Examples recognizing transformations

WEBVTT
Kind: captions
Language: en

00:00:00.736 --> 00:00:02.207
- [Instructor] What we're
going to do in this video

00:00:02.207 --> 00:00:05.586
is get some practice identifying
some transformations.

00:00:05.586 --> 00:00:07.097
And the transformations
we're gonna look at

00:00:07.097 --> 00:00:10.535
are things like rotations
where you are spinning

00:00:10.535 --> 00:00:12.812
something around a point.

00:00:12.812 --> 00:00:14.057
We're gonna look at translations,

00:00:14.057 --> 00:00:17.298
where you're shifting all
the points of a figure.

00:00:17.298 --> 00:00:18.340
We're gonna look at reflection,

00:00:18.340 --> 00:00:22.423
where you flip a figure
over some type of a line.

00:00:23.873 --> 00:00:24.992
And we'll look at dilations,

00:00:24.992 --> 00:00:27.516
where you're essentially
going to either shrink

00:00:27.516 --> 00:00:30.183
or expand some type of a figure.

00:00:31.183 --> 00:00:32.228
So with that out of the way,

00:00:32.228 --> 00:00:33.503
let's think about this question.

00:00:33.503 --> 00:00:35.726
What single transformation was applied

00:00:35.726 --> 00:00:38.393
to triangle A to get triangle B?

00:00:40.567 --> 00:00:42.332
So it looks like triangle
A and triangle B,

00:00:42.332 --> 00:00:43.571
they're the same size,

00:00:43.571 --> 00:00:45.319
and what's really
happened is that every one

00:00:45.319 --> 00:00:47.912
of these points has been shifted.

00:00:47.912 --> 00:00:48.888
Or another way I could say it,

00:00:48.888 --> 00:00:51.060
they have all been translated

00:00:51.060 --> 00:00:53.148
a little bit to the right and up.

00:00:53.148 --> 00:00:55.482
And so, right like this,

00:00:55.482 --> 00:00:57.767
they have all been translated.

00:00:57.767 --> 00:01:01.850
So this right over here
is clearly a translation.

00:01:03.685 --> 00:01:05.768
Let's do another example.

00:01:09.834 --> 00:01:13.001
What single transformation was applied

00:01:13.930 --> 00:01:16.452
to triangle A to get to triangle B?

00:01:16.452 --> 00:01:18.965
So if I look at these diagrams,

00:01:18.965 --> 00:01:21.728
this point seems to
correspond with that one.

00:01:21.728 --> 00:01:24.156
This one corresponds with that one.

00:01:24.156 --> 00:01:26.767
So it doesn't look like
a straight translation

00:01:26.767 --> 00:01:29.427
because they would have been
translated in different ways,

00:01:29.427 --> 00:01:32.385
so it's definitely not
a straight translation.

00:01:32.385 --> 00:01:33.218
Let's think about it.

00:01:33.218 --> 00:01:34.865
Looks like there might be a rotation here.

00:01:34.865 --> 00:01:36.984
So maybe it looks like
that point went over there.

00:01:36.984 --> 00:01:39.304
That point went over there.

00:01:39.304 --> 00:01:41.425
This point went over here,

00:01:41.425 --> 00:01:43.288
and so we could be rotating around

00:01:43.288 --> 00:01:45.930
some point right about here.

00:01:45.930 --> 00:01:47.510
And if you rotate around that point,

00:01:47.510 --> 00:01:51.237
you could get to a situation
that looks like a triangle B.

00:01:51.237 --> 00:01:52.280
And I don't know the exact point

00:01:52.280 --> 00:01:54.584
that we're rotating around,
but this looks pretty clear,

00:01:54.584 --> 00:01:55.917
like a rotation.

00:01:57.760 --> 00:01:59.843
Let's do another example.

00:02:04.842 --> 00:02:06.972
What single transformation was applied

00:02:06.972 --> 00:02:11.399
to quadrilateral A to
get to quadrilateral B?

00:02:11.399 --> 00:02:12.640
So let's see, it looks like

00:02:12.640 --> 00:02:15.723
this point corresponds to that point.

00:02:16.564 --> 00:02:19.068
And then this point
corresponds to that point,

00:02:19.068 --> 00:02:21.094
and that point corresponds to that point,

00:02:21.094 --> 00:02:23.127
so they actually look like
reflections of each other.

00:02:23.127 --> 00:02:26.839
If you were to imagine
some type of a mirror

00:02:26.839 --> 00:02:29.452
right over here, they're
actually mirror images.

00:02:29.452 --> 00:02:30.877
This got flipped over the line,

00:02:30.877 --> 00:02:33.141
that got flipped over the line,

00:02:33.141 --> 00:02:35.447
and that got flipped over the line.

00:02:35.447 --> 00:02:36.729
So it's pretty clear that this right

00:02:36.729 --> 00:02:38.896
over here is a reflection.

00:02:40.695 --> 00:02:43.862
All right, let's do one more of these.

00:02:45.241 --> 00:02:46.818
What single transformation was applied

00:02:46.818 --> 00:02:51.068
to quadrilateral A to
get to quadrilateral B?

00:02:51.068 --> 00:02:53.568
All right, so this looks like,

00:02:55.265 --> 00:02:57.667
so quadrilateral B is clearly bigger.

00:02:57.667 --> 00:02:59.498
So this is a non-rigid transformation.

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The distance between corresponding points

00:03:02.340 --> 00:03:04.462
looks like it has increased.

00:03:04.462 --> 00:03:05.295
Now you might be saying, well,

00:03:05.295 --> 00:03:06.779
wouldn't that be, it looks like

00:03:06.779 --> 00:03:08.375
if you're making something
bigger or smaller,

00:03:08.375 --> 00:03:10.656
that looks like a dilation.

00:03:10.656 --> 00:03:13.646
But it looks like this
has been moved as well.

00:03:13.646 --> 00:03:15.073
Has it been translated?

00:03:15.073 --> 00:03:17.561
And the key here to realize is around,

00:03:17.561 --> 00:03:19.425
what is your center of dilation?

00:03:19.425 --> 00:03:24.064
So for example, if your
center of dilation is,

00:03:24.064 --> 00:03:25.427
let's say, right over here,

00:03:25.427 --> 00:03:28.192
then all of these things are
gonna be stretched that way.

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And so this point might go to there,

00:03:30.359 --> 00:03:33.423
that point might go over there,

00:03:33.423 --> 00:03:34.810
this point might go over here,

00:03:34.810 --> 00:03:36.420
and then that point might go over here.

00:03:36.420 --> 00:03:38.548
So this is definitely a dilation,

00:03:38.548 --> 00:03:40.161
where you are, your center where

00:03:40.161 --> 00:03:41.697
everything is expanding from,

00:03:41.697 --> 00:03:44.614
is just outside of our trapezoid A.


Transformations - dilation

WEBVTT
Kind: captions
Language: en

00:00:00.246 --> 00:00:02.833
- [Instructor] In previous
videos, we started talking about

00:00:02.833 --> 00:00:04.842
the idea of transformations.

00:00:04.842 --> 00:00:07.618
In particular, we talked
about rigid transformations.

00:00:07.618 --> 00:00:11.586
So for example, you can shift something.

00:00:11.586 --> 00:00:14.303
This would be a translation.

00:00:14.303 --> 00:00:17.000
So the thing that I'm moving
around is a translation

00:00:17.000 --> 00:00:19.007
of our original triangle.

00:00:19.007 --> 00:00:20.648
You could have a rotation.

00:00:20.648 --> 00:00:25.299
So that thing that I
translated, I am now rotating it

00:00:25.299 --> 00:00:27.832
as you see right over there.

00:00:27.832 --> 00:00:28.995
And you can also have a reflection.

00:00:28.995 --> 00:00:31.705
The tool that I'm using doesn't
make reflection too easy.

00:00:31.705 --> 00:00:35.155
But that's essentially
flipping it over a line.

00:00:35.155 --> 00:00:37.412
But what we're going to
talk about in this video

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is a non-rigid transformation.

00:00:40.206 --> 00:00:42.541
And what makes something
a rigid transformation

00:00:42.541 --> 00:00:45.580
is that lengths between
points are reserved.

00:00:45.580 --> 00:00:47.657
But in a non-rigid transformation,

00:00:47.657 --> 00:00:50.380
those lengths do not need to be preserved.

00:00:50.380 --> 00:00:54.252
So for example, this rotated
and translated triangle

00:00:54.252 --> 00:00:56.718
that I'm moving around right
here, in fact I'm continuing

00:00:56.718 --> 00:00:58.848
to translate it as I talk.

00:00:58.848 --> 00:01:00.474
I can dilate it.

00:01:00.474 --> 00:01:02.738
And one way to think about
dilation is that we're just

00:01:02.738 --> 00:01:04.940
scaling it down or scaling it up.

00:01:04.940 --> 00:01:08.178
So for example, here,
I am scaling it down.

00:01:08.178 --> 00:01:09.567
That is a dilation.

00:01:09.567 --> 00:01:11.095
Or I can scale it up.

00:01:11.095 --> 00:01:14.863
This is also a dilation or even going off

00:01:14.863 --> 00:01:16.552
of the graph paper.

00:01:16.552 --> 00:01:18.420
So the whole point
here's just to appreciate

00:01:18.420 --> 00:01:20.749
that we don't just have
the rigid transformations,

00:01:20.749 --> 00:01:22.693
we can have other types
of transformations,

00:01:22.693 --> 00:01:25.803
and a dilation is one
of them in your toolkit

00:01:25.803 --> 00:01:28.150
that you will often see,
especially when you get introduced

00:01:28.150 --> 00:01:30.650
to the idea of transformation.


TI-84 geometpdf and geometcdf functions

WEBVTT
Kind: captions
Language: en

00:00:00.773 --> 00:00:02.180
- [Instructor] What we're
going to do in this video

00:00:02.180 --> 00:00:03.907
is learn how to use a graphing calculator,

00:00:03.907 --> 00:00:05.973
in particular a TI84.

00:00:05.973 --> 00:00:08.391
If you're using any other TI
Texas Instrument calculator

00:00:08.391 --> 00:00:10.965
it'll be very similar in
order to answer some questions

00:00:10.965 --> 00:00:13.414
dealing with geometric random variables.

00:00:13.414 --> 00:00:15.203
So, here we have a scenario.

00:00:15.203 --> 00:00:16.900
I keep picking cards from a standard deck

00:00:16.900 --> 00:00:19.235
until I get a king.

00:00:19.235 --> 00:00:22.033
So this is a class geometric
random variable here

00:00:22.033 --> 00:00:24.387
and it's important that
in this parentheses

00:00:24.387 --> 00:00:26.324
it says I replace the cards
if they are not a king

00:00:26.324 --> 00:00:28.857
and this important as we
talk about on other videos

00:00:28.857 --> 00:00:32.760
because the probability of
success each time can't change.

00:00:32.760 --> 00:00:36.436
And so we could define
some random variable X

00:00:36.436 --> 00:00:38.739
this is a geometric random
variable as being equal to

00:00:38.739 --> 00:00:42.072
the number of picks until we get a king.

00:00:46.852 --> 00:00:50.164
When we replace the cards
if they are not a king.

00:00:50.164 --> 00:00:52.151
And for this geometric random variable,

00:00:52.151 --> 00:00:54.010
what's the probability
of success on each trial?

00:00:54.010 --> 00:00:55.731
Remember what are the
conditions for a geometric

00:00:55.731 --> 00:00:57.237
random variable is that
probability of success

00:00:57.237 --> 00:01:00.029
does not change on each trial.

00:01:00.029 --> 00:01:03.253
Well the probability of
success is going to be equal to

00:01:03.253 --> 00:01:04.886
there's four kings in a
standard deck of 52, this is

00:01:04.886 --> 00:01:07.701
the same thing as one over 13.

00:01:07.701 --> 00:01:09.953
So this first question is
what is the probability that

00:01:09.953 --> 00:01:11.958
I need to pick five cards?

00:01:11.958 --> 00:01:14.248
Well this would be the
probability that our geometric

00:01:14.248 --> 00:01:17.163
random variable X is equal to
five and you could actually

00:01:17.163 --> 00:01:19.771
figure this out by hand,
but the whole point here

00:01:19.771 --> 00:01:21.957
is to think about how to
use a calculator and there's

00:01:21.957 --> 00:01:26.124
a function called geometpdf
which stands for geometric

00:01:27.701 --> 00:01:31.095
probability distribution
function, where what you have

00:01:31.095 --> 00:01:33.556
to pass it is the probability
of success on any given

00:01:33.556 --> 00:01:37.723
trial, one out of 13, and
then the particular value

00:01:38.920 --> 00:01:41.126
of that random variable
that you want to figure out

00:01:41.126 --> 00:01:43.878
the probability for, so
five right over there.

00:01:43.878 --> 00:01:45.735
Now just to be clear, if
you're doing this on an AP exam

00:01:45.735 --> 00:01:48.626
and this is one of the reasons
why a calculator is useful,

00:01:48.626 --> 00:01:52.256
you can use this on an AP
exam, AP statistics exam.

