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PROFESSOR: Hi, and welcome
back to the 14.01 problem

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00:00:25,750 --> 00:00:27,110
solving videos.

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00:00:27,110 --> 00:00:30,870
Today we're going to do Fall
2010 problem set 6,

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00:00:30,870 --> 00:00:32,120
problem number 3.

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00:00:34,670 --> 00:00:37,790
Moldavia is a small country that
currently trades freely

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00:00:37,790 --> 00:00:39,460
in the world barley market.

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00:00:39,460 --> 00:00:42,580
Demand and supply for barley in
Moldavia is governed by the

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00:00:42,580 --> 00:00:44,110
following schedules.

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00:00:44,110 --> 00:00:47,010
The demand is given by
quantity demanded

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00:00:47,010 --> 00:00:49,380
equals 4 minus p.

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00:00:49,380 --> 00:00:53,370
The supply is given by the
quantity supplied equals p.

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00:00:53,370 --> 00:00:57,870
And the world price of barley
is $1 per bushel.

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00:00:57,870 --> 00:01:00,890
Part A asks us to calculate
the free trade equilibrium

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00:01:00,890 --> 00:01:03,880
price and quantity of
barley in Moldavia.

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00:01:03,880 --> 00:01:07,520
How many bushels do they import
or export, and on a

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00:01:07,520 --> 00:01:11,420
well-labeled graph depict this
equilibrium situation and

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00:01:11,420 --> 00:01:14,720
shade the gains from trade
relative to the autarkic no

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00:01:14,720 --> 00:01:18,380
trade equilibrium in Moldavia.

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00:01:18,380 --> 00:01:20,880
So what we're going to be doing
in this problem is we're

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00:01:20,880 --> 00:01:23,640
going to be working with three
different functions.

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00:01:23,640 --> 00:01:25,470
The first is the domestic
demand.

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00:01:25,470 --> 00:01:29,860
This is how much people in
Moldavia want barley.

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00:01:29,860 --> 00:01:32,710
The domestic supply tells us how
much the suppliers within

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00:01:32,710 --> 00:01:35,160
the country are willing
to supply.

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00:01:35,160 --> 00:01:38,290
And the international price is
telling us if we open up the

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00:01:38,290 --> 00:01:40,560
borders to trade without
any tariffs or any

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00:01:40,560 --> 00:01:42,090
barriers for trade.

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00:01:42,090 --> 00:01:44,830
This is what the equilibrium
price, or the new equilibrium

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00:01:44,830 --> 00:01:46,690
price will become.

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00:01:46,690 --> 00:01:50,240
So let's pretend for a second
that we're in autarky where

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00:01:50,240 --> 00:01:51,740
there's no trade at all.

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00:01:51,740 --> 00:01:54,960
In that case the supply
function, which is our

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00:01:54,960 --> 00:01:57,380
domestic supply, and
demand function

40
00:01:57,380 --> 00:01:59,100
are going to be equal.

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00:01:59,100 --> 00:02:03,370
And in this case we're going
to have a quantity supplied

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00:02:03,370 --> 00:02:07,120
that'll be right here at
the equilibrium point.

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00:02:07,120 --> 00:02:10,740
Now what's going to happen is
that we're going to have the

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00:02:10,740 --> 00:02:13,840
international price come in when
we open up or borders.

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00:02:13,840 --> 00:02:16,470
And it's going to function
like a price cap.

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00:02:16,470 --> 00:02:19,350
So instead of the price being
way up here when we only have

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00:02:19,350 --> 00:02:23,850
domestic suppliers, we're going
to see that the price is

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00:02:23,850 --> 00:02:28,150
going to shift down
to p equals 1 to

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00:02:28,150 --> 00:02:29,720
the equilibrium price.

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00:02:29,720 --> 00:02:36,810
And what's going to happen is
consumers are going to be able

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00:02:36,810 --> 00:02:40,560
to consume more out to this
point which we'll calculate.

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00:02:40,560 --> 00:02:46,540
Suppliers domestically will only
be willing to supply a

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00:02:46,540 --> 00:02:48,620
quantity at this point.

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00:02:48,620 --> 00:02:53,340
And that means that all of this
in the middle, which in

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00:02:53,340 --> 00:02:54,960
earlier problems we would
have thought of

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00:02:54,960 --> 00:02:56,320
as the excess demand.

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00:02:56,320 --> 00:02:57,990
It's no longer excess.

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00:02:57,990 --> 00:03:00,440
These consumers can actually
get a product.

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00:03:00,440 --> 00:03:01,700
And the way they're
going to get this

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00:03:01,700 --> 00:03:08,020
product is through imports.

