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PROFESSOR: Hi, and welcome
back to the 14.01 problem

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solving videos.

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Today we're going to do Fall
2010 problem set 6,

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problem number 3.

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Moldavia is a small country that
currently trades freely

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in the world barley market.

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Demand and supply for barley in
Moldavia is governed by the

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following schedules.

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The demand is given by
quantity demanded

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equals 4 minus p.

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The supply is given by the
quantity supplied equals p.

00:00:53.370 --> 00:00:57.870
And the world price of barley
is $1 per bushel.

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Part A asks us to calculate
the free trade equilibrium

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price and quantity of
barley in Moldavia.

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How many bushels do they import
or export, and on a

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well-labeled graph depict this
equilibrium situation and

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shade the gains from trade
relative to the autarkic no

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trade equilibrium in Moldavia.

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So what we're going to be doing
in this problem is we're

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going to be working with three
different functions.

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The first is the domestic
demand.

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This is how much people in
Moldavia want barley.

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The domestic supply tells us how
much the suppliers within

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the country are willing
to supply.

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And the international price is
telling us if we open up the

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borders to trade without
any tariffs or any

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barriers for trade.

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This is what the equilibrium
price, or the new equilibrium

00:01:44.830 --> 00:01:46.690
price will become.

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So let's pretend for a second
that we're in autarky where

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there's no trade at all.

00:01:51.740 --> 00:01:54.960
In that case the supply
function, which is our

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domestic supply, and
demand function

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are going to be equal.

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And in this case we're going
to have a quantity supplied

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that'll be right here at
the equilibrium point.

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Now what's going to happen is
that we're going to have the

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international price come in when
we open up or borders.

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And it's going to function
like a price cap.

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So instead of the price being
way up here when we only have

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domestic suppliers, we're going
to see that the price is

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going to shift down
to p equals 1 to

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the equilibrium price.

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And what's going to happen is
consumers are going to be able

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to consume more out to this
point which we'll calculate.

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Suppliers domestically will only
be willing to supply a

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quantity at this point.

00:02:48.620 --> 00:02:53.340
And that means that all of this
in the middle, which in

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earlier problems we would
have thought of

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as the excess demand.

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It's no longer excess.

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These consumers can actually
get a product.

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And the way they're
going to get this

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product is through imports.

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And we need to calculate how
much people are going to

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demand, how much the domestic
suppliers will produce, and

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what the difference
is made up by the

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international importers.

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So to start off, let's think
about what's going to happen

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when we have free trade.

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Well in free trade we're
going to start off

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with our demand function.

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And instead of setting this
demand function equal to the

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supply function, we're just
going to plug in the

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international price for the
free trade scenario.

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So we can see that in free
trade people are going to

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demand three of the products.

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Now at the price of one,
however, the suppliers aren't

00:04:06.340 --> 00:04:08.750
going to be willing to
supply these three.

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So we can calculate how much
they'll actually be willing to

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supply at the price of one.

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So just plugging in the price
we find the quantity that

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they're willing to supply is
going to be equal to 1.

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So that means that the
difference here is going to

00:04:25.030 --> 00:04:26.910
have to be made up by imports.

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So importers are going
to be equal to 2.

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Now compared to the autarky
scenario, what we had is we

00:04:51.790 --> 00:04:53.720
would set the quantity
demanded equal to

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the quantity supplied.

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And we would have found that the
price would be equal to 2

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and the quantity supplied would
have been equal to 2.

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Now we can represent
on the graph in

00:05:08.800 --> 00:05:10.130
this autarky situation.

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I'm going to outline in blue
what the total consumer and

00:05:13.640 --> 00:05:16.260
producer surplus would've
looked like.

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So we would have had a consumer
surplus which would

00:05:19.680 --> 00:05:26.040
have just been the space below
the demand curve up until the

00:05:26.040 --> 00:05:29.320
equilibrium price of 2.

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So this would have been
our consumer surplus.

00:05:31.930 --> 00:05:33.030
And we would have
had a producer

00:05:33.030 --> 00:05:34.910
surplus up to the price.

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It's a triangle up
to the price but

00:05:37.930 --> 00:05:40.030
above the supply curve.

00:05:42.930 --> 00:05:47.050
So the total surplus beforehand
was this box.

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Afterwards what we're going to
have is we're going to have a

00:05:53.350 --> 00:05:55.670
new consumer surplus because
more people are

00:05:55.670 --> 00:05:57.530
accessing the product.