00:01:52.256 --> 00:01:54.628
It's important to tell the
graders if you're doing it

00:01:54.628 --> 00:01:56.916
on the free response that
this right over here is your

00:01:56.916 --> 00:01:59.284
P and that this right over
here is your five just so

00:01:59.284 --> 00:02:02.454
it's very clear that where you
actually got this information

00:02:02.454 --> 00:02:04.822
from or why you're actually typing it in.

00:02:04.822 --> 00:02:06.791
But let's just see how it
works, what this probability

00:02:06.791 --> 00:02:09.558
is actually going to amount to.

00:02:09.558 --> 00:02:12.283
Alright so I have my calculator
now and I just need to type

00:02:12.283 --> 00:02:15.687
in geometpdf and then those parameters.

00:02:15.687 --> 00:02:17.396
And so the place where I
find that function I press

00:02:17.396 --> 00:02:21.923
2nd, distribution right over
here, it's a little above

00:02:21.923 --> 00:02:23.846
the vars button.

00:02:23.846 --> 00:02:26.039
And then I click up, I can
scroll down or I could just

00:02:26.039 --> 00:02:27.682
go to the bottom of the list
and you can see the second

00:02:27.682 --> 00:02:31.235
from the bottom is
geometpdf, click Enter there.

00:02:31.235 --> 00:02:34.715
My P value, my probability
of success on each trial

00:02:34.715 --> 00:02:37.397
is one out of 13, and I want
to figure out the probability

00:02:37.397 --> 00:02:40.812
that I have to pick five cards.

00:02:40.812 --> 00:02:44.199
And so then click Enter,
click Enter again,

00:02:44.199 --> 00:02:48.081
and there you have it, it's about 0.056.

00:02:48.081 --> 00:02:50.664
So this is approximately 0.056.

00:02:54.582 --> 00:02:56.923
Now let's answer another
question, so here they say

00:02:56.923 --> 00:02:59.284
what is the probability that
I need to pick less than

00:02:59.284 --> 00:03:00.117
10 cards?

00:03:01.618 --> 00:03:05.701
So this is the probability
that X is less than 10

00:03:08.023 --> 00:03:10.418
or I could say this is equal
to the probability that

00:03:10.418 --> 00:03:13.085
X is less than or equal to nine.

00:03:14.644 --> 00:03:16.615
And I could say well this
is the probability that X

00:03:16.615 --> 00:03:19.451
is equal to one plus the
probability that X is equal to

00:03:19.451 --> 00:03:23.618
two all the way to the probability
that X is equal to nine.

00:03:25.906 --> 00:03:27.862
But that would take a
while, even if I used this

00:03:27.862 --> 00:03:29.540
function right over here.

00:03:29.540 --> 00:03:31.880
But lucky for us, there's
a cumulative distribution

00:03:31.880 --> 00:03:33.973
function, take some space
from the next question,

00:03:33.973 --> 00:03:38.140
this is going to be equal
to geometcdf, cumulative

00:03:39.803 --> 00:03:42.667
distribution function and once
again I pass the probability

00:03:42.667 --> 00:03:47.315
of success on any trial and
then up to including nine.

00:03:47.315 --> 00:03:49.550
So let's get the calculator out again.

00:03:49.550 --> 00:03:53.429
So we go to 2nd, distribution,
I click up and there we

00:03:53.429 --> 00:03:56.278
have it geomet cumulative
distribution function, press

00:03:56.278 --> 00:04:00.630
Enter, one out of 13 chance
of success on any trial.

00:04:00.630 --> 00:04:04.047
Up to and including nine, and then Enter.

00:04:05.702 --> 00:04:09.869
And there you have it, it's
approximately 51.3% or 0.513.

00:04:10.837 --> 00:04:13.420
So this is approximately 0.513.

00:04:16.606 --> 00:04:17.861
Now let's do one more.

00:04:17.861 --> 00:04:20.041
What is the probability that
I need to pick more than

00:04:20.041 --> 00:04:21.318
12 cards?

00:04:21.318 --> 00:04:22.783
And like I'll pause the video
and see if you can figure

00:04:22.783 --> 00:04:24.454
this one out, what function
would I use on my calculator,

00:04:24.454 --> 00:04:26.646
how would I set it up?

00:04:26.646 --> 00:04:28.832
Well the probability, this
is the probability that X

00:04:28.832 --> 00:04:32.999
is going to be greater than
12, which is equal to one

00:04:34.974 --> 00:04:39.141
minus the probably that x
is less than or equal to 12.

00:04:41.832 --> 00:04:44.806
And now this we could just use
the cumulative distribution

00:04:44.806 --> 00:04:48.639
function again, so this
is one minus geometcdf

00:04:51.286 --> 00:04:55.453
cumulative distribution
function, cdf, of one over 13

00:04:59.366 --> 00:05:02.037
and up to and including 12.

00:05:02.037 --> 00:05:04.196
So what is this going to be equal to?

00:05:04.196 --> 00:05:09.188
So 2nd, distribution, I click
up, I get to the function.

00:05:09.188 --> 00:05:12.949
Click Enter, and so I
already have that first,

00:05:12.949 --> 00:05:16.549
the probability of success on
every trial is one over 13,

00:05:16.549 --> 00:05:21.170
and then cumulative up to
12 and so I click Enter.

00:05:21.170 --> 00:05:24.985
And then well I could click
Enter there, but I really want

00:05:24.985 --> 00:05:28.914
to get one minus this
value, so I can do one minus

00:05:28.914 --> 00:05:33.081
2nd Answer, which would be
just one minus that value,

00:05:35.206 --> 00:05:39.543
which will be equal to there
you have it, it's about 38.3%

00:05:39.543 --> 00:05:40.376
or 0.383.

00:05:41.778 --> 00:05:45.945
So this is approximately
equal to 0.383 and we're done.


When there aren't gains from trade

WEBVTT
Kind: captions
Language: en

00:00:00.961 --> 00:00:02.778
- [Instructor] So let's say
we're in a very simplified world

00:00:02.778 --> 00:00:05.586
where we have two countries,
Country A and Country B

00:00:05.586 --> 00:00:09.152
and they're each capable of
producing apples or bananas

00:00:09.152 --> 00:00:12.213
or some combination of them
and what this chart tells us

00:00:12.213 --> 00:00:16.102
if Country A put all their
energy behind apples in a day

00:00:16.102 --> 00:00:18.219
they could produce three apples,

00:00:18.219 --> 00:00:21.987
and if they put all of their
energy behind bananas in a day

00:00:21.987 --> 00:00:23.988
they could produce six bananas.

00:00:23.988 --> 00:00:26.985
Similarly, Country B, if
they put all of their energy

00:00:26.985 --> 00:00:29.630
behind apples in a day they
could produce two apples,

00:00:29.630 --> 00:00:32.912
and Country B if they put all
of their energy behind bananas

00:00:32.912 --> 00:00:36.010
in a day they could produce four bananas.

00:00:36.010 --> 00:00:40.416
So given this, who has the
comparative advantage in apples

00:00:40.416 --> 00:00:42.641
and who has the comparative
advantage in bananas

00:00:42.641 --> 00:00:44.747
and how should they trade?

00:00:44.747 --> 00:00:47.825
Pause this video and try to
figure it out on your own.

00:00:47.825 --> 00:00:51.014
All right so when we're thinking
about comparative advantage

00:00:51.014 --> 00:00:52.146
we really want to think about,

00:00:52.146 --> 00:00:53.812
well, what is the opportunity cost

00:00:53.812 --> 00:00:56.293
of producing an apple in each country

00:00:56.293 --> 00:00:57.349
and what is the opportunity cost

00:00:57.349 --> 00:01:00.033
of producing a banana in each country?

00:01:00.033 --> 00:01:02.983
And so let me make another
little subcolumn right over here.

00:01:02.983 --> 00:01:05.681
Opportunity cost, and so
what is the opportunity cost

00:01:05.681 --> 00:01:07.764
of an apple in Country A?

00:01:09.206 --> 00:01:12.043
And pause this video at any
point if you get inspired.

00:01:12.043 --> 00:01:14.192
Well, to produce three apples

00:01:14.192 --> 00:01:16.746
they would have to trade off six bananas.

00:01:16.746 --> 00:01:18.454
And so that means that per apple,

00:01:18.454 --> 00:01:20.871
they are not producing two bananas.

00:01:20.871 --> 00:01:23.871
So this is two bananas, two bananas.

00:01:26.511 --> 00:01:29.844
I'll just write bana, bananas per apple.

00:01:32.382 --> 00:01:34.762
And their opportunity cost for bananas

00:01:34.762 --> 00:01:36.269
is just going to be
the reciprocal of that.

00:01:36.269 --> 00:01:39.686
So one over two apples, apples per banana

00:01:43.810 --> 00:01:46.802
and then for Country B we
can do a similar calculation

00:01:46.802 --> 00:01:48.696
and you might be noticing
something interesting

00:01:48.696 --> 00:01:49.894
is about to happen.

00:01:49.894 --> 00:01:53.955
What's Country B's
opportunity cost of apples?

00:01:53.955 --> 00:01:55.465
Well, one way to think about it,

00:01:55.465 --> 00:01:57.036
if they produce two apples,

00:01:57.036 --> 00:01:59.288
that means they're giving up four bananas.

00:01:59.288 --> 00:02:01.931
Or they're giving up
two bananas per apple.

00:02:01.931 --> 00:02:04.764
So two bananas, bananas per apple.

00:02:08.652 --> 00:02:10.275
And once again, if we
want to think in terms

00:02:10.275 --> 00:02:11.962
of the opportunity cost of a banana,

00:02:11.962 --> 00:02:14.676
well, to produce four bananas
they're giving up two apples.

00:02:14.676 --> 00:02:18.259
So this is one half of
an apple per banana.

00:02:21.877 --> 00:02:24.849
Per, I'll just write,
banana right over there.

00:02:24.849 --> 00:02:27.301
So this one is a little bit interesting.

00:02:27.301 --> 00:02:31.134
They have the same
opportunity cost for apples

00:02:34.369 --> 00:02:37.183
in terms of bananas, and they
have the some opportunity cost

00:02:37.183 --> 00:02:40.558
for bananas in terms of apples.

00:02:40.558 --> 00:02:45.063
And so because they have
the same opportunity costs.

00:02:45.063 --> 00:02:49.230
So let me write this down,
same opportunity costs.

00:02:54.776 --> 00:02:57.434
There is no comparative advantage.

00:02:57.434 --> 00:03:00.969
So no comparative advantage in either.

00:03:00.969 --> 00:03:02.636
Advantage in either.

00:03:06.188 --> 00:03:08.520
And so based on our very simple model here

00:03:08.520 --> 00:03:11.020
there are no gains from trade.

00:03:16.350 --> 00:03:18.332
Another way we could visualize this

00:03:18.332 --> 00:03:21.306
that maybe makes it maybe
hopefully a little bit more clear.

00:03:21.306 --> 00:03:24.360
So let me make one axis here.

00:03:24.360 --> 00:03:26.573
I'm trying to draw a
straight line, all right.

00:03:26.573 --> 00:03:30.290
And then this is my other
axis right over here.

00:03:30.290 --> 00:03:34.491
And let's make this one right
over here, this horizontal one

00:03:34.491 --> 00:03:36.718
let's make this the apples axis

00:03:36.718 --> 00:03:40.858
and let's make the vertical
one the bananas axis.

00:03:40.858 --> 00:03:45.256
And we're saying per
day and this of course

00:03:45.256 --> 00:03:49.339
is apples per day and so
if we look at Country A.

00:03:52.345 --> 00:03:53.797
Let me do Country A in a new color.

00:03:53.797 --> 00:03:55.650
So Country A, let's say orange.

00:03:55.650 --> 00:03:57.737
If they put all their energy behind apples

00:03:57.737 --> 00:04:00.070
they could produce one, two.

00:04:01.268 --> 00:04:02.415
Let me spread this out a little bit.

00:04:02.415 --> 00:04:06.582
They could produce one,
two, three apples in a day.

00:04:08.152 --> 00:04:09.991
If they put all their
energy behind bananas

00:04:09.991 --> 00:04:14.158
they could produce, let's just
say this is two, four, six.

00:04:16.171 --> 00:04:19.503
So that's six, this is four, this is two.

00:04:19.503 --> 00:04:21.473
This is three right over here.

00:04:21.473 --> 00:04:24.281
Let me put markers in-between
to make this clear.

00:04:24.281 --> 00:04:26.666
So if they put all of
their energy into bananas

00:04:26.666 --> 00:04:28.472
they could produce six in a day

00:04:28.472 --> 00:04:30.364
and so their production possibilities

00:04:30.364 --> 00:04:33.788
if we assume it is a linear trade-off

00:04:33.788 --> 00:04:35.985
would look something like this

00:04:35.985 --> 00:04:37.701
and the slope right over here,

00:04:37.701 --> 00:04:41.108
this would be the opportunity cost.

00:04:41.108 --> 00:04:44.742
So the slope right over here,
every time we increase apples

00:04:44.742 --> 00:04:47.575
by one we decrease bananas by two.