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00:03:08,020 --> 00:03:10,840
And we need to calculate how
much people are going to

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00:03:10,840 --> 00:03:15,010
demand, how much the domestic
suppliers will produce, and

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00:03:15,010 --> 00:03:16,640
what the difference
is made up by the

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00:03:16,640 --> 00:03:19,300
international importers.

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00:03:19,300 --> 00:03:23,770
So to start off, let's think
about what's going to happen

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00:03:23,770 --> 00:03:25,400
when we have free trade.

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00:03:25,400 --> 00:03:27,600
Well in free trade we're
going to start off

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00:03:27,600 --> 00:03:28,850
with our demand function.

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00:03:32,900 --> 00:03:39,280
And instead of setting this
demand function equal to the

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00:03:39,280 --> 00:03:42,320
supply function, we're just
going to plug in the

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00:03:42,320 --> 00:03:45,140
international price for the
free trade scenario.

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00:03:57,300 --> 00:04:00,530
So we can see that in free
trade people are going to

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00:04:00,530 --> 00:04:03,630
demand three of the products.

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00:04:03,630 --> 00:04:06,340
Now at the price of one,
however, the suppliers aren't

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00:04:06,340 --> 00:04:08,750
going to be willing to
supply these three.

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00:04:08,750 --> 00:04:11,120
So we can calculate how much
they'll actually be willing to

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00:04:11,120 --> 00:04:13,010
supply at the price of one.

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00:04:16,640 --> 00:04:19,290
So just plugging in the price
we find the quantity that

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00:04:19,290 --> 00:04:22,560
they're willing to supply is
going to be equal to 1.

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00:04:22,560 --> 00:04:25,030
So that means that the
difference here is going to

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00:04:25,030 --> 00:04:26,910
have to be made up by imports.

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00:04:26,910 --> 00:04:36,930
So importers are going
to be equal to 2.

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00:04:39,640 --> 00:04:51,790
Now compared to the autarky
scenario, what we had is we

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00:04:51,790 --> 00:04:53,720
would set the quantity
demanded equal to

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00:04:53,720 --> 00:04:54,970
the quantity supplied.

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00:04:57,790 --> 00:05:01,390
And we would have found that the
price would be equal to 2

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00:05:01,390 --> 00:05:06,110
and the quantity supplied would
have been equal to 2.

88
00:05:06,110 --> 00:05:08,800
Now we can represent
on the graph in

89
00:05:08,800 --> 00:05:10,130
this autarky situation.

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00:05:10,130 --> 00:05:13,640
I'm going to outline in blue
what the total consumer and

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00:05:13,640 --> 00:05:16,260
producer surplus would've
looked like.

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00:05:16,260 --> 00:05:19,680
So we would have had a consumer
surplus which would

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00:05:19,680 --> 00:05:26,040
have just been the space below
the demand curve up until the

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00:05:26,040 --> 00:05:29,320
equilibrium price of 2.

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00:05:29,320 --> 00:05:31,930
So this would have been
our consumer surplus.

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00:05:31,930 --> 00:05:33,030
And we would have
had a producer

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00:05:33,030 --> 00:05:34,910
surplus up to the price.

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00:05:34,910 --> 00:05:37,930
It's a triangle up
to the price but

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00:05:37,930 --> 00:05:40,030
above the supply curve.

100
00:05:42,930 --> 00:05:47,050
So the total surplus beforehand
was this box.

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00:05:47,050 --> 00:05:53,350
Afterwards what we're going to
have is we're going to have a

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00:05:53,350 --> 00:05:55,670
new consumer surplus because
more people are

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00:05:55,670 --> 00:05:57,530
accessing the product.

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00:05:57,530 --> 00:06:01,580
So our new consumer surplus
is right here.

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00:06:05,310 --> 00:06:10,820
Our new producer surplus is
this triangle out here.

106
00:06:10,820 --> 00:06:13,640
And looking at our graph, the
only difference between the

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00:06:13,640 --> 00:06:19,680
free trade scenario and the
autarky scenario is this box

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00:06:19,680 --> 00:06:25,050
right here that I'm
shading in.

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00:06:25,050 --> 00:06:26,870
So you can see that what
actually happened here

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00:06:26,870 --> 00:06:28,500
conceptually is that
the domestic

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00:06:28,500 --> 00:06:29,800
producers were worse off.

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00:06:29,800 --> 00:06:31,910
Their producer surplus
decreased.