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So our new consumer surplus
is right here.

00:06:05.310 --> 00:06:10.820
Our new producer surplus is
this triangle out here.

00:06:10.820 --> 00:06:13.640
And looking at our graph, the
only difference between the

00:06:13.640 --> 00:06:19.680
free trade scenario and the
autarky scenario is this box

00:06:19.680 --> 00:06:25.050
right here that I'm
shading in.

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So you can see that what
actually happened here

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conceptually is that
the domestic

00:06:28.500 --> 00:06:29.800
producers were worse off.

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Their producer surplus
decreased.

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But the consumer surplus
increased so much that

00:06:35.410 --> 00:06:39.620
overall, the total surplus
within this country increased

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by an amount equal to the area
of this box, which we could

00:06:42.970 --> 00:06:46.130
calculate if we needed to.

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Let's go ahead and move on to
part B. Part B says the prime

00:06:50.610 --> 00:06:54.200
minister of Moldavia,
sympathetic as always,

00:06:54.200 --> 00:06:56.790
believes he can help those hurt
by free trade in barley

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relative to the situation
and autarky.

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He taxes the party that has
benefited from free trade

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equal to the amount per bushel
that is the difference between

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the autarkic price of barley,
which we calculated right

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here, the difference between
that price and the free trade

00:07:22.840 --> 00:07:27.510
price of barley, which
is equal to 1.

00:07:27.510 --> 00:07:31.120
Furthermore, he rebates the
entire government revenue of

00:07:31.120 --> 00:07:34.380
the tax back to the party
harmed by free trade.

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In a new, well-labeled
diagram show the

00:07:37.000 --> 00:07:39.920
post-tax equilibrium situation.

00:07:39.920 --> 00:07:43.450
Calculate and show the new
equilibrium price and quantity

00:07:43.450 --> 00:07:47.890
of barley in Moldavia, the
changes in the quantity of

00:07:47.890 --> 00:07:51.390
imports or exports, the amount
of revenue collected by the

00:07:51.390 --> 00:07:56.020
prime minister, and who pays the
larger burden of this tax,

00:07:56.020 --> 00:08:01.110
consumers or producers
in Moldavia and why.

00:08:01.110 --> 00:08:03.450
So there's a lot of things that
we need to answer in this

00:08:03.450 --> 00:08:06.930
problem, but the first step is
going to be to really think

00:08:06.930 --> 00:08:10.360
about how this tax is going to
affect the equilibrium that we

00:08:10.360 --> 00:08:12.080
calculated.

00:08:12.080 --> 00:08:13.830
And so this tax is going
to be paid by

00:08:13.830 --> 00:08:15.540
the group that benefits.

00:08:15.540 --> 00:08:18.480
So looking at our graph we said
that the consumers are

00:08:18.480 --> 00:08:19.450
benefiting.

00:08:19.450 --> 00:08:21.810
We saw that their consumer
surplus changed from this

00:08:21.810 --> 00:08:24.590
triangle to the much
larger triangle.

00:08:24.590 --> 00:08:27.500
So they're going to be the group
that's paying this tax.

00:08:27.500 --> 00:08:30.200
So we're going to have
a new domestic demand

00:08:30.200 --> 00:08:31.725
curve for this scenario.

00:08:36.309 --> 00:08:40.210
And so we started with our
demand curve of qd

00:08:40.210 --> 00:08:42.630
equals 4 minus p.

00:08:42.630 --> 00:08:47.550
I'm going to get the inverse
demand so that it's p

00:08:47.550 --> 00:08:51.340
equals 4 minus qd.

00:08:51.340 --> 00:08:54.180
And now instead of their inverse
demand being equal to

00:08:54.180 --> 00:08:57.150
this, we have to
add in the tax.

00:08:57.150 --> 00:09:03.590
So the demand curve is going to
shift so that t plus p is

00:09:03.590 --> 00:09:07.870
equal to 4 minus qd.

00:09:07.870 --> 00:09:10.720
So basically when they think
about how much they're willing

00:09:10.720 --> 00:09:13.060
to buy, it's going
to be reduced.

00:09:13.060 --> 00:09:16.020
The whole demand curve is going
to shift down by the

00:09:16.020 --> 00:09:17.730
amount of the tax.

00:09:17.730 --> 00:09:19.325
And so we can represent
this graphically.

00:09:34.560 --> 00:09:37.720
The demand curve is going
to shift down an amount

00:09:37.720 --> 00:09:39.480
equal to the tax.