00:04:49.569 --> 00:04:53.736
So in this situation, we
would have, so the slope here

00:04:56.607 --> 00:04:59.171
is equal to, well, it's
actually a negative slope.

00:04:59.171 --> 00:05:03.338
It's equal to negative two
bananas, bananas per apple.

00:05:06.074 --> 00:05:07.976
So this right over here, this slope

00:05:07.976 --> 00:05:09.543
based on how I picked the axes,

00:05:09.543 --> 00:05:13.323
this is giving me the
opportunity cost for apples

00:05:13.323 --> 00:05:14.406
in terms of bananas.

00:05:14.406 --> 00:05:15.553
Every time I increase an apple

00:05:15.553 --> 00:05:18.130
how many bananas am I actually giving up?

00:05:18.130 --> 00:05:19.961
So that is my opportunity cost there.

00:05:19.961 --> 00:05:21.920
And now if we think about Country B.

00:05:21.920 --> 00:05:24.448
Let me do this in a new color.

00:05:24.448 --> 00:05:26.187
I'm running out of colors.

00:05:26.187 --> 00:05:28.962
Country B right over here
they could either produce

00:05:28.962 --> 00:05:32.893
four bananas or two apples
or things in-between.

00:05:32.893 --> 00:05:35.988
But notice, it has the exact same slope

00:05:35.988 --> 00:05:38.453
The slope is the opportunity cost.

00:05:38.453 --> 00:05:40.359
And if we switch these
axes right over here

00:05:40.359 --> 00:05:43.572
then the slope would be the
opportunity cost for bananas

00:05:43.572 --> 00:05:46.255
in terms of apples, but
the big takeaway here,

00:05:46.255 --> 00:05:49.135
if you see the production
possibilities of two countries

00:05:49.135 --> 00:05:51.125
and we're talking about two goods

00:05:51.125 --> 00:05:52.898
and they have the same slope,

00:05:52.898 --> 00:05:54.435
then that means their opportunity costs

00:05:54.435 --> 00:05:55.954
are going to be the same, and there's not

00:05:55.954 --> 00:05:57.449
going to be a gain from trade.

00:05:57.449 --> 00:05:59.415
Remember, the whole point
of comparative advantage

00:05:59.415 --> 00:06:03.223
and trading is that both
countries will benefit.

00:06:03.223 --> 00:06:04.979
That's really the big takeaway here.

00:06:04.979 --> 00:06:06.058
But there are situations

00:06:06.058 --> 00:06:07.440
where both countries wouldn't benefit

00:06:07.440 --> 00:06:09.804
because they have the
same opportunity cost

00:06:09.804 --> 00:06:11.610
and this was an example of one of them.

00:06:11.610 --> 00:06:15.163
Now the other case,
sometimes one will have

00:06:15.163 --> 00:06:16.428
a comparative advantage over the other.

00:06:16.428 --> 00:06:18.441
They do have different opportunity costs

00:06:18.441 --> 00:06:20.368
and then you might have
no gains from trade.

00:06:20.368 --> 00:06:21.201
Maybe there's some way

00:06:21.201 --> 00:06:23.498
that they can't know each
other's opportunity costs.

00:06:23.498 --> 00:06:24.813
There's some way that they don't trade.

00:06:24.813 --> 00:06:28.346
Maybe irrespective of
what the models tell us

00:06:28.346 --> 00:06:30.018
about comparative advantage
some country says,

00:06:30.018 --> 00:06:31.338
hey, I don't want to produce bananas.

00:06:31.338 --> 00:06:34.310
Apples are the future, that's
a higher skilled industry,

00:06:34.310 --> 00:06:37.154
whatever else, so there's
definitely scenarios,

00:06:37.154 --> 00:06:40.543
especially even in our model,
in our very simplified model

00:06:40.543 --> 00:06:42.502
where there might not be gains from trade.

00:06:42.502 --> 00:06:44.389
And the classic one of course is when

00:06:44.389 --> 00:06:46.738
there's no comparative
advantage and both countries

00:06:46.738 --> 00:06:49.108
have the same opportunity
costs in the goods.


Comparative advantage worked example

WEBVTT
Kind: captions
Language: en

00:00:01.184 --> 00:00:03.061
- [Instructor] The
countries of Kalos and Johto

00:00:03.061 --> 00:00:04.546
can produce two goods.

00:00:04.546 --> 00:00:07.330
Shiny charms and berries.

00:00:07.330 --> 00:00:09.016
Yep, you got to love these worlds

00:00:09.016 --> 00:00:12.095
created in these economics questions.

00:00:12.095 --> 00:00:14.455
The table below describe the production

00:00:14.455 --> 00:00:17.143
possibilities of each country in a day.

00:00:17.143 --> 00:00:18.778
So here it tells us that Kalos,

00:00:18.778 --> 00:00:21.329
if it puts all of its
energy behind charms,

00:00:21.329 --> 00:00:23.322
it can produce 10 charms in a day.

00:00:23.322 --> 00:00:25.387
But if it put all of its
energy behind berries,

00:00:25.387 --> 00:00:27.975
it can produce 20 berries in a day.

00:00:27.975 --> 00:00:29.646
And then Johto, all of its energy

00:00:29.646 --> 00:00:34.348
behind charms, 25, all of its
energy behind berries, 75.

00:00:34.348 --> 00:00:36.479
Given these numbers are
based on both countries

00:00:36.479 --> 00:00:40.380
having the same labor and capital inputs,

00:00:40.380 --> 00:00:43.797
who has the absolute advantage in charms?

00:00:45.137 --> 00:00:48.443
So pause the video and see
if you can figure this out.

00:00:48.443 --> 00:00:50.100
All right, so let's just remind ourselves.

00:00:50.100 --> 00:00:53.256
Absolute advantage is just
who is more efficient?

00:00:53.256 --> 00:00:56.523
Who, given the same
inputs, can produce more?

00:00:56.523 --> 00:00:58.181
And they told us that these countries,

00:00:58.181 --> 00:01:00.921
they have the same labor
and capital inputs,

00:01:00.921 --> 00:01:02.142
so this is really just a question

00:01:02.142 --> 00:01:04.261
of who can produce more charms in a day?

00:01:04.261 --> 00:01:06.152
And you can see very clearly that Johto

00:01:06.152 --> 00:01:08.163
can produce more charms in a day.

00:01:08.163 --> 00:01:10.994
And so I would say Johto,

00:01:10.994 --> 00:01:13.827
because they produce, let me write

00:01:16.153 --> 00:01:17.303
that a little bit neater,

00:01:17.303 --> 00:01:20.053
they produce more charms per day.

00:01:23.811 --> 00:01:25.061
Charms per day.

00:01:26.254 --> 00:01:27.671
With same inputs.

00:01:29.627 --> 00:01:30.627
Same inputs.

00:01:32.206 --> 00:01:34.641
So they are more efficient.

00:01:34.641 --> 00:01:35.891
More efficient.

00:01:36.942 --> 00:01:39.592
So they have the absolute advantage.

00:01:39.592 --> 00:01:41.078
Now this is an interesting thing,

00:01:41.078 --> 00:01:43.110
because our intuition might say

00:01:43.110 --> 00:01:45.124
well whoever has the absolute advantage,

00:01:45.124 --> 00:01:47.729
maybe they're the ones that
should be producing charms.

00:01:47.729 --> 00:01:49.086
But this is what's interesting when

00:01:49.086 --> 00:01:50.586
we study comparative advantage.

00:01:50.586 --> 00:01:52.596
That is not always the case.

00:01:52.596 --> 00:01:55.625
And I suspect that this
question will lead us there.

00:01:55.625 --> 00:01:57.790
All right, next question.

00:01:57.790 --> 00:01:59.786
They say calculate the opportunity cost

00:01:59.786 --> 00:02:01.369
in Kalos of charms.

00:02:02.955 --> 00:02:06.705
So the opportunity cost,
in Kalos, of charms.

00:02:07.559 --> 00:02:11.833
So when Kalos decides
to produce 10 charms,

00:02:11.833 --> 00:02:14.450
they're trading off 20 berries.

00:02:14.450 --> 00:02:15.615
Or another way of thinking about it,

00:02:15.615 --> 00:02:19.218
it costs them 20 berries
to produce 10 charms.

00:02:19.218 --> 00:02:22.135
So we could say it costs 20 berries

00:02:27.104 --> 00:02:30.854
for 10 charms, which is
equal to two berries,

00:02:34.921 --> 00:02:37.588
two berries per charm, in Kalos.

00:02:41.512 --> 00:02:42.345
So there you have it.

00:02:42.345 --> 00:02:43.499
The opportunity cost, they trade off

00:02:43.499 --> 00:02:45.155
two berries per charm.

00:02:45.155 --> 00:02:46.872
And actually, let me make
it a little column here.

00:02:46.872 --> 00:02:47.841
The opportunity cost.

00:02:47.841 --> 00:02:50.591
So this is two berries per charm.

00:02:52.478 --> 00:02:53.911
And I have a feeling, and if you're taking

00:02:53.911 --> 00:02:57.083
an exam, say an AP exam,
it's not a bad idea

00:02:57.083 --> 00:02:58.463
to just fill this thing out,

00:02:58.463 --> 00:02:59.405
so what is the opportunity cost,

00:02:59.405 --> 00:03:00.513
they haven't asked us that yet,

00:03:00.513 --> 00:03:02.122
but I'm just gonna do it really fast.

00:03:02.122 --> 00:03:06.107
What is the opportunity
cost of charms in Johto?

00:03:06.107 --> 00:03:08.837
Well, they are trading
off, to produce 25 charms,

00:03:08.837 --> 00:03:11.092
they trade off 75 berries.

00:03:11.092 --> 00:03:13.260
So this would be 75 divided by 25,

00:03:13.260 --> 00:03:16.427
this would be three berries per charm.

00:03:17.708 --> 00:03:22.554
75 berries for 25 charms
is three berries per charm.

00:03:22.554 --> 00:03:24.493
And if you want to know the
opportunity cost of berries,

00:03:24.493 --> 00:03:27.234
well you can just take the
reciprocal of each of these.

00:03:27.234 --> 00:03:29.613
So in Kalos, the opportunity cost

00:03:29.613 --> 00:03:32.696
is one half charms, charms per berry.

00:03:36.552 --> 00:03:40.719
And then in Johto, it is
one third charms per berry.

00:03:44.310 --> 00:03:48.028
That if they wanted to produce 25 berries,

00:03:48.028 --> 00:03:49.955
if they wanted to produce 75 berries,

00:03:49.955 --> 00:03:53.011
they would trade off 25 charms.

00:03:53.011 --> 00:03:55.736
So it would cost them 25
charms to produce 75 berries,

00:03:55.736 --> 00:03:57.894
or one third of a charm per berry.

00:03:57.894 --> 00:03:59.590
So I'm just doing a little bit of extra.

00:03:59.590 --> 00:04:00.817
But then it's gonna be useful,

00:04:00.817 --> 00:04:02.346
because in the next
question, they actually

00:04:02.346 --> 00:04:05.797
are asking us, who, we'll
scroll up a little bit.

00:04:05.797 --> 00:04:08.311
They're saying who has
the comparative advantage

00:04:08.311 --> 00:04:10.709
in berries, explain.

00:04:10.709 --> 00:04:13.903
So berries, whoever has
the lower opportunity cost

00:04:13.903 --> 00:04:15.919
has the comparative advantage.

00:04:15.919 --> 00:04:19.624
So we see here that Johto has the lower

00:04:19.624 --> 00:04:21.916
opportunity cost in berries.

00:04:21.916 --> 00:04:24.666
One third is lower than one half.

00:04:25.623 --> 00:04:28.477
It's a lower opportunity
cost of producing a berry.

00:04:28.477 --> 00:04:30.894
So Johto has one third charms

00:04:37.472 --> 00:04:41.222
per berry opportunity
cost, opportunity cost.

00:04:45.066 --> 00:04:47.316
Which is lower than Kalos',

00:04:52.215 --> 00:04:56.382
Kalos' one half charms per
berry opportunity cost.

00:05:02.435 --> 00:05:05.724
So Johto has comparative advantage.

00:05:05.724 --> 00:05:07.807
So Johto has comparative,

00:05:12.042 --> 00:05:14.792
comparative advantage in berries.

00:05:20.344 --> 00:05:22.268
And I apologize a little
bit for my penmanship,

00:05:22.268 --> 00:05:24.833
I'm trying to save time by
writing a little bit fast,

00:05:24.833 --> 00:05:26.816
but hopefully me saying it
out loud at the same time

00:05:26.816 --> 00:05:29.297
is making it somewhat legible.

00:05:29.297 --> 00:05:30.130
All right.

00:05:30.130 --> 00:05:31.150
So the next question.

00:05:31.150 --> 00:05:34.086
If these countries were
to specialize in trade,

00:05:34.086 --> 00:05:37.149
who would produce which good, explain.

00:05:37.149 --> 00:05:38.395
Well whoever have the
comparative advantage

00:05:38.395 --> 00:05:40.425
of each will produce that one.

