WEBVTT

00:02.430 --> 00:04.850
Prof: All right,
well, today I'm going to talk

00:04.852 --> 00:06.252
about Social Security again.

00:06.250 --> 00:09.350
There's going to be one more
discussion of Social Security

00:09.345 --> 00:09.775
later.

00:09.780 --> 00:12.930
I'm going to defer most of my
plan until later,

00:12.930 --> 00:16.560
but I want to finish the
discussion so that we totally

00:16.560 --> 00:18.410
understand the subject.

00:18.410 --> 00:22.140
It'll also allow me talk about
demography and introduce one of

00:22.135 --> 00:25.615
the most famous models in
economics called the Overlapping

00:25.617 --> 00:26.897
Generation Model.

00:26.900 --> 00:32.470
So in the 1940s someone named
Maurice Allais,

00:32.466 --> 00:38.156
a French economist,
introduced the Overlapping

00:38.159 --> 00:42.839
Generations Model into
economics.

00:42.840 --> 00:49.900
He wrote it in French and it
was sort of rediscovered by

00:49.900 --> 00:53.110
Samuelson in the 1950s.

00:53.110 --> 00:55.610
I'm not sure whether Samuelson
had read Allais.

00:55.610 --> 00:59.510
I think Samuelson may well have
read Allais, but anyway

00:59.514 --> 01:03.134
Samuelson--so these were 1947,
something like that,

01:03.128 --> 01:06.308
1958 in which Samuelson
rediscovered it.

01:06.310 --> 01:10.720
And you'll see it's a very
basic thought and it seemed at

01:10.721 --> 01:15.291
first to challenge everything
that we've learned so far.

01:15.290 --> 01:18.880
So the idea of the Overlapping
Generations Model is that time

01:18.882 --> 01:22.532
doesn't have a beginning and an
end like we've assumed so far,

01:22.533 --> 01:24.273
time might go on forever.

01:24.269 --> 01:27.519
Now, whether or not you believe
time--

01:27.519 --> 01:30.049
whether there's scientific
proof that time goes on forever

01:30.051 --> 01:32.851
or scientific proof that the
universe has to come to an end,

01:32.849 --> 01:35.179
let's face it,
many of our institutions

01:35.176 --> 01:37.376
presume that time goes on
forever.

01:37.379 --> 01:42.499
The chief most important among
them is Social Security which

01:42.497 --> 01:47.267
we'll see is the easiest thing
to, the model's design to

01:47.268 --> 01:48.568
understand.

01:48.569 --> 01:54.929
The idea of Social Security is
the pay as you go Social

01:54.925 --> 01:56.215
Security.

01:56.220 --> 02:00.530
The idea of Frances Perkins was
that every young generation was

02:00.534 --> 02:04.064
going to give money to the old,
but they shouldn't worry so

02:04.058 --> 02:06.328
much about it because when they
got old the next young

02:06.334 --> 02:07.884
generation would give them
money.

02:07.879 --> 02:10.959
Obviously if you thought time
was going to come to an end the

02:10.956 --> 02:13.706
last young generation,
knowing that they were the last

02:13.705 --> 02:15.685
generation,
would refuse to give money to

02:15.692 --> 02:18.492
the old because they weren't
going to get anything back when

02:18.485 --> 02:19.285
they were old.

02:19.288 --> 02:21.788
But then the second to last
generation knowing that when

02:21.789 --> 02:24.019
they got old that they'd get
nothing from the last

02:24.016 --> 02:27.196
generation's young they wouldn't
give anything either to the old,

02:27.199 --> 02:30.089
and working backwards like that
if everybody's rational and it's

02:30.086 --> 02:32.786
common knowledge that the world
is going to end nobody would

02:32.792 --> 02:35.132
ever participate in the Social
Security scheme.

02:35.128 --> 02:38.668
So it's clear that there's some
thought that the world might

02:38.669 --> 02:41.849
end, or at least there's a
thought that it's not worth

02:41.848 --> 02:44.068
bothering about the world
ending.

02:44.068 --> 02:49.428
So the Overlapping Generations
Model is meant to take that idea

02:49.434 --> 02:54.284
extremely seriously and imagine
life going on forever.

02:54.280 --> 02:58.280
So let's take the simplest
example where there's a

02:58.277 --> 03:01.867
generation that
begins--generations last when

03:01.867 --> 03:03.987
they're young and old.