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00:06:31,910 --> 00:06:35,410
But the consumer surplus
increased so much that

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00:06:35,410 --> 00:06:39,620
overall, the total surplus
within this country increased

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00:06:39,620 --> 00:06:42,970
by an amount equal to the area
of this box, which we could

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00:06:42,970 --> 00:06:46,130
calculate if we needed to.

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00:06:46,130 --> 00:06:50,610
Let's go ahead and move on to
part B. Part B says the prime

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00:06:50,610 --> 00:06:54,200
minister of Moldavia,
sympathetic as always,

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00:06:54,200 --> 00:06:56,790
believes he can help those hurt
by free trade in barley

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00:06:56,790 --> 00:06:59,810
relative to the situation
and autarky.

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00:06:59,810 --> 00:07:04,610
He taxes the party that has
benefited from free trade

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00:07:04,610 --> 00:07:09,450
equal to the amount per bushel
that is the difference between

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00:07:09,450 --> 00:07:14,650
the autarkic price of barley,
which we calculated right

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00:07:14,650 --> 00:07:22,840
here, the difference between
that price and the free trade

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00:07:22,840 --> 00:07:27,510
price of barley, which
is equal to 1.

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00:07:27,510 --> 00:07:31,120
Furthermore, he rebates the
entire government revenue of

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00:07:31,120 --> 00:07:34,380
the tax back to the party
harmed by free trade.

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00:07:34,380 --> 00:07:37,000
In a new, well-labeled
diagram show the

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00:07:37,000 --> 00:07:39,920
post-tax equilibrium situation.

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00:07:39,920 --> 00:07:43,450
Calculate and show the new
equilibrium price and quantity

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00:07:43,450 --> 00:07:47,890
of barley in Moldavia, the
changes in the quantity of

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00:07:47,890 --> 00:07:51,390
imports or exports, the amount
of revenue collected by the

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00:07:51,390 --> 00:07:56,020
prime minister, and who pays the
larger burden of this tax,

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00:07:56,020 --> 00:08:01,110
consumers or producers
in Moldavia and why.

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00:08:01,110 --> 00:08:03,450
So there's a lot of things that
we need to answer in this

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00:08:03,450 --> 00:08:06,930
problem, but the first step is
going to be to really think

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00:08:06,930 --> 00:08:10,360
about how this tax is going to
affect the equilibrium that we

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00:08:10,360 --> 00:08:12,080
calculated.

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00:08:12,080 --> 00:08:13,830
And so this tax is going
to be paid by

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00:08:13,830 --> 00:08:15,540
the group that benefits.

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00:08:15,540 --> 00:08:18,480
So looking at our graph we said
that the consumers are

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00:08:18,480 --> 00:08:19,450
benefiting.

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00:08:19,450 --> 00:08:21,810
We saw that their consumer
surplus changed from this

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00:08:21,810 --> 00:08:24,590
triangle to the much
larger triangle.

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00:08:24,590 --> 00:08:27,500
So they're going to be the group
that's paying this tax.

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00:08:27,500 --> 00:08:30,200
So we're going to have
a new domestic demand

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00:08:30,200 --> 00:08:31,725
curve for this scenario.

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00:08:36,309 --> 00:08:40,210
And so we started with our
demand curve of qd

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00:08:40,210 --> 00:08:42,630
equals 4 minus p.

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00:08:42,630 --> 00:08:47,550
I'm going to get the inverse
demand so that it's p

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00:08:47,550 --> 00:08:51,340
equals 4 minus qd.

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00:08:51,340 --> 00:08:54,180
And now instead of their inverse
demand being equal to

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00:08:54,180 --> 00:08:57,150
this, we have to
add in the tax.

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00:08:57,150 --> 00:09:03,590
So the demand curve is going to
shift so that t plus p is

155
00:09:03,590 --> 00:09:07,870
equal to 4 minus qd.

156
00:09:07,870 --> 00:09:10,720
So basically when they think
about how much they're willing

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00:09:10,720 --> 00:09:13,060
to buy, it's going
to be reduced.

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00:09:13,060 --> 00:09:16,020
The whole demand curve is going
to shift down by the

159
00:09:16,020 --> 00:09:17,730
amount of the tax.

160
00:09:17,730 --> 00:09:19,325
And so we can represent
this graphically.

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00:09:34,560 --> 00:09:37,720
The demand curve is going
to shift down an amount

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00:09:37,720 --> 00:09:39,480
equal to the tax.

163
00:09:39,480 --> 00:09:42,410
I'm going to put dt represent
the demand

164
00:09:42,410 --> 00:09:44,450
curve after the tax.