00:05:40.425 --> 00:05:43.342
So Kalos has comparative advantage,

00:05:44.531 --> 00:05:47.531
Kalos has lower opportunity cost in,

00:05:50.840 --> 00:05:54.127
in let's see, they have
the lower opportunity cost

00:05:54.127 --> 00:05:56.336
when you compare them to, oh let me see,

00:05:56.336 --> 00:05:57.373
let me put it this way.

00:05:57.373 --> 00:05:59.212
For charms, let me write I this way,

00:05:59.212 --> 00:06:03.296
Kalos has a lower
opportunity cost for charms.

00:06:03.296 --> 00:06:05.796
Kalos has advantage in charms.

00:06:10.952 --> 00:06:13.452
And then we already said Johto

00:06:15.281 --> 00:06:17.364
has advantage in berries.

00:06:21.055 --> 00:06:24.222
And so, Kalos, I keep saying it weird,

00:06:26.813 --> 00:06:28.646
Kalos produces charms,

00:06:34.208 --> 00:06:37.625
Johto produces berries, produces berries.

00:06:42.025 --> 00:06:43.211
And once again, this goes back

00:06:43.211 --> 00:06:45.188
to something we touched on at
the beginning of the video.

00:06:45.188 --> 00:06:48.135
Even though Johto has
the absolute advantage,

00:06:48.135 --> 00:06:51.016
in fact they have the
absolute advantage in either,

00:06:51.016 --> 00:06:52.600
Johto is not, even though they can produce

00:06:52.600 --> 00:06:55.356
charms way more efficiently than Kalos,

00:06:55.356 --> 00:06:58.608
Johto is actually in this, if you buy

00:06:58.608 --> 00:07:00.797
all the arguments of
comparative advantages,

00:07:00.797 --> 00:07:03.024
Johto should actually produce the berries,

00:07:03.024 --> 00:07:05.343
while Kalos should produce the charms,

00:07:05.343 --> 00:07:07.217
because they have a lower opportunity cost

00:07:07.217 --> 00:07:08.923
in terms of berries.

00:07:08.923 --> 00:07:12.152
Now let's answer this last
question right over here.

00:07:12.152 --> 00:07:14.418
What would be a trading price that Johto

00:07:14.418 --> 00:07:18.671
and Kalos would agree
on to trade charms for?

00:07:18.671 --> 00:07:20.319
Now you might be saying,
well what's a price,

00:07:20.319 --> 00:07:21.685
I'm used to saying that in terms

00:07:21.685 --> 00:07:24.523
of just maybe dollars or
some type of currency,

00:07:24.523 --> 00:07:27.932
how do I answer a price right over here?

00:07:27.932 --> 00:07:30.168
Well, the key is that we can give a price

00:07:30.168 --> 00:07:32.611
in terms of opportunity cost.

00:07:32.611 --> 00:07:35.926
So they want a price of charms.

00:07:35.926 --> 00:07:39.121
So it really could be in terms of berries.

00:07:39.121 --> 00:07:39.995
So let's see.

00:07:39.995 --> 00:07:42.721
Let's look at each of
their cost of charms.

00:07:42.721 --> 00:07:46.553
So, Kalos' opportunity costs of a charm

00:07:46.553 --> 00:07:48.275
is two berries per charm,

00:07:48.275 --> 00:07:50.713
Johto's in three berries per charm.

00:07:50.713 --> 00:07:53.353
So let me rewrite that over here.

00:07:53.353 --> 00:07:56.853
So Kalos, Kalos opportunity cost of charms

00:08:02.994 --> 00:08:05.077
is two berries per charm.

00:08:10.115 --> 00:08:13.532
And then Johto opportunity cost of charms

00:08:16.702 --> 00:08:18.952
is three berries per charm.

00:08:20.978 --> 00:08:22.229
And here we're going to appreciate

00:08:22.229 --> 00:08:24.009
why comparative advantage works.

00:08:24.009 --> 00:08:27.072
We said that Kalos would be the one

00:08:27.072 --> 00:08:29.421
that would focus on the charms.

00:08:29.421 --> 00:08:30.254
And so notice.

00:08:30.254 --> 00:08:33.254
If they can sell the charms to Johto

00:08:34.615 --> 00:08:36.362
for something that is higher

00:08:36.362 --> 00:08:38.190
than their opportunity cost,

00:08:38.190 --> 00:08:40.719
and lower than Johto's opportunity cost,

00:08:40.719 --> 00:08:42.335
then they both benefit.

00:08:42.335 --> 00:08:44.041
And so a good price, let's say you could

00:08:44.041 --> 00:08:45.403
go halfway between the two,

00:08:45.403 --> 00:08:47.322
but it really could be
anything in between the two,

00:08:47.322 --> 00:08:49.989
let's say 2.5 berries per charm.

00:08:54.653 --> 00:08:56.136
They both benefit.

00:08:56.136 --> 00:08:57.756
So they would trade at this,

00:08:57.756 --> 00:09:00.339
trade at 2.5 berries per charm.

00:09:01.677 --> 00:09:03.109
Why does this make sense for Johto,

00:09:03.109 --> 00:09:05.081
even though they have
the absolute advantage?

00:09:05.081 --> 00:09:08.852
Well if they produce nothing but charms,

00:09:08.852 --> 00:09:12.351
it would cost them, or
no matter what they do,

00:09:12.351 --> 00:09:14.595
it'll cost them three berries per charm.

00:09:14.595 --> 00:09:17.076
But now they figured out
a way, through trade,

00:09:17.076 --> 00:09:20.843
to get charms at two and
a half berries per charm.

00:09:20.843 --> 00:09:24.817
And so this will be a
better deal for Johto.

00:09:24.817 --> 00:09:26.533
And so one thing to appreciate

00:09:26.533 --> 00:09:28.025
when we talk about comparative advantage,

00:09:28.025 --> 00:09:29.260
some people think that it's about

00:09:29.260 --> 00:09:31.491
one country benefiting
more than the other.

00:09:31.491 --> 00:09:32.935
But if we assume all of the assumptions

00:09:32.935 --> 00:09:36.027
about comparative advantage in our models,

00:09:36.027 --> 00:09:38.344
then it's actually about both countries

00:09:38.344 --> 00:09:39.795
that are trading benefit.

00:09:39.795 --> 00:09:41.162
They will both be better off.

00:09:41.162 --> 00:09:44.280
They will both get gains from trade,

00:09:44.280 --> 00:09:46.613
and both will be better off.


Binompdf and binomcdf functions

WEBVTT
Kind: captions
Language: en

00:00:00.937 --> 00:00:02.523
- [Instructor] What we're
going to do in this video

00:00:02.523 --> 00:00:05.010
is use a graphing calculator
to answer some questions

00:00:05.010 --> 00:00:07.724
dealing with binomial random variables

00:00:07.724 --> 00:00:10.882
and this is useful because if
you're taking the AP Stats,

00:00:10.882 --> 00:00:13.079
the Advanced Placement Statistics test,

00:00:13.079 --> 00:00:15.140
you are allowed to use
a graphing calculator

00:00:15.140 --> 00:00:18.198
and so this could actually
save you significant time.

00:00:18.198 --> 00:00:20.870
So it says here I have a 0.35 probability

00:00:20.870 --> 00:00:22.477
of making a free throw.

00:00:22.477 --> 00:00:24.001
What is the probability of making

00:00:24.001 --> 00:00:26.988
four out of seven free throws?

00:00:26.988 --> 00:00:30.613
Well this is a classic binomial
random variable question.

00:00:30.613 --> 00:00:34.030
If we said the binomial random variable x

00:00:34.940 --> 00:00:37.107
is equal to number of made

00:00:39.614 --> 00:00:41.531
free throws from seven,

00:00:44.235 --> 00:00:47.019
I can say seven trials or seven shots,

00:00:47.019 --> 00:00:48.436
seven trials with

00:00:50.890 --> 00:00:53.729
the probability of success

00:00:53.729 --> 00:00:56.812
is equal to 0.35 for each free throw.

00:00:57.894 --> 00:01:01.349
So really this question amounts
to what is the probability

00:01:01.349 --> 00:01:05.574
that my binomial random
variable x is equal to four?

00:01:05.574 --> 00:01:06.689
Now what we're going to see is

00:01:06.689 --> 00:01:09.301
we can use a function on our TI-84,

00:01:09.301 --> 00:01:10.718
not named binomc,

00:01:13.201 --> 00:01:14.714
or binompdf, I should say,

00:01:14.714 --> 00:01:17.173
binompdf which is short

00:01:17.173 --> 00:01:20.334
for binomial probability
distribution function,

00:01:20.334 --> 00:01:22.325
and what you're going to want to do here

00:01:22.325 --> 00:01:24.275
is use three arguments.

00:01:24.275 --> 00:01:26.957
So the first one is the number of trials.

00:01:26.957 --> 00:01:28.734
So in this case, it is seven,

00:01:28.734 --> 00:01:30.664
and if you're doing it on
the free response section

00:01:30.664 --> 00:01:33.227
of the AP test, you
should make it very clear

00:01:33.227 --> 00:01:35.685
that that right over there is your n,

00:01:35.685 --> 00:01:37.521
the graders will actually look for that

00:01:37.521 --> 00:01:40.465
to make sure that you're not
just guessing what goes where.

00:01:40.465 --> 00:01:42.346
So you would say that is my n

00:01:42.346 --> 00:01:46.198
and then you would say
your probability, 0.35,

00:01:46.198 --> 00:01:48.230
and once again if you're taking the test,

00:01:48.230 --> 00:01:49.521
you should mark that.

00:01:49.521 --> 00:01:51.216
That is your p.

00:01:51.216 --> 00:01:52.772
And then last but not least,

00:01:52.772 --> 00:01:55.686
what is the probability
that a binomial variable

00:01:55.686 --> 00:01:57.442
when you're taking seven
trials with a probability

00:01:57.442 --> 00:02:00.716
of success of each of them being 0.35

00:02:00.716 --> 00:02:03.782
that you have exactly four successes.

00:02:03.782 --> 00:02:05.590
So now lets get our calculator out

00:02:05.590 --> 00:02:07.886
and actually do that.

00:02:07.886 --> 00:02:10.620
Alright, so now we have our
graphing calculator out.

00:02:10.620 --> 00:02:12.620
So there's a couple of ways to input this.

00:02:12.620 --> 00:02:14.887
You could just type it in
directly, that could take time.

00:02:14.887 --> 00:02:18.564
You could do second in this
little blue distribution here.

00:02:18.564 --> 00:02:19.792
So there you have it.

00:02:19.792 --> 00:02:20.970
In order to get to the function,

00:02:20.970 --> 00:02:22.221
you could either scroll down

00:02:22.221 --> 00:02:24.822
or you could scroll up to
get to the bottom of the list

00:02:24.822 --> 00:02:27.402
and you see it right over here, binompdf.

00:02:27.402 --> 00:02:29.585
You could do alphaA to
go there really fast

00:02:29.585 --> 00:02:33.811
or you could just scroll
up here, click enter,

00:02:33.811 --> 00:02:36.859
and then, you have the number of trials

00:02:36.859 --> 00:02:37.872
that you want to deal with.

00:02:37.872 --> 00:02:40.475
Well we're gonna take seven trials,

00:02:40.475 --> 00:02:44.558
the probability of success
in each trial is 0.35,

00:02:46.225 --> 00:02:48.846
and then my x value,

00:02:48.846 --> 00:02:50.117
well I wanna find the probability

00:02:50.117 --> 00:02:53.377
that my binomial random
variable is equal to four,

00:02:53.377 --> 00:02:55.815
four successes out of the trials.

00:02:55.815 --> 00:02:57.777
And now let me go to paste

00:02:57.777 --> 00:03:00.264
and this is actually
going to type in exactly

00:03:00.264 --> 00:03:01.637
what we had before.

00:03:01.637 --> 00:03:03.454
Notice this is the exact same thing.

00:03:03.454 --> 00:03:06.798
So I have seven trials,
p is equals to 0.35,

00:03:06.798 --> 00:03:08.168
and I wanna know the probability of having

00:03:08.168 --> 00:03:09.886
exactly four successes,

00:03:09.886 --> 00:03:12.353
and then I just click enter

00:03:12.353 --> 00:03:14.853
and I get, there you go, 0.14.

00:03:16.427 --> 00:03:18.010
So this is equal to

00:03:20.135 --> 00:03:21.718
approximately 0.14.

00:03:24.481 --> 00:03:28.192
Now based on the same
binomial random variable,

00:03:28.192 --> 00:03:30.679
if we're then asked
what is the probability

00:03:30.679 --> 00:03:34.296
of making less than five free throws?

00:03:34.296 --> 00:03:35.942
So we could say this is the probability

00:03:35.942 --> 00:03:38.696
that x is less than five

00:03:38.696 --> 00:03:41.337
or we could say this is the probability

00:03:41.337 --> 00:03:44.670
that x is less than or equal to four,

00:03:45.602 --> 00:03:47.290
and the reason why I write it this way

00:03:47.290 --> 00:03:48.335
is because using it this way

00:03:48.335 --> 00:03:50.826
you can now use the binomial cumulative

00:03:50.826 --> 00:03:53.862
distribution function on my calculator.

