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PROFESSOR: Hi, welcome
back to the 14.01

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00:00:24,770 --> 00:00:26,360
problem solving videos.

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00:00:26,360 --> 00:00:29,300
Today we're going to work
on p-set 1 problem

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00:00:29,300 --> 00:00:31,980
number 3 from Fall 2010.

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00:00:31,980 --> 00:00:33,160
And we're going to work
through all four

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00:00:33,160 --> 00:00:34,540
parts of this problem.

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00:00:34,540 --> 00:00:38,120
But to start off I'm just going
to read through part A.

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Consider the market
for apple juice.

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00:00:40,230 --> 00:00:43,120
In this market the supply curve
is given by quantity

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00:00:43,120 --> 00:00:48,500
supplied equals 10 pj minus 5
pa, and the demand curve is

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00:00:48,500 --> 00:00:53,390
given by quantity demanded
equals 100 minus 15 pj plus 10

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00:00:53,390 --> 00:00:58,590
pt, where j denotes apple juice,
a denotes apples, and t

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00:00:58,590 --> 00:01:00,110
denotes tea.

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00:01:00,110 --> 00:01:04,019
Part A asks us to assume
that pa is fixed at $1

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00:01:04,019 --> 00:01:06,100
and pt equals 5.

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00:01:06,100 --> 00:01:08,900
We need to calculate the
equilibrium price and quantity

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00:01:08,900 --> 00:01:12,160
in the apple juice market.

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00:01:12,160 --> 00:01:15,500
So to start off this problem,
I wrote down both the supply

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00:01:15,500 --> 00:01:17,120
and the demand functions.

26
00:01:17,120 --> 00:01:19,580
But before we get started with
the algebra, I wanted to come

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00:01:19,580 --> 00:01:21,530
over to this graph and I
wanted to think about

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00:01:21,530 --> 00:01:25,620
conceptually what we're
going to be doing.

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00:01:25,620 --> 00:01:28,030
When we solve for an equilibrium
price and the

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00:01:28,030 --> 00:01:30,840
equilibrium quantity, all we're
doing is we're finding

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00:01:30,840 --> 00:01:36,050
the point at which the quantity
supplied and the

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00:01:36,050 --> 00:01:38,200
quantity demanded is equal.

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00:01:38,200 --> 00:01:41,700
Looking at the graph, that point
is going to be right

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00:01:41,700 --> 00:01:47,940
here where the two
curves intersect.

35
00:01:47,940 --> 00:01:52,920
So this will be q star, our
equilibrium quantity, and this

36
00:01:52,920 --> 00:01:57,020
will be p star, our
equilibrium price.

37
00:01:57,020 --> 00:01:59,160
So for part A we're just solving
for the equilibrium

38
00:01:59,160 --> 00:02:00,560
price and quantity.

39
00:02:00,560 --> 00:02:03,690
And they try to trip you up on
this problem by throwing in

40
00:02:03,690 --> 00:02:06,500
the price of apples and
the price of tea.

41
00:02:06,500 --> 00:02:09,340
But since they tell us what
these prices are initially,

42
00:02:09,340 --> 00:02:10,830
we're just going to plug
these into our supply

43
00:02:10,830 --> 00:02:12,250
and our demand functions.

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00:02:12,250 --> 00:02:15,760
And once we do that, we'll have
isolated the pj variable

45
00:02:15,760 --> 00:02:17,770
and the q variable so we'll
be able to solve

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00:02:17,770 --> 00:02:20,320
through for this problem.

47
00:02:20,320 --> 00:02:25,620
So starting off with part A.
We're going to go ahead and

48
00:02:25,620 --> 00:02:29,590
we're going to set the quantity
supplied equal to the

49
00:02:29,590 --> 00:02:31,680
quantity demanded.

50
00:02:31,680 --> 00:02:35,080
And so for my supply function,
I've already plugged in pa.

51
00:02:35,080 --> 00:02:41,010
And after plugging in pa I found
that 10 pj minus 5 is

52
00:02:41,010 --> 00:02:42,620
the supply curve.

53
00:02:42,620 --> 00:02:51,960
And the demand curve is equal
to 150 minus 15 pj.

54
00:02:51,960 --> 00:02:54,460
Solving out for pj I find
that the equilibrium

55
00:02:54,460 --> 00:02:58,200
price is equal to 6.2.