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00:09:44,450 --> 00:09:49,850
And the distance from here, from
our initial equilibrium,

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00:09:49,850 --> 00:09:53,010
down to where the demand
curve is now is going

167
00:09:53,010 --> 00:09:56,420
to be equal to t.

168
00:09:56,420 --> 00:09:59,700
And so we can go ahead since we
know the tax is going to be

169
00:09:59,700 --> 00:10:03,830
equal to the difference between
the autarkic price and

170
00:10:03,830 --> 00:10:06,430
the free trade price,
or 2 minus 1.

171
00:10:06,430 --> 00:10:08,500
We know that t is going
to be equal to 1.

172
00:10:13,830 --> 00:10:16,010
So now we have a new
equation for our

173
00:10:16,010 --> 00:10:17,260
quantity that's demanded.

174
00:10:27,260 --> 00:10:31,220
And we can again set, since we
are still open up to trade,

175
00:10:31,220 --> 00:10:33,900
we're going to set the price
equal to 1 and we can solve

176
00:10:33,900 --> 00:10:35,150
for the new quantity demanded.

177
00:10:43,730 --> 00:10:47,310
So in this scenario since
we're taxing the group,

178
00:10:47,310 --> 00:10:48,740
they're not willing
to buy as much.

179
00:10:48,740 --> 00:10:50,460
The quantity that they're
demanding has shifted

180
00:10:50,460 --> 00:10:52,930
from 3 down to 2.

181
00:10:52,930 --> 00:10:56,810
And how we can represent that
is initially we had the

182
00:10:56,810 --> 00:11:02,580
international price right
here at p equals 1.

183
00:11:05,150 --> 00:11:17,330
So in our initial scenario they
were demanding qd and

184
00:11:17,330 --> 00:11:21,840
domestic suppliers were
supplying at qs.

185
00:11:21,840 --> 00:11:25,990
And now in the new scenario what
we're going to see is see

186
00:11:25,990 --> 00:11:35,820
that the qt, or the quantity
that's demanded with the tax,

187
00:11:35,820 --> 00:11:39,890
has shifted down because of the
tax shifting the demand

188
00:11:39,890 --> 00:11:41,140
curve down as a whole.

189
00:11:43,700 --> 00:11:46,000
Now the last thing, or the other
things that this problem

190
00:11:46,000 --> 00:11:48,810
asks us is how much tax revenue
are they going to

191
00:11:48,810 --> 00:11:52,770
receive and how are the imports
and the domestic

192
00:11:52,770 --> 00:11:55,200
supply going to change.

193
00:11:55,200 --> 00:11:59,550
Well the quantity that's
supplied by domestic producers

194
00:11:59,550 --> 00:12:03,420
given that the demand is still
above 1, the quantity that's

195
00:12:03,420 --> 00:12:08,600
going to be supplied in this new
scenario is still going to

196
00:12:08,600 --> 00:12:10,600
be equal to 1.

197
00:12:10,600 --> 00:12:12,960
And what we're going to see is
this reduction in demand is

198
00:12:12,960 --> 00:12:15,260
only going to affect
the importers.

199
00:12:15,260 --> 00:12:20,150
So before, we had 3 and
then minus 1 for the

200
00:12:20,150 --> 00:12:21,640
amount that's supplied.

201
00:12:21,640 --> 00:12:27,350
Now instead, the imports are
going to be reduced by 1.

202
00:12:30,130 --> 00:12:33,400
And a total tax revenue that's
going to be collected is going

203
00:12:33,400 --> 00:12:42,140
to be equal to the quantity
that's demanded times t.

204
00:12:45,940 --> 00:12:49,690
So we have that the total tax
revenue in the situation is

205
00:12:49,690 --> 00:12:51,530
equal to $2.

206
00:12:51,530 --> 00:12:55,720
So in part A we saw a scenario
where we calculated and looked

207
00:12:55,720 --> 00:13:00,030
at what quantity was supplied
and what price was given when

208
00:13:00,030 --> 00:13:01,890
there was no free
trade at all.

209
00:13:01,890 --> 00:13:03,720
When it was complete autarky.

210
00:13:03,720 --> 00:13:05,220
Now what we're going to do is
we're going to look at the

211
00:13:05,220 --> 00:13:07,800
free trade scenario where
there's the tax.

212
00:13:07,800 --> 00:13:09,530
And we're going to specifically
look at the

213
00:13:09,530 --> 00:13:10,890
producer surplus.

214
00:13:10,890 --> 00:13:14,490
We're going to compare the
producer surplus in autarky to

215
00:13:14,490 --> 00:13:17,530
the producer surplus when
there's free trade but they're

216
00:13:17,530 --> 00:13:20,390
receiving the $2 rebate
from the government.