00:03:53.862 --> 00:03:56.112
So if I just type in binom,

00:03:57.144 --> 00:04:01.165
and once again, I'm
gonna seven of binomcdf,

00:04:01.165 --> 00:04:04.043
I should say, cumulative
distribution function

00:04:04.043 --> 00:04:06.469
and I'm gonna take seven trials

00:04:06.469 --> 00:04:10.761
and the probability of
success in each trial is 0.35

00:04:10.761 --> 00:04:13.085
and now when I type in four here,

00:04:13.085 --> 00:04:14.236
it doesn't mean what is the probability

00:04:14.236 --> 00:04:16.418
that I make exactly four free throws,

00:04:16.418 --> 00:04:19.202
it is the probability
that I make zero, one,

00:04:19.202 --> 00:04:22.444
two, three, or four free throws.

00:04:22.444 --> 00:04:23.793
So all of the possible outcomes

00:04:23.793 --> 00:04:26.385
of my binomial random variable up to

00:04:26.385 --> 00:04:30.173
and including this value right over here.

00:04:30.173 --> 00:04:31.837
So let me get that,

00:04:31.837 --> 00:04:34.337
let me get my calculator back,

00:04:35.273 --> 00:04:39.458
so once again, I can go
to second, distribution,

00:04:39.458 --> 00:04:41.815
I'll scroll up to go to
the bottom of the list

00:04:41.815 --> 00:04:42.648
and here you see it,

00:04:42.648 --> 00:04:45.728
binomial cumulative distribution function.

00:04:45.728 --> 00:04:48.590
So let me go there, click enter.

00:04:48.590 --> 00:04:51.538
And once again, seven trials,

00:04:51.538 --> 00:04:52.621
my p is 0.35,

00:04:55.499 --> 00:04:57.612
and my x value is four,

00:04:57.612 --> 00:04:59.339
but now this is not going to
be giving me the probability

00:04:59.339 --> 00:05:02.590
that my binomial random
variable equals four,

00:05:02.590 --> 00:05:04.105
this is going to give me the probability

00:05:04.105 --> 00:05:07.710
that I get any value up
to and including four.

00:05:07.710 --> 00:05:09.611
So this should be a higher probability.

00:05:09.611 --> 00:05:13.611
And there you have it,
it is approximately 0.94.

00:05:16.436 --> 00:05:18.936
So this is approximately 0.94.

00:05:20.765 --> 00:05:21.871
So hopefully you found that helpful.

00:05:21.871 --> 00:05:23.720
These calculators can be very useful

00:05:23.720 --> 00:05:26.306
especially on something
like an AP Stats exam.


Equilibrium, allocative efficiency and total surplus

WEBVTT
Kind: captions
Language: en

00:00:01.341 --> 00:00:03.126
- [Instructor] What we're
going to do in this video

00:00:03.126 --> 00:00:05.709
is think about the market for chocolate

00:00:05.709 --> 00:00:07.320
and we're going to think about
supply and demand curves,

00:00:07.320 --> 00:00:09.149
but we're going to get an intuition

00:00:09.149 --> 00:00:11.079
for them in a slightly different way.

00:00:11.079 --> 00:00:12.670
In particular for the demand curve

00:00:12.670 --> 00:00:16.753
we will think about the
idea of marginal benefit.

00:00:19.520 --> 00:00:22.030
Now marginal benefit, when
we're talking about margin

00:00:22.030 --> 00:00:23.307
it's really thinking about, well,

00:00:23.307 --> 00:00:24.619
what happens on the increment?

00:00:24.619 --> 00:00:28.070
What happens for each
little extra that you do?

00:00:28.070 --> 00:00:30.221
So this is saying, what
is the benefit that I get

00:00:30.221 --> 00:00:34.360
if I get a little bit more
of, in this case, chocolate?

00:00:34.360 --> 00:00:35.928
Well, from the market's point of view,

00:00:35.928 --> 00:00:37.219
imagine if there was no chocolate,

00:00:37.219 --> 00:00:38.940
but there's people in the market who

00:00:38.940 --> 00:00:41.671
crave chocolate, who dream of chocolate.

00:00:41.671 --> 00:00:43.817
If all of a sudden they were able to

00:00:43.817 --> 00:00:46.100
get their hands on some chocolate,

00:00:46.100 --> 00:00:48.138
they would get a huge benefit for

00:00:48.138 --> 00:00:51.061
that incremental amount of chocolate.

00:00:51.061 --> 00:00:53.104
Maybe for these folks, their benefit,

00:00:53.104 --> 00:00:56.039
which we could quantify
as, in terms of dollars,

00:00:56.039 --> 00:01:00.091
maybe their benefit is
50 dollars per pound.

00:01:00.091 --> 00:01:01.269
One way to think about
it, they'd be willing

00:01:01.269 --> 00:01:03.591
to pay 50 dollars because
they get that much benefit,

00:01:03.591 --> 00:01:05.571
or if they paid less than 50 dollars,

00:01:05.571 --> 00:01:08.470
let's say they paid 10 dollars for it,

00:01:08.470 --> 00:01:12.388
well then they're getting
40 dollars of extra benefit

00:01:12.388 --> 00:01:15.900
a kind of surplus of benefit
from being able to get it

00:01:15.900 --> 00:01:19.650
at a price lower than
their marginal benefit.

00:01:21.392 --> 00:01:24.280
But then let's say more
chocolate becomes available.

00:01:24.280 --> 00:01:28.262
People still like it but some
of that really deep need,

00:01:28.262 --> 00:01:31.391
that deep addiction for
chocolate has been satiated,

00:01:31.391 --> 00:01:34.481
and so the marginal benefit
tends for, in most markets,

00:01:34.481 --> 00:01:39.141
the marginal benefit tends to
go down as quantity increases.

00:01:39.141 --> 00:01:41.840
One way to think about it,
that first initial amount

00:01:41.840 --> 00:01:45.401
of quantity if you, so
we have some small amount

00:01:45.401 --> 00:01:48.011
of quantity right over here,
I'll say delta quantity.

00:01:48.011 --> 00:01:50.620
That first quantity, if
you multiply it times

00:01:50.620 --> 00:01:53.830
the marginal benefit, well
that gives you an area

00:01:53.830 --> 00:01:56.440
roughly of a rectangle
like this, it's not quite

00:01:56.440 --> 00:01:59.128
rectangular at the top,
it's more of a trapezoid

00:01:59.128 --> 00:02:01.031
if this is downward sloping, but you could

00:02:01.031 --> 00:02:03.841
approximate it as a rectangle.

00:02:03.841 --> 00:02:06.741
But either way, the area right over here,

00:02:06.741 --> 00:02:09.492
the area under the marginal benefit curve,

00:02:09.492 --> 00:02:11.242
you could think about this as, well,

00:02:11.242 --> 00:02:14.040
that's just the benefit
that the market is getting

00:02:14.040 --> 00:02:17.623
from consuming this
chocolate in this case.

00:02:19.442 --> 00:02:22.771
And so let's just continue on this trend.

00:02:22.771 --> 00:02:24.437
If there's more and more chocolate

00:02:24.437 --> 00:02:26.350
the market will get benefit from it,

00:02:26.350 --> 00:02:28.892
but people aren't as
excited about it anymore.

00:02:28.892 --> 00:02:30.811
They're saying, oh, well,
the chocolate's around,

00:02:30.811 --> 00:02:32.242
yeah, it'd be nice to
have a little bit more,

00:02:32.242 --> 00:02:33.821
but I don't need so much more.

00:02:33.821 --> 00:02:35.121
And at some point people might be

00:02:35.121 --> 00:02:37.501
all chocolated out, and they have maybe

00:02:37.501 --> 00:02:39.150
even zero marginal benefit from

00:02:39.150 --> 00:02:40.710
that incremental amount of chocolate,

00:02:40.710 --> 00:02:41.942
chocolate has filled up the town,

00:02:41.942 --> 00:02:44.520
there's nowhere to actually put it.

00:02:44.520 --> 00:02:46.191
Now that won't always be the case,

00:02:46.191 --> 00:02:48.060
you might go someplace like that,

00:02:48.060 --> 00:02:49.191
but either way you think about it

00:02:49.191 --> 00:02:52.771
we would view this as our
marginal benefit curve.

00:02:52.771 --> 00:02:54.870
And notice, this is exactly the same as

00:02:54.870 --> 00:02:57.918
a demand curve in the
market for chocolate.

00:02:57.918 --> 00:03:00.120
We have plotted price versus quantity

00:03:00.120 --> 00:03:02.582
in the market for
chocolate, but we've thought

00:03:02.582 --> 00:03:05.742
about it in terms of marginal benefit.

00:03:05.742 --> 00:03:08.262
Now on the supply side
there's a related idea,

00:03:08.262 --> 00:03:12.429
we're going to think about
marginal cost, marginal cost.

00:03:14.351 --> 00:03:17.152
So let's say at first there's no chocolate

00:03:17.152 --> 00:03:19.312
being produced in this market.

00:03:19.312 --> 00:03:21.271
And a savvy entrepreneur says, hey,

00:03:21.271 --> 00:03:22.922
I know some folks who are
addicted to chocolate,

00:03:22.922 --> 00:03:25.051
they would get a lot of benefit from it,

00:03:25.051 --> 00:03:27.231
so I'm going to try to
produce some chocolate.

00:03:27.231 --> 00:03:28.321
And they look around and they find out,

00:03:28.321 --> 00:03:31.200
hey, there's actually a
derelict chocolate factory

00:03:31.200 --> 00:03:33.441
in town that no one is
using and it's surrounded

00:03:33.441 --> 00:03:36.761
by these wild cocoa bushes
that are perfect for chocolate.

00:03:36.761 --> 00:03:38.041
And there are some people in town

00:03:38.041 --> 00:03:39.652
who are actually unemployed, but they are

00:03:39.652 --> 00:03:41.782
amazing at producing chocolate.

00:03:41.782 --> 00:03:44.662
And so the first units of chocolate,

00:03:44.662 --> 00:03:48.829
the marginal cost to produce
it is actually quite low.

00:03:49.811 --> 00:03:51.573
But once you utilize those folks,

00:03:51.573 --> 00:03:52.992
you utilize that derelict factory,

00:03:52.992 --> 00:03:55.602
you utilize those free
cocoa bushes or whatever,

00:03:55.602 --> 00:03:57.802
cocoa trees, well then
you've got to plant new ones,

00:03:57.802 --> 00:03:59.068
you've got to train new employees,

00:03:59.068 --> 00:04:00.600
you've got to build a new factory.

00:04:00.600 --> 00:04:02.533
And so to produce that next increment,

00:04:02.533 --> 00:04:04.802
well that's going to cost
a little bit more and then

00:04:04.802 --> 00:04:06.651
a little bit more and
then a little bit more,

00:04:06.651 --> 00:04:10.050
which is the general
trend in most markets.

00:04:10.050 --> 00:04:12.651
Initially that first amount
you produce in as cheap a way,

00:04:12.651 --> 00:04:14.671
using the low hanging fruit, as possible,

00:04:14.671 --> 00:04:16.732
but then you've got to go up the tree,

00:04:16.732 --> 00:04:19.471
find higher and higher fruit,
maybe I'm mixing metaphors.

00:04:19.471 --> 00:04:22.551
But your cost, your marginal cost per unit

00:04:22.551 --> 00:04:25.872
goes higher and higher and higher.

00:04:25.872 --> 00:04:27.303
Now, what have we constructed here?

00:04:27.303 --> 00:04:29.892
Well you might say, hey, Sal,
that's a marginal cost curve.

00:04:29.892 --> 00:04:32.852
But once again, this
also could be viewed as

00:04:32.852 --> 00:04:36.860
the supply curve for
this particular market.

00:04:36.860 --> 00:04:38.582
Now what is happening at these

00:04:38.582 --> 00:04:41.002
low quantities right over here?

00:04:41.002 --> 00:04:43.669
Well, the cost of production is,

00:04:44.851 --> 00:04:46.750
let's say they produce
this delta Q amount,

00:04:46.750 --> 00:04:50.482
the cost of production would be the area

00:04:50.482 --> 00:04:54.392
right over here under
the marginal cost curve,

00:04:54.392 --> 00:04:56.232
that would be the cost of production.

00:04:56.232 --> 00:04:57.301
But they're able to sell it,

00:04:57.301 --> 00:05:00.153
the benefit to the market I should say,

00:05:00.153 --> 00:05:03.352
would be the total area
under this red curve,

00:05:03.352 --> 00:05:06.312
would be the benefit to the market,

00:05:06.312 --> 00:05:08.692
the total area under this curve.

00:05:08.692 --> 00:05:12.053
So if you have the total
benefit to the market,

00:05:12.053 --> 00:05:13.992
you take out the cost, then what you have

00:05:13.992 --> 00:05:16.883
in between these curves,
you could view this

00:05:16.883 --> 00:05:20.502
as a surplus, you could view this as

00:05:20.502 --> 00:05:23.547
a surplus of benefit right over here.

00:05:23.547 --> 00:05:26.285
So let me write this
down, this is surplus,

00:05:26.285 --> 00:05:28.708
and you won't hear this
term but I like to use it,

00:05:28.708 --> 00:05:29.927
because it makes it intuitive on what

00:05:29.927 --> 00:05:32.458
we're talking about,
this is surplus benefit.