00:09:39.480 --> 00:09:42.410
I'm going to put dt represent
the demand

00:09:42.410 --> 00:09:44.450
curve after the tax.

00:09:44.450 --> 00:09:49.850
And the distance from here, from
our initial equilibrium,

00:09:49.850 --> 00:09:53.010
down to where the demand
curve is now is going

00:09:53.010 --> 00:09:56.420
to be equal to t.

00:09:56.420 --> 00:09:59.700
And so we can go ahead since we
know the tax is going to be

00:09:59.700 --> 00:10:03.830
equal to the difference between
the autarkic price and

00:10:03.830 --> 00:10:06.430
the free trade price,
or 2 minus 1.

00:10:06.430 --> 00:10:08.500
We know that t is going
to be equal to 1.

00:10:13.830 --> 00:10:16.010
So now we have a new
equation for our

00:10:16.010 --> 00:10:17.260
quantity that's demanded.

00:10:27.260 --> 00:10:31.220
And we can again set, since we
are still open up to trade,

00:10:31.220 --> 00:10:33.900
we're going to set the price
equal to 1 and we can solve

00:10:33.900 --> 00:10:35.150
for the new quantity demanded.

00:10:43.730 --> 00:10:47.310
So in this scenario since
we're taxing the group,

00:10:47.310 --> 00:10:48.740
they're not willing
to buy as much.

00:10:48.740 --> 00:10:50.460
The quantity that they're
demanding has shifted

00:10:50.460 --> 00:10:52.930
from 3 down to 2.

00:10:52.930 --> 00:10:56.810
And how we can represent that
is initially we had the

00:10:56.810 --> 00:11:02.580
international price right
here at p equals 1.

00:11:05.150 --> 00:11:17.330
So in our initial scenario they
were demanding qd and

00:11:17.330 --> 00:11:21.840
domestic suppliers were
supplying at qs.

00:11:21.840 --> 00:11:25.990
And now in the new scenario what
we're going to see is see

00:11:25.990 --> 00:11:35.820
that the qt, or the quantity
that's demanded with the tax,

00:11:35.820 --> 00:11:39.890
has shifted down because of the
tax shifting the demand

00:11:39.890 --> 00:11:41.140
curve down as a whole.

00:11:43.700 --> 00:11:46.000
Now the last thing, or the other
things that this problem

00:11:46.000 --> 00:11:48.810
asks us is how much tax revenue
are they going to

00:11:48.810 --> 00:11:52.770
receive and how are the imports
and the domestic

00:11:52.770 --> 00:11:55.200
supply going to change.

00:11:55.200 --> 00:11:59.550
Well the quantity that's
supplied by domestic producers

00:11:59.550 --> 00:12:03.420
given that the demand is still
above 1, the quantity that's

00:12:03.420 --> 00:12:08.600
going to be supplied in this new
scenario is still going to

00:12:08.600 --> 00:12:10.600
be equal to 1.

00:12:10.600 --> 00:12:12.960
And what we're going to see is
this reduction in demand is

00:12:12.960 --> 00:12:15.260
only going to affect
the importers.

00:12:15.260 --> 00:12:20.150
So before, we had 3 and
then minus 1 for the

00:12:20.150 --> 00:12:21.640
amount that's supplied.

00:12:21.640 --> 00:12:27.350
Now instead, the imports are
going to be reduced by 1.

00:12:30.130 --> 00:12:33.400
And a total tax revenue that's
going to be collected is going

00:12:33.400 --> 00:12:42.140
to be equal to the quantity
that's demanded times t.

00:12:45.940 --> 00:12:49.690
So we have that the total tax
revenue in the situation is

00:12:49.690 --> 00:12:51.530
equal to $2.

00:12:51.530 --> 00:12:55.720
So in part A we saw a scenario
where we calculated and looked

00:12:55.720 --> 00:13:00.030
at what quantity was supplied
and what price was given when

00:13:00.030 --> 00:13:01.890
there was no free
trade at all.

00:13:01.890 --> 00:13:03.720
When it was complete autarky.

00:13:03.720 --> 00:13:05.220
Now what we're going to do is
we're going to look at the

00:13:05.220 --> 00:13:07.800
free trade scenario where
there's the tax.

00:13:07.800 --> 00:13:09.530
And we're going to specifically
look at the

00:13:09.530 --> 00:13:10.890
producer surplus.