56
00:02:58,200 --> 00:03:00,300
And since I know this is an
equilibrium price I'm going to

57
00:03:00,300 --> 00:03:03,400
go ahead and I'm going to
label this with a star.

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00:03:06,430 --> 00:03:08,880
Solving through for the
equilibrium quantity all we

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00:03:08,880 --> 00:03:11,950
have to do is we have to take
this equilibrium price we

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00:03:11,950 --> 00:03:15,390
found and plug it back into
either the supply curve or the

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00:03:15,390 --> 00:03:16,980
demand curve.

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00:03:16,980 --> 00:03:18,500
I'm going to go ahead and I'm
going to plug it into the

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00:03:18,500 --> 00:03:19,750
supply function.

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00:03:26,450 --> 00:03:29,740
And that lets us solve for the
equilibrium quantity denoted

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00:03:29,740 --> 00:03:31,150
with the star.

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00:03:31,150 --> 00:03:36,180
And that in this case is 57.

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00:03:36,180 --> 00:03:40,220
So looking at our graph, the
equilibrium price and the

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00:03:40,220 --> 00:03:42,820
equilibrium quantity, we
can now label them.

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00:03:42,820 --> 00:03:46,370
We can label the price,
6.2, and the

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00:03:46,370 --> 00:03:53,170
equilibrium quantity 57.

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00:03:53,170 --> 00:03:56,650
Let's go ahead and move on to
part B. Part B is going to be

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00:03:56,650 --> 00:04:00,430
the exact same scenario as we
started off with in part A,

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00:04:00,430 --> 00:04:03,600
only what we're going to do now
is we're going to shift

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00:04:03,600 --> 00:04:08,520
the supply curve by changing
the price of apples.

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00:04:08,520 --> 00:04:12,050
Part B states, suppose that a
poor harvest season raises the

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00:04:12,050 --> 00:04:14,815
price of apples to
pa equals 2.

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00:04:19,730 --> 00:04:22,700
Find the new equilibrium price
and quantity of apple juice

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00:04:22,700 --> 00:04:26,280
and draw a graph to illustrate
the answer.

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00:04:26,280 --> 00:04:28,620
Now what's happening in this
scenario is that the demand

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00:04:28,620 --> 00:04:30,080
curve is completely
unaffected.

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00:04:30,080 --> 00:04:31,960
The only thing that's
changing is our

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00:04:31,960 --> 00:04:34,350
supply curve is shifting.

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00:04:34,350 --> 00:04:37,390
So when we look at our supply
curve we have to think about

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00:04:37,390 --> 00:04:40,030
conceptually what do
apples represent.

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00:04:40,030 --> 00:04:42,000
Well they're an input
for the suppliers.

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00:04:42,000 --> 00:04:45,090
It's something they have to use
to make the apple juice.

87
00:04:45,090 --> 00:04:47,980
And if the price of apples is
increasing then we intuitively

88
00:04:47,980 --> 00:04:52,180
know that this quantity, or this
q star that they produce

89
00:04:52,180 --> 00:04:54,240
before, it's going to be
more expensive for

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00:04:54,240 --> 00:04:55,680
them to produce it.

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00:04:55,680 --> 00:04:58,800
And, in fact, it's going to
be more expensive for the

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00:04:58,800 --> 00:05:03,510
suppliers to produce
any given quantity.

93
00:05:03,510 --> 00:05:07,240
So this means that the supply
curve for part B is shifting

94
00:05:07,240 --> 00:05:09,580
up and to the left.

95
00:05:09,580 --> 00:05:12,980
I'm going to denote this by
labeling our new supply curve

96
00:05:12,980 --> 00:05:16,050
sb for Part B.

97
00:05:16,050 --> 00:05:18,605
So for Part B all we're going
to do is we're going to plug

98
00:05:18,605 --> 00:05:20,460
in this new pa price.

99
00:05:20,460 --> 00:05:21,760
And then we're going to
do the same thing.

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00:05:21,760 --> 00:05:23,570
We're going to set the quantity
supplied and the

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00:05:23,570 --> 00:05:24,990
quantity demanded equal.

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00:05:39,100 --> 00:05:43,630
When we solve through for a new
supply curve we find that

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00:05:43,630 --> 00:05:49,220
10pj minus 10 is our
new supply curve.