00:05:32.458 --> 00:05:34.237
So as long as there's surplus benefit

00:05:34.237 --> 00:05:35.747
the suppliers are going to say, hey, wow,

00:05:35.747 --> 00:05:38.157
I can produce this cheaply, people have a,

00:05:38.157 --> 00:05:39.875
people get a lot of benefit for it,

00:05:39.875 --> 00:05:41.188
they'd be definitely willing to pay

00:05:41.188 --> 00:05:43.908
10 dollars a pound wherever I am.

00:05:43.908 --> 00:05:45.197
If people are getting this much benefit,

00:05:45.197 --> 00:05:46.497
they're definitely going to be willing

00:05:46.497 --> 00:05:48.808
to pay 10 dollars for it.

00:05:48.808 --> 00:05:50.987
So I'm going to produce some, or actually

00:05:50.987 --> 00:05:52.369
I'm going to produce some
and I could even charge,

00:05:52.369 --> 00:05:55.048
I could charge anywhere
in between these areas.

00:05:55.048 --> 00:05:56.589
Maybe I could charge right over here

00:05:56.589 --> 00:05:58.466
and I get some of the benefit and then

00:05:58.466 --> 00:06:01.108
the consumers get some of the benefit.

00:06:01.108 --> 00:06:04.675
But then another maybe
entrepreneur realizes, hey,

00:06:04.675 --> 00:06:06.997
well, there's more benefit to be had

00:06:06.997 --> 00:06:09.081
in this market, so they keep producing,

00:06:09.081 --> 00:06:13.032
they keep producing as long
as there is benefit here,

00:06:13.032 --> 00:06:15.261
as long as the marginal benefit is

00:06:15.261 --> 00:06:17.722
higher than the marginal
cost, all the way until

00:06:17.722 --> 00:06:20.401
we get to that point right over here.

00:06:20.401 --> 00:06:24.520
Now what happens, what
happens right over here?

00:06:24.520 --> 00:06:25.941
Well we talked about
just supply and demand,

00:06:25.941 --> 00:06:27.480
we talk about that's an efficient price

00:06:27.480 --> 00:06:30.380
and efficient quantity,
but let's just think about,

00:06:30.380 --> 00:06:32.940
we said up until this point it makes sense

00:06:32.940 --> 00:06:34.931
to produce more and more and more.

00:06:34.931 --> 00:06:38.600
Even this increment, if we're
already at this quantity,

00:06:38.600 --> 00:06:41.261
it makes sense to produce
even a little bit more

00:06:41.261 --> 00:06:44.220
because you're going to have this cost,

00:06:44.220 --> 00:06:46.402
you're going to have this cost to incur,

00:06:46.402 --> 00:06:49.458
but then the market
could have all of this,

00:06:49.458 --> 00:06:52.758
the market could have all of this benefit,

00:06:52.758 --> 00:06:55.258
which is larger than the cost.

00:06:56.610 --> 00:06:58.029
And so you say, well, as long as I sell it

00:06:58.029 --> 00:06:59.950
for something in between we can split

00:06:59.950 --> 00:07:03.558
that surplus benefit, so to speak.

00:07:03.558 --> 00:07:06.018
But once these two lines intersect

00:07:06.018 --> 00:07:10.185
and we have the situation
where our marginal benefit,

00:07:11.479 --> 00:07:15.327
marginal benefit, is equal
to our marginal cost,

00:07:15.327 --> 00:07:17.290
well at that point there
is no surplus benefit

00:07:17.290 --> 00:07:20.088
now to be had, there's no really

00:07:20.088 --> 00:07:22.100
incentive to produce more than this.

00:07:22.100 --> 00:07:24.980
Beyond this point, your
incremental cost of production,

00:07:24.980 --> 00:07:28.540
your marginal cost is higher
than your marginal benefit.

00:07:28.540 --> 00:07:30.991
So, if you actually wanted
to give it to someone

00:07:30.991 --> 00:07:32.610
for their benefit, you
would be taking a loss.

00:07:32.610 --> 00:07:34.680
Or even if you just think
about the market itself,

00:07:34.680 --> 00:07:37.425
the society would be incurring more

00:07:37.425 --> 00:07:39.579
incremental cost per unit than they would

00:07:39.579 --> 00:07:42.905
be getting of benefit, so why even do it?

00:07:42.905 --> 00:07:44.920
And so this point right over here

00:07:44.920 --> 00:07:48.478
where these two lines,
these two curves intersect

00:07:48.478 --> 00:07:50.490
and we've talked about this
with just supply and demand,

00:07:50.490 --> 00:07:52.751
but when we think about it
in terms of marginal benefit

00:07:52.751 --> 00:07:55.920
and marginal cost, we
think about this quantity

00:07:55.920 --> 00:07:59.090
right over here, let's
just call it Q subzero,

00:07:59.090 --> 00:08:02.848
this quantity is considered allocatively

00:08:02.848 --> 00:08:05.939
efficient, allocatively efficient.

00:08:05.939 --> 00:08:10.106
Which is a very fancy word,
allocatively efficient.

00:08:11.910 --> 00:08:13.411
Why is that the case?

00:08:13.411 --> 00:08:16.240
Well, any other quantity
would not be efficient.

00:08:16.240 --> 00:08:19.790
For example, let's say
for some reason we were at

00:08:19.790 --> 00:08:23.957
this quantity right over
here, let's say Q, Q one.

00:08:25.679 --> 00:08:29.968
Well what happens at this
quantity right over here?

00:08:29.968 --> 00:08:34.570
Well, at this quantity, at
this quantity right over here,

00:08:34.570 --> 00:08:38.413
the marginal benefit is
higher than the marginal cost.

00:08:38.413 --> 00:08:42.580
Marginal benefit is greater
than the marginal cost.

00:08:43.733 --> 00:08:45.821
And so we're leaving a
bunch of stuff on the table,

00:08:45.821 --> 00:08:49.181
the market is leaving a
bunch of surplus benefit,

00:08:49.181 --> 00:08:52.513
you could say total surplus, on the table.

00:08:52.513 --> 00:08:56.132
And so this benefit that
the market could have had,

00:08:56.132 --> 00:09:00.863
but it does not get, this
is called a deadweight loss,

00:09:00.863 --> 00:09:05.030
deadweight loss, and we talk
about it in other videos.

00:09:06.413 --> 00:09:09.189
Remember, in the allocatively
efficient quantity

00:09:09.189 --> 00:09:11.542
we have this huge total surplus,

00:09:11.542 --> 00:09:15.922
which is the area under
the marginal benefit curve

00:09:15.922 --> 00:09:18.672
and above the marginal cost curve

00:09:19.789 --> 00:09:22.030
up until the point of intersection.

00:09:22.030 --> 00:09:24.083
But if you do a quantity less than that

00:09:24.083 --> 00:09:25.671
allocatively efficient quantity,

00:09:25.671 --> 00:09:26.931
your marginal benefit is higher than

00:09:26.931 --> 00:09:28.990
your marginal cost, and you are leaving,

00:09:28.990 --> 00:09:33.070
you are leaving all of this
total surplus on the table,

00:09:33.070 --> 00:09:35.782
regardless of how you would
have actually allocated it

00:09:35.782 --> 00:09:39.713
or distributed it between the
consumers or the producers.

00:09:39.713 --> 00:09:41.493
And what if you produced a quantity larger

00:09:41.493 --> 00:09:44.239
than the allocatively efficient quantity?

00:09:44.239 --> 00:09:46.598
Once again, very fancy word, so let's say

00:09:46.598 --> 00:09:48.841
that's Q two, what happens over here?

00:09:48.841 --> 00:09:52.761
Well, here you're able to take advantage

00:09:52.761 --> 00:09:55.503
of all of this surplus right over here,

00:09:55.503 --> 00:09:57.622
this total surplus right over here,

00:09:57.622 --> 00:10:00.381
but now you're creating negative surplus.

00:10:00.381 --> 00:10:04.048
So, in this part, now
all of this area shows

00:10:05.723 --> 00:10:09.791
a net negative benefit, or
a net I guess I should say

00:10:09.791 --> 00:10:13.861
a net cost that our market is incurring.

00:10:13.861 --> 00:10:16.241
And so this here it was
a deadweight loss because

00:10:16.241 --> 00:10:18.412
we were leaving stuff on the
table that we could have had.

00:10:18.412 --> 00:10:22.363
Here we're producing at
a cost that our market,

00:10:22.363 --> 00:10:24.423
not just our suppliers
are producing at a cost,

00:10:24.423 --> 00:10:26.171
the benefit our market is getting

00:10:26.171 --> 00:10:28.852
is less for each incremental unit,

00:10:28.852 --> 00:10:32.352
is less than, or is far less than the cost

00:10:33.229 --> 00:10:37.813
and so we are incurring a
net negative total surplus.

00:10:37.813 --> 00:10:39.980
And so this, too, would be considered,

00:10:39.980 --> 00:10:43.992
this, too, would be considered
a dead, let me write that

00:10:43.992 --> 00:10:47.672
in a color you can see, a deadweight loss.

00:10:47.672 --> 00:10:49.231
Deadweight loss we often
assume it was, hey,

00:10:49.231 --> 00:10:51.083
we're leaving some total
surplus on the table,

00:10:51.083 --> 00:10:54.354
but we also have
deadweight loss in the case

00:10:54.354 --> 00:10:57.605
where we are producing unnecessarily

00:10:57.605 --> 00:11:01.854
because the benefit is
less than the actual cost.

00:11:01.854 --> 00:11:04.083
And so whether our
marginal benefit is greater

00:11:04.083 --> 00:11:06.312
than our marginal cost, or in this case

00:11:06.312 --> 00:11:09.592
our marginal cost is greater
than our marginal benefit,

00:11:09.592 --> 00:11:12.724
we are going to produce deadweight
loss in either situation.

00:11:12.724 --> 00:11:15.172
And a properly functioning
market should be

00:11:15.172 --> 00:11:18.625
producing the quantity that
is allocatively efficient.

00:11:18.625 --> 00:11:21.152
In an ideal world and of
course all of our models assume

00:11:21.152 --> 00:11:24.633
a lot of assumptions to make
things a little bit cleaner,

00:11:24.633 --> 00:11:28.212
so we can do lines to
describe market behavior.


Visualizing marginal utility MU and total utility TU functions

WEBVTT
Kind: captions
Language: en

00:00:00.822 --> 00:00:02.633
- [Sal] What we're going
to do is think about

00:00:02.633 --> 00:00:06.800
the graphs of marginal utility
and total utility curves.

00:00:08.182 --> 00:00:09.483
And so right over here,

00:00:09.483 --> 00:00:11.271
I have a table showing me

00:00:11.271 --> 00:00:15.543
the marginal utility I get
from getting tennis balls.

00:00:15.543 --> 00:00:18.051
And so it says look if
I have no tennis balls

00:00:18.051 --> 00:00:19.723
and I'm not able to play tennis,

00:00:19.723 --> 00:00:22.045
so I'm pretty happy when
I get that first ball.

00:00:22.045 --> 00:00:25.644
It gives me a marginal utility of 100.

00:00:25.644 --> 00:00:28.384
Now you might say 100 what Sal?

00:00:28.384 --> 00:00:29.559
And I would say to you
well that's the thing

00:00:29.559 --> 00:00:31.022
about marginal utility.

00:00:31.022 --> 00:00:33.344
We're using fairly abstract units here.

00:00:33.344 --> 00:00:35.248
We're not speaking in terms of dollar

00:00:35.248 --> 00:00:36.873
or opportunity cost.

00:00:36.873 --> 00:00:39.265
We're just have this abstract unit,

00:00:39.265 --> 00:00:41.563
we could call it utility units if we want,

00:00:41.563 --> 00:00:43.514
but what really matters is the relation

00:00:43.514 --> 00:00:45.232
between these values.

00:00:45.232 --> 00:00:47.183
So for example, that second ball,

00:00:47.183 --> 00:00:49.365
it's nice, now I can lose that first ball

00:00:49.365 --> 00:00:51.687
or I don't have to chase
that first ball around

00:00:51.687 --> 00:00:54.311
as frequently, but it's not as,

00:00:54.311 --> 00:00:57.028
I don't get as much incremental utility

00:00:57.028 --> 00:00:59.234
as I got from that first ball.

00:00:59.234 --> 00:01:00.859
That first ball allowed me to play tennis.

00:01:00.859 --> 00:01:01.904
Now the second ball,

00:01:01.904 --> 00:01:02.903
I was already playing tennis,

00:01:02.903 --> 00:01:04.249
now my tennis is just going to be

00:01:04.249 --> 00:01:05.759
a little bit more pleasant.

00:01:05.759 --> 00:01:07.686
So the marginal utility
one way to think about it,

00:01:07.686 --> 00:01:09.427
this is 80 and this is 100,

00:01:09.427 --> 00:01:12.283
the marginal utility of
that second ball is 80%

00:01:12.283 --> 00:01:15.256
of what that first ball is.