217
00:13:20,390 --> 00:13:25,250
So part C asks us, are the free
trade losers better off

218
00:13:25,250 --> 00:13:27,610
or worse off after the
rebate than they were

219
00:13:27,610 --> 00:13:30,470
under autarky and why.

220
00:13:30,470 --> 00:13:32,900
Let's start off by drawing
graphs to represent both of

221
00:13:32,900 --> 00:13:34,860
these scenarios.

222
00:13:34,860 --> 00:13:40,080
In autarky what would happen
is there would be no

223
00:13:40,080 --> 00:13:41,470
international price.

224
00:13:41,470 --> 00:13:49,190
And instead we would just have
the equilibrium price right

225
00:13:49,190 --> 00:13:58,560
here, with a quantity demanded
of 2 and a price of 2 as well.

226
00:13:58,560 --> 00:14:06,810
So in the autarky situation we
can calculate the producer

227
00:14:06,810 --> 00:14:11,240
surplus as this triangle
right here.

228
00:14:11,240 --> 00:14:14,020
To calculate the producer
surplus in autarky it's just

229
00:14:14,020 --> 00:14:19,440
going to be 1/2 times
2 times 2.

230
00:14:19,440 --> 00:14:23,170
So beforehand, the producer
surplus, the area of this

231
00:14:23,170 --> 00:14:25,330
triangle, is equal to 2.

232
00:14:25,330 --> 00:14:28,560
Let's look at the scenario after
they're open up to free

233
00:14:28,560 --> 00:14:32,510
trade but with the producers
getting that $2 rebate from

234
00:14:32,510 --> 00:14:33,760
the government.

235
00:14:44,680 --> 00:14:49,210
So in this scenario, the
international price of one

236
00:14:49,210 --> 00:14:51,870
caps the price that the
suppliers are going to get.

237
00:14:51,870 --> 00:14:55,620
And so the suppliers in this
scenario are also only going

238
00:14:55,620 --> 00:14:58,350
to supply a quantity
of one as well.

239
00:14:58,350 --> 00:15:01,270
So the producer surplus
in this scenario

240
00:15:01,270 --> 00:15:03,710
is a smaller triangle.

241
00:15:03,710 --> 00:15:07,990
But the added benefit is that
a chunk of the producer

242
00:15:07,990 --> 00:15:13,110
surplus, the $2, is also being
added in to the producer

243
00:15:13,110 --> 00:15:16,030
surplus that would have existed
under free trade.

244
00:15:16,030 --> 00:15:18,830
So we're going to calculate the
area of this triangle, add

245
00:15:18,830 --> 00:15:22,530
in the $2 government rebate to
get the new producer surplus

246
00:15:22,530 --> 00:15:23,780
in the free trade situation.

247
00:15:26,300 --> 00:15:31,890
So normally the area of that
triangle would only be 1/2.

248
00:15:31,890 --> 00:15:36,020
But since we're adding in the
government rebate of $2, we

249
00:15:36,020 --> 00:15:42,610
find that in the free trade
scenario the producer surplus

250
00:15:42,610 --> 00:15:46,610
has increased to 2.5.

251
00:15:46,610 --> 00:15:50,960
So since the producer surplus
increased to 2.5 we can say

252
00:15:50,960 --> 00:15:54,840
that the producers are better
off under the free trade

253
00:15:54,840 --> 00:15:58,720
system with the caveat that
they're receiving a government

254
00:15:58,720 --> 00:16:00,880
revenue or a tax.

255
00:16:00,880 --> 00:16:02,870
So to quickly summarize
the parts of the

256
00:16:02,870 --> 00:16:04,480
problem that we saw.

257
00:16:04,480 --> 00:16:08,340
What we saw here is we looked
at the autarkic situation

258
00:16:08,340 --> 00:16:10,020
where there's no free trade.

259
00:16:10,020 --> 00:16:12,070
And then we looked at how
producers and consumers are

260
00:16:12,070 --> 00:16:15,150
affected when borders are open
up to free trade without any

261
00:16:15,150 --> 00:16:17,010
government intervention.

262
00:16:17,010 --> 00:16:19,790
After that we saw what happens
when the government has a

263
00:16:19,790 --> 00:16:24,380
policy of taking away from
the group of consumers or

264
00:16:24,380 --> 00:16:28,950
producers that benefit and
giving set revenue back to the

265
00:16:28,950 --> 00:16:29,940
other group.

266
00:16:29,940 --> 00:16:34,370
And we compared the producers'
surplus before and after the

267
00:16:34,370 --> 00:16:35,620
new government intervention.