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PROFESSOR: Hi, and welcome
back to the 14.01 problem
solving videos.
Today we're going to do Fall
2010 problem set 6,
problem number 3.
Moldavia is a small country that
currently trades freely
in the world barley market.
Demand and supply for barley in
Moldavia is governed by the
following schedules.
The demand is given by
quantity demanded
equals 4 minus p.
The supply is given by the
quantity supplied equals p.
And the world price of barley
is $1 per bushel.
Part A asks us to calculate
the free trade equilibrium
price and quantity of
barley in Moldavia.
How many bushels do they import
or export, and on a
well-labeled graph depict this
equilibrium situation and
shade the gains from trade
relative to the autarkic no
trade equilibrium in Moldavia.
So what we're going to be doing
in this problem is we're
going to be working with three
different functions.
The first is the domestic
demand.
This is how much people in
Moldavia want barley.
The domestic supply tells us how
much the suppliers within
the country are willing
to supply.
And the international price is
telling us if we open up the
borders to trade without
any tariffs or any
barriers for trade.
This is what the equilibrium
price, or the new equilibrium
price will become.
So let's pretend for a second
that we're in autarky where
there's no trade at all.
In that case the supply
function, which is our
domestic supply, and
demand function
are going to be equal.
And in this case we're going
to have a quantity supplied
that'll be right here at
the equilibrium point.
Now what's going to happen is
that we're going to have the
international price come in when
we open up or borders.
And it's going to function
like a price cap.
So instead of the price being
way up here when we only have
domestic suppliers, we're going
to see that the price is
going to shift down
to p equals 1 to
the equilibrium price.
And what's going to happen is
consumers are going to be able
to consume more out to this
point which we'll calculate.
Suppliers domestically will only
be willing to supply a
quantity at this point.
And that means that all of this
in the middle, which in
earlier problems we would
have thought of
as the excess demand.
It's no longer excess.
These consumers can actually
get a product.
And the way they're
going to get this
product is through imports.
And we need to calculate how
much people are going to
demand, how much the domestic
suppliers will produce, and
what the difference
is made up by the
international importers.
So to start off, let's think
about what's going to happen
when we have free trade.
Well in free trade we're
going to start off
with our demand function.
And instead of setting this
demand function equal to the
supply function, we're just
going to plug in the
international price for the
free trade scenario.
So we can see that in free
trade people are going to
demand three of the products.
Now at the price of one,
however, the suppliers aren't
going to be willing to
supply these three.
So we can calculate how much
they'll actually be willing to
supply at the price of one.
So just plugging in the price
we find the quantity that
they're willing to supply is
going to be equal to 1.
So that means that the
difference here is going to
have to be made up by imports.
So importers are going
to be equal to 2.
Now compared to the autarky
scenario, what we had is we
would set the quantity
demanded equal to
the quantity supplied.
And we would have found that the
price would be equal to 2
and the quantity supplied would
have been equal to 2.
Now we can represent
on the graph in
this autarky situation.
I'm going to outline in blue
what the total consumer and
producer surplus would've
looked like.
So we would have had a consumer
surplus which would
have just been the space below
the demand curve up until the
equilibrium price of 2.
So this would have been
our consumer surplus.
And we would have
had a producer
surplus up to the price.
It's a triangle up
to the price but
above the supply curve.
So the total surplus beforehand
was this box.
Afterwards what we're going to
have is we're going to have a
new consumer surplus because
more people are
accessing the product.
So our new consumer surplus
is right here.
Our new producer surplus is
this triangle out here.
And looking at our graph, the
only difference between the
free trade scenario and the
autarky scenario is this box
right here that I'm
shading in.
So you can see that what
actually happened here
conceptually is that
the domestic
producers were worse off.
Their producer surplus
decreased.
But the consumer surplus
increased so much that
overall, the total surplus
within this country increased
by an amount equal to the area
of this box, which we could
calculate if we needed to.
Let's go ahead and move on to
part B. Part B says the prime
minister of Moldavia,
sympathetic as always,
believes he can help those hurt
by free trade in barley
relative to the situation
and autarky.
He taxes the party that has
benefited from free trade
equal to the amount per bushel
that is the difference between
the autarkic price of barley,
which we calculated right
here, the difference between
that price and the free trade
price of barley, which
is equal to 1.
Furthermore, he rebates the
entire government revenue of
the tax back to the party
harmed by free trade.
In a new, well-labeled
diagram show the
post-tax equilibrium situation.
Calculate and show the new
equilibrium price and quantity
of barley in Moldavia, the
changes in the quantity of
imports or exports, the amount
of revenue collected by the
prime minister, and who pays the
larger burden of this tax,
consumers or producers
in Moldavia and why.
So there's a lot of things that
we need to answer in this
problem, but the first step is
going to be to really think
about how this tax is going to
affect the equilibrium that we
calculated.