00:01:15.256 --> 00:01:16.904
Now I promised that I would graph these,

00:01:16.904 --> 00:01:19.133
so let's get a graph out here

00:01:19.133 --> 00:01:20.271
So there we go.

00:01:20.271 --> 00:01:22.849
And let's start plotting these
and see what it looks like.

00:01:22.849 --> 00:01:26.053
Well that first ball
gave me a utility of 100.

00:01:26.053 --> 00:01:29.071
The second ball gives me a utility of 80.

00:01:29.071 --> 00:01:30.558
Third ball, you see the trend.

00:01:30.558 --> 00:01:32.485
This is a downward sloping,

00:01:32.485 --> 00:01:34.807
if this was a line, these
are discrete values here,

00:01:34.807 --> 00:01:37.082
but if I cared about 1/2 of a tennis ball

00:01:37.082 --> 00:01:39.033
or 3/4 of a tennis ball,

00:01:39.033 --> 00:01:40.867
then I could connect
the dots here as well.

00:01:40.867 --> 00:01:43.282
But you can see that it
is downward sloping line

00:01:43.282 --> 00:01:44.954
if you were to connect the dots.

00:01:44.954 --> 00:01:47.454
So three balls, utility of 60.

00:01:49.505 --> 00:01:52.802
If I have four balls,
it's a utility of 40.

00:01:52.802 --> 00:01:55.565
Five balls, utility of 20.

00:01:55.565 --> 00:01:57.516
And once again, when
I get that fifth ball,

00:01:57.516 --> 00:02:00.000
yeah it's nice, but now my
pockets are getting pretty full

00:02:00.000 --> 00:02:01.997
and I was all, it's hard to play tennis

00:02:01.997 --> 00:02:03.135
with those full pockets.

00:02:03.135 --> 00:02:04.598
By the time I get that sixth ball,

00:02:04.598 --> 00:02:07.431
I get no marginal utility from that.

00:02:07.431 --> 00:02:09.103
I don't have a place to store it,

00:02:09.103 --> 00:02:11.146
it's I don't really,
I'm not really into it.

00:02:11.146 --> 00:02:12.980
And then that seventh ball,

00:02:12.980 --> 00:02:13.979
I actually view it as a negative.

00:02:13.979 --> 00:02:15.326
It's one extra ball to worry about.

00:02:15.326 --> 00:02:19.436
No place to store it, it's
taking up space in my life.

00:02:19.436 --> 00:02:21.432
And so if you were to connect the dots,

00:02:21.432 --> 00:02:23.081
we're talking about a discrete case,

00:02:23.081 --> 00:02:24.892
but oftentimes you could
think about something

00:02:24.892 --> 00:02:26.262
that's a little bit more continuous

00:02:26.262 --> 00:02:28.956
where the quantity is more
granular if you said pounds

00:02:28.956 --> 00:02:31.347
of chocolate or something like that,

00:02:31.347 --> 00:02:33.042
then you could imagine

00:02:33.042 --> 00:02:35.434
in general for a marginal utility curve,

00:02:35.434 --> 00:02:38.184
to be able to connect these dots.

00:02:39.173 --> 00:02:41.425
And you see in this case,

00:02:41.425 --> 00:02:42.981
it is downward sloping.

00:02:42.981 --> 00:02:45.651
So this is the marginal utility,

00:02:45.651 --> 00:02:47.323
the marginal utility curve.

00:02:47.323 --> 00:02:49.823
Notice that it is slopes down,

00:02:50.690 --> 00:02:51.690
slopes down.

00:02:53.731 --> 00:02:55.055
And this you're generally
going to see this

00:02:55.055 --> 00:02:56.866
for any marginal utility curve

00:02:56.866 --> 00:03:00.721
because the incremental
benefit of that next amount,

00:03:00.721 --> 00:03:03.809
that next unit, is seldom as good

00:03:03.809 --> 00:03:05.550
as the benefit of getting it before.

00:03:05.550 --> 00:03:06.665
You get tired of the thing,

00:03:06.665 --> 00:03:07.687
you start running out of space,

00:03:07.687 --> 00:03:10.380
you've already consumed
more than you need of it.

00:03:10.380 --> 00:03:11.913
And this is consistent with what we know

00:03:11.913 --> 00:03:13.584
from the law of demand.

00:03:13.584 --> 00:03:15.001
And the law of demand,

00:03:15.001 --> 00:03:16.951
every incremental amount of quantity,

00:03:16.951 --> 00:03:18.879
people are like well I already have some,

00:03:18.879 --> 00:03:19.924
and this might not be,

00:03:19.924 --> 00:03:21.317
the law of demand is not talking about

00:03:21.317 --> 00:03:22.315
just an individual,

00:03:22.315 --> 00:03:24.150
it's talking about a market,

00:03:24.150 --> 00:03:27.052
but the market as a whole
is made up of individuals,

00:03:27.052 --> 00:03:28.445
and if each individual is saying,

00:03:28.445 --> 00:03:31.557
hey you know that first
unit really matters to me,

00:03:31.557 --> 00:03:34.064
but the next unit, it's
nice, but not as good,

00:03:34.064 --> 00:03:35.318
so I'd pay less for it.

00:03:35.318 --> 00:03:36.294
And then the unit after that,

00:03:36.294 --> 00:03:37.780
it's nice, so I might pay less for it.

00:03:37.780 --> 00:03:39.591
And so if you aggregate
all those individuals,

00:03:39.591 --> 00:03:41.332
that's where that law
of demand comes from.

00:03:41.332 --> 00:03:42.586
These are consistent ideas,

00:03:42.586 --> 00:03:44.606
and that's why the demand curve,

00:03:44.606 --> 00:03:47.625
you are also, it is sloping down.

00:03:47.625 --> 00:03:49.854
Price is usually on this
axis instead of utility,

00:03:49.854 --> 00:03:54.127
and you could imagine price
as being a proxy for utility.

00:03:54.127 --> 00:03:58.097
And quantity of course is on
this axis right over here.

00:03:58.097 --> 00:04:00.698
So this is quantity of balls.

00:04:00.698 --> 00:04:03.066
So that's our marginal utility curve.

00:04:03.066 --> 00:04:05.179
What about total utility?

00:04:05.179 --> 00:04:06.012
So let me

00:04:10.566 --> 00:04:13.399
have a table here that
shows total utility.

00:04:13.399 --> 00:04:15.117
And total utility from marginal utility

00:04:15.117 --> 00:04:17.284
is pretty straightforward.

00:04:21.712 --> 00:04:23.128
All you do is say okay,

00:04:23.128 --> 00:04:24.614
well that first ball,

00:04:24.614 --> 00:04:27.215
when I have one ball, my
total utility is the same

00:04:27.215 --> 00:04:29.305
as my marginal utility.

00:04:29.305 --> 00:04:33.670
And so you're going to have
that same starting place

00:04:33.670 --> 00:04:36.433
at when your consumption
is just beginning.

00:04:36.433 --> 00:04:38.918
But then your total
utility from two balls,

00:04:38.918 --> 00:04:42.122
well I had 100 utility
units from the first ball,

00:04:42.122 --> 00:04:44.583
and then I get 80 more
from that second ball,

00:04:44.583 --> 00:04:46.302
so it's gonna be 180.

00:04:46.302 --> 00:04:49.802
So for two balls, my total utility is 180.

00:04:52.385 --> 00:04:54.545
All I'm doing is I just
added that to that.

00:04:54.545 --> 00:04:57.285
Now for three balls I
add that to that to that.

00:04:57.285 --> 00:05:00.628
I take 180 and I add the 60 extra

00:05:00.628 --> 00:05:02.765
utility units I get for that third ball,

00:05:02.765 --> 00:05:05.087
and now I'm at 240.

00:05:05.087 --> 00:05:08.670
So that third ball
gives me, gets me to 240

00:05:09.661 --> 00:05:10.938
right over there.

00:05:10.938 --> 00:05:13.608
Now the fourth ball, once again,

00:05:13.608 --> 00:05:16.534
I'm just gonna take 240
and add the incremental

00:05:16.534 --> 00:05:19.065
utility of that fourth
ball, the marginal utility

00:05:19.065 --> 00:05:20.551
of that fourth ball.

00:05:20.551 --> 00:05:22.711
That gets me to 280.

00:05:22.711 --> 00:05:24.628
So that gets me to 280,

00:05:26.147 --> 00:05:27.814
which is right over,

00:05:29.235 --> 00:05:32.068
let's see, 20, 30, 20, 40, 60, 80.

00:05:33.090 --> 00:05:36.109
So this is right over there.

00:05:36.109 --> 00:05:37.548
Now that fifth ball,

00:05:37.548 --> 00:05:40.265
I'm just gonna take the 280
and then the marginal utility

00:05:40.265 --> 00:05:43.075
of the fifth ball, add 20, gets me to 300.

00:05:43.075 --> 00:05:45.025
Fifth ball gets me to 300 which would be

00:05:45.025 --> 00:05:46.608
right around there.

00:05:47.672 --> 00:05:50.598
Now the sixth ball gave me no incremental,

00:05:50.598 --> 00:05:52.339
no marginal utility,

00:05:52.339 --> 00:05:55.056
so my total utility,
when I have six balls,

00:05:55.056 --> 00:05:56.031
stays the same.

00:05:56.031 --> 00:06:00.002
I'm indifferent as to whether
I have five or six balls.

00:06:00.002 --> 00:06:03.601
So the sixth ball, it is
now flat right over here.

00:06:03.601 --> 00:06:04.692
And now the seventh ball,

00:06:04.692 --> 00:06:06.271
I'm tired of these tennis balls.

00:06:06.271 --> 00:06:07.827
I'm being overwhelmed by them.

00:06:07.827 --> 00:06:09.569
I'm finding it stressful.

00:06:09.569 --> 00:06:12.657
And so it actually has a
negative marginal utility,

00:06:12.657 --> 00:06:14.073
and so my total utility,

00:06:14.073 --> 00:06:15.861
if someone forced me to have seven balls,

00:06:15.861 --> 00:06:18.694
my total utility would now go down by 20.

00:06:18.694 --> 00:06:22.456
And so my total utility now would be 280,

00:06:22.456 --> 00:06:23.709
right over here.

00:06:23.709 --> 00:06:25.428
And you could see the
marginal utilities here,

00:06:25.428 --> 00:06:27.355
if you just say look this is plus 80,

00:06:27.355 --> 00:06:29.027
this is plus 60,

00:06:29.027 --> 00:06:30.629
this is plus 40,

00:06:30.629 --> 00:06:32.022
this is plus 20,

00:06:32.022 --> 00:06:33.555
this is plus zero,

00:06:33.555 --> 00:06:35.505
and then this is minus 20.

00:06:35.505 --> 00:06:39.197
And so you see the numbers right over,

00:06:39.197 --> 00:06:40.776
right over there.

00:06:40.776 --> 00:06:43.145
Now this tennis ball example,

00:06:43.145 --> 00:06:44.398
this would be a discrete case.

00:06:44.398 --> 00:06:46.767
You wouldn't have 1/2 a tennis ball or

00:06:46.767 --> 00:06:49.344
pi tennis balls or something like that,

00:06:49.344 --> 00:06:51.225
but if we wanna speak in general terms,

00:06:51.225 --> 00:06:53.013
you could think about connecting the dots,

00:06:53.013 --> 00:06:55.637
if you had a more continuous example.

00:06:55.637 --> 00:06:58.516
And your total utility curve might look

00:06:58.516 --> 00:07:00.183
something like this.

00:07:01.210 --> 00:07:03.857
Now what's interesting is
right when you're beginning

00:07:03.857 --> 00:07:05.296
consumption you're
starting at the same place.

00:07:05.296 --> 00:07:06.388
Well that makes sense.

00:07:06.388 --> 00:07:08.199
Your first unit, you get marginal utility,

00:07:08.199 --> 00:07:10.591
that's gonna be your total utility.

00:07:10.591 --> 00:07:13.423
And this is upward sloping as long as

00:07:13.423 --> 00:07:15.722
you're getting some
positive marginal utility

00:07:15.722 --> 00:07:17.510
from each increment.

00:07:17.510 --> 00:07:20.761
So as long as my marginal
utilities were positive,

00:07:20.761 --> 00:07:22.011
well this graph

00:07:24.105 --> 00:07:25.544
is going to be increasing.

00:07:25.544 --> 00:07:27.518
But notice, because the marginal utilities

00:07:27.518 --> 00:07:30.281
are getting are decreasing
right over here,

00:07:30.281 --> 00:07:32.928
the rate of increase for total utility

00:07:32.928 --> 00:07:36.458
is decreasing, the slope
here is decreasing.

00:07:36.458 --> 00:07:38.362
You can view the marginal utility

00:07:38.362 --> 00:07:41.695
as the slope of the total utility curve.

00:07:43.006 --> 00:07:45.119
And then notice the total utility curve

00:07:45.119 --> 00:07:47.255
has a maximum value,

00:07:47.255 --> 00:07:50.343
it's starting to hit a maximum
value right over there,

00:07:50.343 --> 00:07:54.360
when the marginal utility
curve is hitting zero.

