- [Instructor] We are asked, which of the following
correctly identifies the areas of
consumer surplus, producer surplus,
tax revenue, and deadweight loss
in this market after the tax?
So pause this video, have a go at it.
Even if you struggle with it
it will make your brain more attuned
to when we work through it together.
All right, now let's work through this together.
And I just want to sort of understand
what's going on here before I even try
to answer their questions.
So let's first take a look
at what's going on before the tax.
So before the tax, I have
this supply curve
right over here in blue.
And I have this demand curve.
Where they intersect gives us our
equilibrium price.
Right over here.
And our equilibrium quantity
right over there.
And if we wanted to look at the
consumer surplus
it would be the area above
this horizontal line.
And, below
the demand curve.
So that is our original consumer surplus.
And our original producer surplus is above
the supply curve
and below this price horizontal line.
And so, the total surplus would be
this entire triangle
right over here.
All before the tax.
But they're not asking us before the tax
they want us to figure out everything
after the tax.
So what happens to the tax?
Well, if we assume it's
a tax on
each unit
that is being supplied.
The effect it has, and we see it here,
they've drew it for us.
Is it shifts the effective supply curve up.
And I say the effective one because
that's the one that's going to affect
the equilibrium price, or the new equilibrium price.
But as we'll see there's some nuances
in terms of considering the surplus.
So first, let's think about the consumer.
Well, actually let me label
the now price with the taxes.
So, this is now the R equilibrium price
where we have the taxes.
It's where our demand curve hasn't shifted.
That's where the existing demand curve
intersects with this new shifted
supply with tax curve.
And similarly, that point of intersection
also tells us our quantity
with the taxes.
Now, now that we've understood everything,
or hopefully we have,
let's think about the various surpluses
and the deadly weight losses
and the tax revenues.
So first, let's think about the consumer surplus.
Well, the consumer surplus is going to be
the region above our new
horizontal price.
And below the demand curve.
So that is this region R
right over here.
That still, you have this consumer right over here
who was willing to pay a lot
but still has to pay less than that
even with the taxes.
So they're getting this benefit
more than they would have needed
in order, it would have been willing to pay more
than the tax, and so they're getting
this surplus.
And so if you look at the entire market right now
the total consumer surplus after the tax
is R.
R is equal to
consumer surplus.
And this is all after
the taxes.
Consumer surplus.
Now, what about the producer surplus?
Well, if we weren't dealing with the tax
we would just look above the supply curve
and below this equilibrium price line and say
hey, maybe it's that area.
But remember what's happening from the
producers point of view.
The producer does not see
this new increased price at this quantity.
The producer, remember, they don't get to keep
the tax revenue.
That, they have to give to the government.
So the producer
actually this is the price
that the producer sees.
So you can see this is
this is what
what producers
what producers get
after taxes.
After
taxes, or I say net of taxes.
May be a better way
to think about it.
Net
of taxes.
And so the producer surplus
is going to be the area
below what they're getting
from the market, net of taxes.
And above
what they
the price is at which
they were willing to produce various quantities.
And so the producer surplus is
this area of V over here.
So, V is equal to the producer.
Producer
surplus.
And now, what about
the tax revenue?
Well, the tax revenue is, is essentially
going to be all of this other part
of the total surplus.
This is what goes to the government.
The difference between these two.
If the producers
did not have to give that tax to the government
then they wouldn't have been able to keep all of this.
But this, right over here.
Let me do this in a different color.
So this region, right over here,
is what the government is able to keep.
Notice, it's this quantity
and they get this much tax per unit quantity.
And so this area
is the government, is the revenue to the government.
So, S plus U is equal to
tax revenue.
Tax
revenue.
And then last but not least,
what about the deadweight loss?
Well remember, the deadweight loss
is the difference between the original
the total surplus.
When we just let things naturally go to equilibrium.
The difference between that
and now our new total surplus,
which is now lower because
we have not allowed the market
to function in a very natural way
because of this tax on it.
Well, as we said before,
the original total surplus was
this entire triangle.
Now the total surplus is this trapezoid
that's the sum of all of these areas.
And so what we lost
is this area right over here.
So that is the deadweight loss.
So T plus W
is equal to the
deadweight loss.
And we're done.