104
00:05:49,220 --> 00:05:51,950
And we know that are demand
curve is going to be exactly

105
00:05:51,950 --> 00:06:01,650
the same as the scenario that we
started off with in Part A.

106
00:06:01,650 --> 00:06:04,310
Solving through for the new
equilibrium price we find that

107
00:06:04,310 --> 00:06:10,460
pj is going to be
equal to 6.4.

108
00:06:10,460 --> 00:06:18,650
I'm going to label this new
equilibrium price with a B.

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00:06:18,650 --> 00:06:21,830
And then we can take this
equilibrium price, we can plug

110
00:06:21,830 --> 00:06:24,680
it back into either our
new supply curve

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00:06:24,680 --> 00:06:26,500
or our demand curve.

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00:06:26,500 --> 00:06:31,800
And we can find that the
equilibrium quantity is going

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00:06:31,800 --> 00:06:36,630
to equal 54.

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00:06:36,630 --> 00:06:40,520
And when we look at our graph we
can think about what these

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00:06:40,520 --> 00:06:44,490
quantities and these new
prices looks like.

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00:06:44,490 --> 00:06:51,060
We can see that the quantity for
part B clearly should have

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00:06:51,060 --> 00:06:55,130
shifted down, and it did
drop from 57 to 54.

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00:06:55,130 --> 00:06:59,390
And we can see that the price
is higher than what

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00:06:59,390 --> 00:07:00,710
we started off with.

120
00:07:00,710 --> 00:07:06,000
It rose from 6.2
now up to 6.4.

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00:07:06,000 --> 00:07:08,010
So we can see that our intuition
that the supply

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00:07:08,010 --> 00:07:10,340
curve would shift up because
it's more expensive for

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00:07:10,340 --> 00:07:13,320
suppliers makes sense according
to both our algebra

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00:07:13,320 --> 00:07:14,570
and to our graph.

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00:07:16,520 --> 00:07:19,720
Let's go ahead and try part C.
Part C is going to be another

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00:07:19,720 --> 00:07:22,560
shift, but what's happening now
is this new shift is going

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00:07:22,560 --> 00:07:24,780
to affect the demand curve
not the supply curve.

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00:07:28,090 --> 00:07:33,040
Part C states, suppose that pa
equals 1, but the price of tea

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00:07:33,040 --> 00:07:35,560
drops to pt equals 3.

130
00:07:35,560 --> 00:07:40,470
Find the new equilibrium price
and quantity of apple juice.

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00:07:40,470 --> 00:07:45,120
So for this scenario now, our
pa is back to 1, like it

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00:07:45,120 --> 00:07:49,240
started off with in part one.

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00:07:49,240 --> 00:07:55,820
But now t is dropped
from five to three.

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00:07:55,820 --> 00:07:58,020
Now before we start, let's think
about what t actually

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00:07:58,020 --> 00:08:01,780
represents to the consumers
in this market.

136
00:08:01,780 --> 00:08:04,100
If I'm a consumer and I'm
debating what I want to drink

137
00:08:04,100 --> 00:08:07,330
in the morning, one of my other
choices might be tea.

138
00:08:07,330 --> 00:08:10,540
Now the price of tea drops,
then maybe I'll be less

139
00:08:10,540 --> 00:08:12,640
willing to pay as much for the
apple juice because they can

140
00:08:12,640 --> 00:08:15,340
just go out and get
the cheap tea now.

141
00:08:15,340 --> 00:08:18,820
Looking at our graph, if the
consumer is less willing to

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00:08:18,820 --> 00:08:22,020
pay as much for each quantity
of apple juice as they were

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00:08:22,020 --> 00:08:26,120
before, this scenario means
that the demand curve has

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00:08:26,120 --> 00:08:28,160
shifted down.

145
00:08:28,160 --> 00:08:31,320
So, for example, the equilibrium
quantity that we

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00:08:31,320 --> 00:08:34,580
started off with an point A,
they used to be willing to pay

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00:08:34,580 --> 00:08:37,179
this much, now they would only
be willing to pay this much

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00:08:37,179 --> 00:08:41,230
for the same quantity because
tea is cheaper.