00:07:54.360 --> 00:07:56.357
Because beyond that point,

00:07:56.357 --> 00:07:58.540
where at least in this
example we had negative

00:07:58.540 --> 00:08:00.165
marginal utility.

00:08:00.165 --> 00:08:02.301
And so when you add that seventh unit,

00:08:02.301 --> 00:08:05.134
well that's gonna make your
total utility curve go down,

00:08:05.134 --> 00:08:06.690
and so you're gonna have a negative slope

00:08:06.690 --> 00:08:08.940
in this particular example.


Identifying tax incidence in a graph

WEBVTT
Kind: captions
Language: en

00:00:01.421 --> 00:00:03.618
- [Instructor] We are asked,
which of the following

00:00:03.618 --> 00:00:05.797
correctly identifies the areas of

00:00:05.797 --> 00:00:08.663
consumer surplus, producer surplus,

00:00:08.663 --> 00:00:11.330
tax revenue, and deadweight loss

00:00:12.364 --> 00:00:14.781
in this market after the tax?

00:00:15.695 --> 00:00:17.650
So pause this video, have a go at it.

00:00:17.650 --> 00:00:18.916
Even if you struggle with it

00:00:18.916 --> 00:00:20.803
it will make your brain more attuned

00:00:20.803 --> 00:00:22.826
to when we work through it together.

00:00:22.826 --> 00:00:24.698
All right, now let's work
through this together.

00:00:24.698 --> 00:00:26.149
And I just want to sort of understand

00:00:26.149 --> 00:00:27.631
what's going on here before I even try

00:00:27.631 --> 00:00:28.790
to answer their questions.

00:00:28.790 --> 00:00:29.981
So let's first take a look

00:00:29.981 --> 00:00:32.747
at what's going on before the tax.

00:00:32.747 --> 00:00:35.011
So before the tax, I have

00:00:35.011 --> 00:00:36.548
this supply curve

00:00:36.548 --> 00:00:38.692
right over here in blue.

00:00:38.692 --> 00:00:40.582
And I have this demand curve.

00:00:40.582 --> 00:00:42.632
Where they intersect gives us our

00:00:42.632 --> 00:00:44.319
equilibrium price.

00:00:44.319 --> 00:00:45.997
Right over here.

00:00:45.997 --> 00:00:48.568
And our equilibrium quantity

00:00:48.568 --> 00:00:50.605
right over there.

00:00:50.605 --> 00:00:52.853
And if we wanted to look at the

00:00:52.853 --> 00:00:54.340
consumer surplus

00:00:54.340 --> 00:00:56.913
it would be the area above

00:00:56.913 --> 00:00:58.609
this horizontal line.

00:00:58.609 --> 00:00:59.442
And, below

00:01:00.277 --> 00:01:01.306
the demand curve.

00:01:01.306 --> 00:01:04.343
So that is our original consumer surplus.

00:01:04.343 --> 00:01:06.600
And our original producer surplus is above

00:01:06.600 --> 00:01:07.810
the supply curve

00:01:07.810 --> 00:01:10.957
and below this price horizontal line.

00:01:10.957 --> 00:01:13.589
And so, the total surplus would be

00:01:13.589 --> 00:01:15.509
this entire triangle

00:01:15.509 --> 00:01:16.670
right over here.

00:01:16.670 --> 00:01:18.233
All before the tax.

00:01:18.233 --> 00:01:19.986
But they're not asking us before the tax

00:01:19.986 --> 00:01:21.916
they want us to figure out everything

00:01:21.916 --> 00:01:23.222
after the tax.

00:01:23.222 --> 00:01:25.655
So what happens to the tax?

00:01:25.655 --> 00:01:27.202
Well, if we assume it's

00:01:27.202 --> 00:01:28.410
a tax on

00:01:28.410 --> 00:01:29.561
each unit

00:01:29.561 --> 00:01:31.462
that is being supplied.

00:01:31.462 --> 00:01:33.549
The effect it has, and we see it here,

00:01:33.549 --> 00:01:34.568
they've drew it for us.

00:01:34.568 --> 00:01:37.692
Is it shifts the
effective supply curve up.

00:01:37.692 --> 00:01:39.307
And I say the effective one because

00:01:39.307 --> 00:01:41.409
that's the one that's going to affect

00:01:41.409 --> 00:01:44.405
the equilibrium price, or
the new equilibrium price.

00:01:44.405 --> 00:01:46.158
But as we'll see there's some nuances

00:01:46.158 --> 00:01:49.619
in terms of considering the surplus.

00:01:49.619 --> 00:01:51.365
So first, let's think about the consumer.

00:01:51.365 --> 00:01:53.108
Well, actually let me label

00:01:53.108 --> 00:01:54.716
the now price with the taxes.

00:01:54.716 --> 00:01:56.988
So, this is now the R equilibrium price

00:01:56.988 --> 00:01:58.315
where we have the taxes.

00:01:58.315 --> 00:02:00.596
It's where our demand
curve hasn't shifted.

00:02:00.596 --> 00:02:02.953
That's where the existing demand curve

00:02:02.953 --> 00:02:05.568
intersects with this new shifted

00:02:05.568 --> 00:02:08.015
supply with tax curve.

00:02:08.015 --> 00:02:09.753
And similarly, that point of intersection

00:02:09.753 --> 00:02:11.814
also tells us our quantity

00:02:11.814 --> 00:02:13.164
with the taxes.

00:02:13.164 --> 00:02:15.319
Now, now that we've understood everything,

00:02:15.319 --> 00:02:16.437
or hopefully we have,

00:02:16.437 --> 00:02:18.563
let's think about the various surpluses

00:02:18.563 --> 00:02:20.306
and the deadly weight losses

00:02:20.306 --> 00:02:21.828
and the tax revenues.

00:02:21.828 --> 00:02:25.279
So first, let's think
about the consumer surplus.

00:02:25.279 --> 00:02:27.537
Well, the consumer surplus is going to be

00:02:27.537 --> 00:02:29.428
the region above our new

00:02:29.428 --> 00:02:30.838
horizontal price.

00:02:30.838 --> 00:02:32.951
And below the demand curve.

00:02:32.951 --> 00:02:34.951
So that is this region R

00:02:35.790 --> 00:02:37.059
right over here.

00:02:37.059 --> 00:02:39.842
That still, you have this
consumer right over here

00:02:39.842 --> 00:02:41.761
who was willing to pay a lot

00:02:41.761 --> 00:02:43.205
but still has to pay less than that

00:02:43.205 --> 00:02:44.224
even with the taxes.

00:02:44.224 --> 00:02:45.888
So they're getting this benefit

00:02:45.888 --> 00:02:48.481
more than they would have needed

00:02:48.481 --> 00:02:50.716
in order, it would have
been willing to pay more

00:02:50.716 --> 00:02:52.317
than the tax, and so they're getting

00:02:52.317 --> 00:02:53.402
this surplus.

00:02:53.402 --> 00:02:55.433
And so if you look at the
entire market right now

00:02:55.433 --> 00:02:57.822
the total consumer surplus after the tax

00:02:57.822 --> 00:02:58.819
is R.

00:02:58.819 --> 00:03:00.199
R is equal to

00:03:00.199 --> 00:03:01.391
consumer surplus.

00:03:01.391 --> 00:03:02.875
And this is all after

00:03:02.875 --> 00:03:03.910
the taxes.

00:03:03.910 --> 00:03:05.365
Consumer surplus.

00:03:05.365 --> 00:03:08.535
Now, what about the producer surplus?

00:03:08.535 --> 00:03:10.876
Well, if we weren't dealing with the tax

00:03:10.876 --> 00:03:12.887
we would just look above the supply curve

00:03:12.887 --> 00:03:15.875
and below this equilibrium
price line and say

00:03:15.875 --> 00:03:17.320
hey, maybe it's that area.

00:03:17.320 --> 00:03:19.040
But remember what's happening from the

00:03:19.040 --> 00:03:20.232
producers point of view.

00:03:20.232 --> 00:03:22.127
The producer does not see

00:03:22.127 --> 00:03:25.280
this new increased price at this quantity.

00:03:25.280 --> 00:03:27.219
The producer, remember,
they don't get to keep

00:03:27.219 --> 00:03:28.340
the tax revenue.

00:03:28.340 --> 00:03:30.003
That, they have to give to the government.

00:03:30.003 --> 00:03:31.087
So the producer

00:03:31.087 --> 00:03:32.400
actually this is the price

00:03:32.400 --> 00:03:33.663
that the producer sees.

00:03:33.663 --> 00:03:34.942
So you can see this is

00:03:34.942 --> 00:03:36.673
this is what

00:03:36.673 --> 00:03:37.840
what producers

00:03:39.414 --> 00:03:41.355
what producers get

00:03:41.355 --> 00:03:42.890
after taxes.

00:03:42.890 --> 00:03:44.393
After

00:03:44.393 --> 00:03:46.305
taxes, or I say net of taxes.

00:03:46.305 --> 00:03:47.572
May be a better way

00:03:47.572 --> 00:03:48.578
to think about it.

00:03:48.578 --> 00:03:49.696
Net

00:03:49.696 --> 00:03:51.069
of taxes.

00:03:51.069 --> 00:03:53.319
And so the producer surplus

00:03:54.914 --> 00:03:57.358
is going to be the area

00:03:57.358 --> 00:03:59.413
below what they're getting

00:03:59.413 --> 00:04:01.207
from the market, net of taxes.

00:04:01.207 --> 00:04:02.291
And above

00:04:02.291 --> 00:04:03.320
what they

00:04:03.320 --> 00:04:04.716
the price is at which

00:04:04.716 --> 00:04:06.488
they were willing to
produce various quantities.

00:04:06.488 --> 00:04:08.245
And so the producer surplus is

00:04:08.245 --> 00:04:09.789
this area of V over here.

00:04:09.789 --> 00:04:12.471
So, V is equal to the producer.

00:04:12.471 --> 00:04:13.956
Producer

00:04:13.956 --> 00:04:15.012
surplus.

00:04:15.012 --> 00:04:17.018
And now, what about

00:04:17.018 --> 00:04:18.412
the tax revenue?

00:04:18.412 --> 00:04:21.693
Well, the tax revenue is, is essentially

00:04:21.693 --> 00:04:23.897
going to be all of this other part

00:04:23.897 --> 00:04:24.919
of the total surplus.

00:04:24.919 --> 00:04:27.077
This is what goes to the government.

00:04:27.077 --> 00:04:29.108
The difference between these two.

00:04:29.108 --> 00:04:30.441
If the producers

00:04:31.461 --> 00:04:33.514
did not have to give that
tax to the government

00:04:33.514 --> 00:04:35.806
then they wouldn't have been
able to keep all of this.

00:04:35.806 --> 00:04:37.079
But this, right over here.

00:04:37.079 --> 00:04:38.834
Let me do this in a different color.

00:04:38.834 --> 00:04:41.385
So this region, right over here,

00:04:41.385 --> 00:04:45.323
is what the government is able to keep.

00:04:45.323 --> 00:04:46.869
Notice, it's this quantity

00:04:46.869 --> 00:04:50.457
and they get this much
tax per unit quantity.

00:04:50.457 --> 00:04:51.884
And so this area

00:04:51.884 --> 00:04:55.662
is the government, is the
revenue to the government.

00:04:55.662 --> 00:04:57.662
So, S plus U is equal to

00:04:58.774 --> 00:05:00.388
tax revenue.

00:05:00.388 --> 00:05:01.391
Tax

00:05:01.391 --> 00:05:02.541
revenue.

00:05:02.541 --> 00:05:04.292
And then last but not least,

00:05:04.292 --> 00:05:06.985
what about the deadweight loss?

00:05:06.985 --> 00:05:08.895
Well remember, the deadweight loss

00:05:08.895 --> 00:05:11.505
is the difference between the original

00:05:11.505 --> 00:05:12.835
the total surplus.

00:05:12.835 --> 00:05:15.393
When we just let things
naturally go to equilibrium.

00:05:15.393 --> 00:05:16.811
The difference between that

00:05:16.811 --> 00:05:18.784
and now our new total surplus,

00:05:18.784 --> 00:05:20.228
which is now lower because

00:05:20.228 --> 00:05:21.576
we have not allowed the market

00:05:21.576 --> 00:05:23.361
to function in a very natural way

00:05:23.361 --> 00:05:25.099
because of this tax on it.

00:05:25.099 --> 00:05:26.557
Well, as we said before,

00:05:26.557 --> 00:05:27.897
the original total surplus was

00:05:27.897 --> 00:05:29.472
this entire triangle.

00:05:29.472 --> 00:05:31.812
Now the total surplus is this trapezoid

00:05:31.812 --> 00:05:34.019
that's the sum of all of these areas.

00:05:34.019 --> 00:05:35.452
And so what we lost

00:05:35.452 --> 00:05:37.522
is this area right over here.

00:05:37.522 --> 00:05:39.833
So that is the deadweight loss.

00:05:39.833 --> 00:05:40.750
So T plus W

00:05:41.617 --> 00:05:43.236
is equal to the

00:05:43.236 --> 00:05:44.569
deadweight loss.

00:05:45.538 --> 00:05:46.600
And we're done.