00:13:10.890 --> 00:13:14.490
We're going to compare the
producer surplus in autarky to

00:13:14.490 --> 00:13:17.530
the producer surplus when
there's free trade but they're

00:13:17.530 --> 00:13:20.390
receiving the $2 rebate
from the government.

00:13:20.390 --> 00:13:25.250
So part C asks us, are the free
trade losers better off

00:13:25.250 --> 00:13:27.610
or worse off after the
rebate than they were

00:13:27.610 --> 00:13:30.470
under autarky and why.

00:13:30.470 --> 00:13:32.900
Let's start off by drawing
graphs to represent both of

00:13:32.900 --> 00:13:34.860
these scenarios.

00:13:34.860 --> 00:13:40.080
In autarky what would happen
is there would be no

00:13:40.080 --> 00:13:41.470
international price.

00:13:41.470 --> 00:13:49.190
And instead we would just have
the equilibrium price right

00:13:49.190 --> 00:13:58.560
here, with a quantity demanded
of 2 and a price of 2 as well.

00:13:58.560 --> 00:14:06.810
So in the autarky situation we
can calculate the producer

00:14:06.810 --> 00:14:11.240
surplus as this triangle
right here.

00:14:11.240 --> 00:14:14.020
To calculate the producer
surplus in autarky it's just

00:14:14.020 --> 00:14:19.440
going to be 1/2 times
2 times 2.

00:14:19.440 --> 00:14:23.170
So beforehand, the producer
surplus, the area of this

00:14:23.170 --> 00:14:25.330
triangle, is equal to 2.

00:14:25.330 --> 00:14:28.560
Let's look at the scenario after
they're open up to free

00:14:28.560 --> 00:14:32.510
trade but with the producers
getting that $2 rebate from

00:14:32.510 --> 00:14:33.760
the government.

00:14:44.680 --> 00:14:49.210
So in this scenario, the
international price of one

00:14:49.210 --> 00:14:51.870
caps the price that the
suppliers are going to get.

00:14:51.870 --> 00:14:55.620
And so the suppliers in this
scenario are also only going

00:14:55.620 --> 00:14:58.350
to supply a quantity
of one as well.

00:14:58.350 --> 00:15:01.270
So the producer surplus
in this scenario

00:15:01.270 --> 00:15:03.710
is a smaller triangle.

00:15:03.710 --> 00:15:07.990
But the added benefit is that
a chunk of the producer

00:15:07.990 --> 00:15:13.110
surplus, the $2, is also being
added in to the producer

00:15:13.110 --> 00:15:16.030
surplus that would have existed
under free trade.

00:15:16.030 --> 00:15:18.830
So we're going to calculate the
area of this triangle, add

00:15:18.830 --> 00:15:22.530
in the $2 government rebate to
get the new producer surplus

00:15:22.530 --> 00:15:23.780
in the free trade situation.

00:15:26.300 --> 00:15:31.890
So normally the area of that
triangle would only be 1/2.

00:15:31.890 --> 00:15:36.020
But since we're adding in the
government rebate of $2, we

00:15:36.020 --> 00:15:42.610
find that in the free trade
scenario the producer surplus

00:15:42.610 --> 00:15:46.610
has increased to 2.5.

00:15:46.610 --> 00:15:50.960
So since the producer surplus
increased to 2.5 we can say

00:15:50.960 --> 00:15:54.840
that the producers are better
off under the free trade

00:15:54.840 --> 00:15:58.720
system with the caveat that
they're receiving a government

00:15:58.720 --> 00:16:00.880
revenue or a tax.

00:16:00.880 --> 00:16:02.870
So to quickly summarize
the parts of the

00:16:02.870 --> 00:16:04.480
problem that we saw.

00:16:04.480 --> 00:16:08.340
What we saw here is we looked
at the autarkic situation

00:16:08.340 --> 00:16:10.020
where there's no free trade.

00:16:10.020 --> 00:16:12.070
And then we looked at how
producers and consumers are

00:16:12.070 --> 00:16:15.150
affected when borders are open
up to free trade without any

00:16:15.150 --> 00:16:17.010
government intervention.

00:16:17.010 --> 00:16:19.790
After that we saw what happens
when the government has a

00:16:19.790 --> 00:16:24.380
policy of taking away from
the group of consumers or

00:16:24.380 --> 00:16:28.950
producers that benefit and
giving set revenue back to the

00:16:28.950 --> 00:16:29.940
other group.

00:16:29.940 --> 00:16:34.370
And we compared the producers'
surplus before and after the

00:16:34.370 --> 00:16:35.620
new government intervention.