabetes

in order to maintain
their blood sugar level

so for them, you can almost imagine

they need this just to survive.

It almost has an infinite
marginal benefit for them.

So they're willing, no
matter what the price,

they're essentially willing to take the

insulin that they need to take.

So, for example, even if
the price of insulin were

a dollar, if the doctors in
this town say collectively

all the diabetics need 3,000 vials a year,

they will take 3,000 vials a year.

If the price is $80 a vial,

they'll still take 3,000 vials a year.

So within reason, within a reasonable

price range, you have no change

in quantity demanded.

So, in this case,

at least in a reasonable price range,

the demand curve for insulin is vertical.

Obviously, if we went up to prices like

$9 million per vial, then all of a sudden,

some of the diabetics just won't be able

to afford it, and all of a sudden,

the curve wouldn't be able
to be vertical anymore.

But at least in a reasonable price range,

you have a vertical curve.

So this right over here
is our demand curve.

That is our demand curve.

You might remember when

we talked about elasticity,

this is perfectly inelastic demand.

It's perfectly inelastic
... perfectly inelastic.

The way you can think about it,

I kind of think of a brick

as perfectly inelastic.

No matter how much you
push or pull on the brick

within reason, at least
with my level of strength,

you're not going to be
able to deform the brick.

That's the opposite of a rubber band,

which is very elastic, or you can

think about the definition of elasticity,

the one that we've been using,

elasticity is equal to percent,

change in quantity over
percent, change in price.

Over here, no matter how much we

change price within reason,

at least in this range of
price along this curve,

people are still going to demand

a quantity of 3,000 vials per year.

Let's just draw a supply curve here,

so let's do a supply curve,

looks something like that,

So if you have ... this is supply,

so if you have no taxes,

no regulation of this market,

based on the way I've
drawn it right over here,

the equilibrium price lands us

right around $75.

I did a little research before this video,

it actually turns out that is

about the market price
for a vial of insulin.

The equilibrium quantity, because that is

the exact quantity that people need

is 3,000 vials.

A slightly interesting
thing to think about

in this situation where you have perfectly

inelastic demand, is
what is the producer's

surplus and the consumer's surplus?

The producer's surplus is how much more

money they're getting relative to their,

you can view them as
their opportunity cost

or their incremental marginal cost,

and here we will [unintelligible]

multiple times, this is the producer's

surplus right over here.

It's the area between the prices equal

to the clearing price
and our supply curve.

So, that's our producer surplus.

Producer surplus.

Our consumer surplus is where things

get a little bit interesting.

Consumer surplus is how much more

marginal benefit people are getting

than what they are paying.

We've traditionally said that's the area

between the demand curve and the price.

But now, all of a sudden,
this area is infinite.

This area is infinite.

One way to think about it is that

these diabetics get, you could almost say

close to infinite marginal benefit

from that insulin.

It allows them to have a healthy life.

It allows them to stay alive.

For them, it's essentially priceless.

It's kind of an interesting idea that

you have infinite consumer surplus.

It's not necessarily saying that this

is like a great deal for the diabetics,

it's really just saying that their benefit

is something that they need to survive.

If this was just slightly more elastic,

so if we were to get, maybe to a slghtly

more real world scenario.

In a real world, if things got

a little bit more expensive,

there might be a few diabetics who

would all of a sudden try to lower

their dose or something like that.

The curve, in a real world, actually might

have some very slight elasticity.

It would still be a very steep slope,

but it would actually have
some slight elasticity.

You could imagine if I kept taking this

up and up and up, and at some point,

it actually would bound the area,

but it would, so maybe it goes up here.

Maybe if this was like $2 million up here,

then the demand would
go down dramatically,

but it would be bounded.

But it is a very, very,
very large consumer surplus.

Now with that out of the way,

let's think about what happens

if some misguided politician decides

to tax insulin.

Obviously a very bad idea,

and nothing that I would ever advocate,

but let's think about who
would bear the burden?

I think you could probably guess

who would bear the burden if you had

to put a tax, but we'll actually see it.

We'll think it through with our

supply and our perfectly
inelastic demand curve.

What ends up getting passed is a tax

of $10 per vial.

I'm just making it,
instead of a percentage,

I'm just doing it as a fixed amount

so that we get kind of a fixed shift

in terms of the perceived supply price.

For the producers, this
is what they need to get.

If you want them to produce 3,000 vials,

they need to get $75.

If you [unintelligible] that first vial,

they need to get $60.

What the producers need
to get, plus the tax,

we can draw a new curve.

We've done this multiple times.

For the very first vial,
the producer needs $60,

but then you add the tax there,

it's going to be $70.

For 1,000 vials, it looks
like it's going to be

I don't know, 60 something ...

you add the tax, it's
going to move up to here.

For 3,000 vials, the producers need

around $75, $76, you add $10 to it,

it gets to $85, $86 like that.

What you get is this new curve,

you could use the price from the

consumer's point of view,

or you could view it as

the supply plus tax curve.

I'll call this supply plus tax curve

and that's hard to read, but that

says tax over there.

This is the supply plus tax curve.

Where does that intersect our perfectly

inelastic demand curve?

Well, you can imagine people,

even though the prices are higher,

people still have to get
exactly 3,000 vials per year.

They intersect right at that quantity,

but now we have a new equilibrium price.

Our new equilibrium price
is exactly $10 higher.

If this was $75 or $76,
this is $85 or $86.

This distance right over here is $10.

Let's think about a few things.

Let's think about the total revenue

that the government is going
to get in this situation.

The total revenue is going to be

that $10 times the
3,000 vials per year ...

times 3,000.

So they're going to get $30,000 per year.

Let's think about whose
surplus that came out of.

The tax revenue, this right over here

is the tax revenue.

That right over there is the tax revenue.

The producers are still going to have the

exact same producer surplus,

so all of that tax revenue came directly

out of the consumer surplus.

Another interesting thing to note here is,

because we had this
perfectly inelastic demand,

that even when you raise the price,

it didn't lower the quantity demanded

that we actually don't have
a dead weight loss here

because this was perfectly inelastic.

We're actually having the
same quantity produced

so you have a transfer of surplus from

essentially the diabetics
to the government

in this situation, but you don't have any

lost surplus here because
there's no lost area,

I guess you could say, between where

the supply curve and the
demand curves intersect.

Another way to think about it is

the quantity demand
did not go down because

the price went up.