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00:08:41,230 --> 00:08:44,110
Now we're going to be using the
same supply curve that we

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00:08:44,110 --> 00:08:45,880
started off with before.

151
00:08:45,880 --> 00:08:49,870
So in this scenario we're
looking to set supply and

152
00:08:49,870 --> 00:08:52,470
demand equal and find this
new equilibrium point.

153
00:08:57,480 --> 00:09:00,330
When we go through and we
actually plug in the new pa

154
00:09:00,330 --> 00:09:05,630
and the new pt, we're going to
find that the supply and the

155
00:09:05,630 --> 00:09:06,880
demand functions.

156
00:09:15,410 --> 00:09:22,000
When we set them equal we're
going to set 10 pj minus 5

157
00:09:22,000 --> 00:09:36,360
equal to 130 minus 15 pj.

158
00:09:36,360 --> 00:09:39,640
Again we're going to solve
through for pj.

159
00:09:39,640 --> 00:09:43,190
And we're going to find that our
pjc for part C is going to

160
00:09:43,190 --> 00:09:44,440
be equal to 5.4.

161
00:09:47,030 --> 00:09:50,000
And we're going to find that the
new equilibrium quantity,

162
00:09:50,000 --> 00:09:52,470
again either plugging back
into our supply curve or

163
00:09:52,470 --> 00:10:02,860
demand curve, is going
to be equal to 49.

164
00:10:02,860 --> 00:10:06,410
And when we think back to our
original part A, we found that

165
00:10:06,410 --> 00:10:08,430
the price was 6.2.

166
00:10:08,430 --> 00:10:13,030
Now the price dropped
down to 54 or 5.4.

167
00:10:13,030 --> 00:10:16,190
And what we see here, is that
we did see a price decrease,

168
00:10:16,190 --> 00:10:17,840
or we could have predicted
a price decrease

169
00:10:17,840 --> 00:10:19,480
according to our graph.

170
00:10:19,480 --> 00:10:22,610
And we also find out the
quantity dropped from part A

171
00:10:22,610 --> 00:10:25,670
in 57 now the 49.

172
00:10:25,670 --> 00:10:27,460
And according to our graph, we
would have predicted that

173
00:10:27,460 --> 00:10:30,510
quantity would have
decreased as well.

174
00:10:30,510 --> 00:10:34,530
So the algebra and our
graph both match up.

175
00:10:34,530 --> 00:10:38,180
Let's go ahead and move on to
part D. Now we're going to

176
00:10:38,180 --> 00:10:40,980
look at the effect of a
government intervention on the

177
00:10:40,980 --> 00:10:43,920
market for apple juice.

178
00:10:43,920 --> 00:10:49,640
Part D says, suppose that pa
equals 1 and pt equals 5 and

179
00:10:49,640 --> 00:10:51,590
there's a price ceiling
on apple juice of

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00:10:51,590 --> 00:10:54,050
pj star equals 5.

181
00:10:54,050 --> 00:10:57,470
What is the excess demand for
apple juice as a result?

182
00:10:57,470 --> 00:11:01,480
Draw a graph to illustrate
your answer.

183
00:11:01,480 --> 00:11:03,790
So now we're back to the
original scenario we started

184
00:11:03,790 --> 00:11:09,435
with in part A. We have the
price of apples is equal to 1.

185
00:11:09,435 --> 00:11:15,600
And we're back to the price
of tea equal to five.

186
00:11:18,240 --> 00:11:21,270
And now the only thing that's
different in this scenario for

187
00:11:21,270 --> 00:11:30,330
part D is that the government
said that these suppliers

188
00:11:30,330 --> 00:11:35,820
can't charge any price
higher than 5.

189
00:11:35,820 --> 00:11:38,100
So let's go ahead and let's
think about what this looks

190
00:11:38,100 --> 00:11:40,280
like conceptually on a graph.

191
00:11:57,280 --> 00:11:59,680
In this scenario we started
off with an

192
00:11:59,680 --> 00:12:01,210
equilibrium price of 6.2.

193
00:12:06,140 --> 00:12:07,810
If we were to have a case
where the government was

194
00:12:07,810 --> 00:12:12,450
saying you could charge only as
much as 7 in the market for

195
00:12:12,450 --> 00:12:15,160
apple juice, the suppliers
wouldn't even be affected.