And so this tax is going
to be paid by
the group that benefits.
So looking at our graph we said
that the consumers are
benefiting.
We saw that their consumer
surplus changed from this
triangle to the much
larger triangle.
So they're going to be the group
that's paying this tax.
So we're going to have
a new domestic demand
curve for this scenario.
And so we started with our
demand curve of qd
equals 4 minus p.
I'm going to get the inverse
demand so that it's p
equals 4 minus qd.
And now instead of their inverse
demand being equal to
this, we have to
add in the tax.
So the demand curve is going to
shift so that t plus p is
equal to 4 minus qd.
So basically when they think
about how much they're willing
to buy, it's going
to be reduced.
The whole demand curve is going
to shift down by the
amount of the tax.
And so we can represent
this graphically.
The demand curve is going
to shift down an amount
equal to the tax.
I'm going to put dt represent
the demand
curve after the tax.
And the distance from here, from
our initial equilibrium,
down to where the demand
curve is now is going
to be equal to t.
And so we can go ahead since we
know the tax is going to be
equal to the difference between
the autarkic price and
the free trade price,
or 2 minus 1.
We know that t is going
to be equal to 1.
So now we have a new
equation for our
quantity that's demanded.
And we can again set, since we
are still open up to trade,
we're going to set the price
equal to 1 and we can solve
for the new quantity demanded.
So in this scenario since
we're taxing the group,
they're not willing
to buy as much.
The quantity that they're
demanding has shifted
from 3 down to 2.
And how we can represent that
is initially we had the
international price right
here at p equals 1.
So in our initial scenario they
were demanding qd and
domestic suppliers were
supplying at qs.
And now in the new scenario what
we're going to see is see
that the qt, or the quantity
that's demanded with the tax,
has shifted down because of the
tax shifting the demand
curve down as a whole.
Now the last thing, or the other
things that this problem
asks us is how much tax revenue
are they going to
receive and how are the imports
and the domestic
supply going to change.
Well the quantity that's
supplied by domestic producers
given that the demand is still
above 1, the quantity that's
going to be supplied in this new
scenario is still going to
be equal to 1.
And what we're going to see is
this reduction in demand is
only going to affect
the importers.
So before, we had 3 and
then minus 1 for the
amount that's supplied.
Now instead, the imports are
going to be reduced by 1.
And a total tax revenue that's
going to be collected is going
to be equal to the quantity
that's demanded times t.
So we have that the total tax
revenue in the situation is
equal to $2.
So in part A we saw a scenario
where we calculated and looked
at what quantity was supplied
and what price was given when
there was no free
trade at all.
When it was complete autarky.
Now what we're going to do is
we're going to look at the
free trade scenario where
there's the tax.
And we're going to specifically
look at the
producer surplus.
We're going to compare the
producer surplus in autarky to
the producer surplus when
there's free trade but they're
receiving the $2 rebate
from the government.
So part C asks us, are the free
trade losers better off
or worse off after the
rebate than they were
under autarky and why.
Let's start off by drawing
graphs to represent both of
these scenarios.
In autarky what would happen
is there would be no
international price.
And instead we would just have
the equilibrium price right
here, with a quantity demanded
of 2 and a price of 2 as well.
So in the autarky situation we
can calculate the producer
surplus as this triangle
right here.
To calculate the producer
surplus in autarky it's just
going to be 1/2 times
2 times 2.
So beforehand, the producer
surplus, the area of this
triangle, is equal to 2.
Let's look at the scenario after
they're open up to free
trade but with the producers
getting that $2 rebate from
the government.
So in this scenario, the
international price of one
caps the price that the
suppliers are going to get.
And so the suppliers in this
scenario are also only going
to supply a quantity
of one as well.
So the producer surplus
in this scenario
is a smaller triangle.
But the added benefit is that
a chunk of the producer
surplus, the $2, is also being
added in to the producer
surplus that would have existed
under free trade.
So we're going to calculate the
area of this triangle, add
in the $2 government rebate to
get the new producer surplus
in the free trade situation.
So normally the area of that
triangle would only be 1/2.
But since we're adding in the
government rebate of $2, we
find that in the free trade
scenario the producer surplus
has increased to 2.5.
So since the producer surplus
increased to 2.5 we can say
that the producers are better
off under the free trade
system with the caveat that
they're receiving a government
revenue or a tax.
So to quickly summarize
the parts of the
problem that we saw.
What we saw here is we looked
at the autarkic situation
where there's no free trade.
And then we looked at how
producers and consumers are
affected when borders are open
up to free trade without any
government intervention.
After that we saw what happens
when the government has a
policy of taking away from
the group of consumers or
producers that benefit and
giving set revenue back to the
other group.
And we compared the producers'
surplus before and after the
new government intervention.
