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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.