196
00:12:15,160 --> 00:12:17,580
Because they would say, that
doesn't affect us, we're

197
00:12:17,580 --> 00:12:19,400
charging 6.2.

198
00:12:19,400 --> 00:12:21,170
That's too high.

199
00:12:21,170 --> 00:12:23,300
We're not going to have to
change anything we're doing.

200
00:12:23,300 --> 00:12:25,940
But in this scenario the
government is saying the most

201
00:12:25,940 --> 00:12:27,940
you can charge is 5.

202
00:12:36,150 --> 00:12:40,670
Now at the price of 5, the
quantity supplied, or the

203
00:12:40,670 --> 00:12:45,100
intersection of the price of
5 with the supply curve, is

204
00:12:45,100 --> 00:12:53,420
going to lead to a qs that's
different than the quantity

205
00:12:53,420 --> 00:12:54,670
that's demanded.

206
00:12:56,810 --> 00:12:58,880
And more specifically we're
going to find that too many

207
00:12:58,880 --> 00:13:01,650
people are demanding the product
and there's not enough

208
00:13:01,650 --> 00:13:03,810
being supplied in the market.

209
00:13:03,810 --> 00:13:06,430
This is what we're referring
to when we talk

210
00:13:06,430 --> 00:13:09,340
about excess demand.

211
00:13:09,340 --> 00:13:12,140
We're talking about the space
between the quantity that's

212
00:13:12,140 --> 00:13:14,650
supplied and the quantity
that's demanded.

213
00:13:14,650 --> 00:13:16,900
And that's what we're going
to be solving for.

214
00:13:16,900 --> 00:13:20,650
So by plugging in the price cap
of 5 into both our supply

215
00:13:20,650 --> 00:13:23,420
curve and our demand curve,
we'll be able to find the

216
00:13:23,420 --> 00:13:25,710
difference between the amount
that's supplied and the amount

217
00:13:25,710 --> 00:13:26,960
that's demanded.

218
00:13:29,890 --> 00:13:34,910
So plugging into our supply
curve we can find that the

219
00:13:34,910 --> 00:13:45,010
quantity supplied is going
to be equal to 45.

220
00:13:45,010 --> 00:13:48,410
And plugging into our demand
curve we can find that the

221
00:13:48,410 --> 00:14:00,680
quantity demanded is going
to be equal to 75.

222
00:14:00,680 --> 00:14:02,450
Now one of the biggest problems
that students run

223
00:14:02,450 --> 00:14:04,440
into on this problem is they
think they're done when they

224
00:14:04,440 --> 00:14:05,710
reach this point.

225
00:14:05,710 --> 00:14:08,150
All right, I found the quantity
supplied, I found the

226
00:14:08,150 --> 00:14:09,780
quantity demanded, I know
they're different.

227
00:14:09,780 --> 00:14:11,120
I'm done.

228
00:14:11,120 --> 00:14:14,760
But really what you need to find
is exactly how different

229
00:14:14,760 --> 00:14:17,630
the quantity supplied and the
quantity demanded is.

230
00:14:17,630 --> 00:14:19,210
You need to find out how
many consumers are

231
00:14:19,210 --> 00:14:20,460
left out of the market.

232
00:14:38,370 --> 00:14:40,300
So our excess demand is the
difference between the

233
00:14:40,300 --> 00:14:42,870
quantity supplied and the
quantity demanded.

234
00:14:42,870 --> 00:14:45,130
And that's going to be
30 in this case.

235
00:14:45,130 --> 00:14:48,270
So just to review what we did
in this problem, we started

236
00:14:48,270 --> 00:14:51,770
off by setting a quantity
supplied and a quantity

237
00:14:51,770 --> 00:14:53,790
demanded equal to solve
for a basic

238
00:14:53,790 --> 00:14:55,770
equilibrium price and quantity.

239
00:14:55,770 --> 00:14:58,150
We then looked at shifts in
supply and demand and looked

240
00:14:58,150 --> 00:15:00,950
at how that affected the price
and quantity in a market.

241
00:15:00,950 --> 00:15:03,630
And finally, we ended with part
D with looking at the

242
00:15:03,630 --> 00:15:05,570
effect of a government
intervention.

243
00:15:05,570 --> 00:15:08,770
How does a price cap affect
how many people can get a

244
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product compared to how many
people want a product.