03:03.990 --> 03:09.610
So let's say we're at time 1
here, and there's a generation

03:09.610 --> 03:13.780
that's young and a generation
that's old.

03:13.780 --> 03:15.720
Maybe I'll write it a little
bit lower.

03:15.719 --> 03:20.109
Sorry about that.

03:20.110 --> 03:24.090
So there's an old generation
and a young generation and the

03:24.092 --> 03:26.772
endowment of the old generation
is 1.

03:26.770 --> 03:30.010
The young generation has 3 when
it's young, 1 when it's old,

03:30.014 --> 03:31.884
3 when it's young,
1 when it's old,

03:31.883 --> 03:34.033
3 when it's young,
1 when it's old.

03:34.030 --> 03:37.820
So when you're young you have 3
apples.

03:37.818 --> 03:39.458
When you're old you have 1
apple.

03:39.460 --> 03:41.840
The next generation when it's
young has 3 apples.

03:41.840 --> 03:45.520
When it's old it has 1 apple
and so on forever.

03:45.520 --> 03:52.840
So this'll be T = 1 here,
2 here, 3 here,

03:52.842 --> 03:56.322
4 here, etcetera.

03:56.319 --> 03:59.429
So it goes on forever like that.

03:59.430 --> 04:02.790
Now, what did Allais and
Samuelson both basically say?

04:02.788 --> 04:05.448
They both basically said,
look, everybody when they're

04:05.451 --> 04:07.011
young is incredibly well off.

04:07.009 --> 04:07.569
They're working.

04:07.569 --> 04:08.559
They're productive.

04:08.560 --> 04:13.580
When they're old and retired
and feeble they don't have very

04:13.578 --> 04:15.958
much, but what can you do?

04:15.960 --> 04:17.540
Where can you trade?

04:17.540 --> 04:22.120
According to Samuelson what
does the old have to trade?

04:22.120 --> 04:28.150
It doesn't look like there's
any trade that can take place.

04:28.149 --> 04:33.579
So it seems like it would be
very helpful if the young would

04:33.584 --> 04:37.504
give the old something,
and when they got old the next

04:37.495 --> 04:39.765
generations young could give
them something.

04:39.769 --> 04:43.309
So the young could constantly
be making gifts to the old.

04:43.310 --> 04:47.000
That was Allais and Samuelson's
idea and it's very closely

04:47.000 --> 04:48.880
related to Social Security.

04:48.879 --> 04:52.959
So Samuelson got a little
carried away with his idea and

04:52.961 --> 04:57.271
he said that Social Security was
the greatest and only true

04:57.267 --> 05:01.347
beneficial Ponzi scheme ever
invented because in a Ponzi

05:01.350 --> 05:05.800
scheme,
this has gotten a lot of

05:05.803 --> 05:12.353
attention lately thanks to our
famous Madoff.

05:12.350 --> 05:17.420
So a Ponzi scheme is basically
an investment strategy where you

05:17.420 --> 05:20.610
take the money that people give
you,

05:20.610 --> 05:24.320
and you buy yachts with it,
and then when they ask for

05:24.317 --> 05:28.647
their money back you tell them
that you've gotten great returns

05:28.653 --> 05:33.133
and you just hand them money
that new people have given you.

05:33.129 --> 05:34.879
So they think you've gotten
great returns.

05:34.879 --> 05:37.819
And when that second generation
of people wants their money back

05:37.824 --> 05:39.494
you tell them,
well, you've invested it

05:39.485 --> 05:41.105
brilliantly,
you've gotten great returns,

05:41.112 --> 05:43.482
but all you're doing is giving
them the money that the third

05:43.476 --> 05:45.996
generation is giving you,
and you keep going like that

05:45.997 --> 05:48.907
until finally you owe so much
money you can't find new people

05:48.910 --> 05:51.870
fast enough to pay the people
off and then everybody discovers

05:51.870 --> 05:53.910
the Ponzi scheme and it all
unravels.

05:53.910 --> 05:57.640
And the people at the beginning
have made out very well and the

05:57.644 --> 06:00.834
people at end who,
you know, the second to last

06:00.826 --> 06:04.656
generation they've lost all
their money and then lawsuits

06:04.661 --> 06:05.621
accumulate.

06:05.620 --> 06:10.080
And it's quite interesting that
in the Ponzi scheme the very

06:10.084 --> 06:14.784
first generations that benefited
are not free because the whole

06:14.778 --> 06:16.518
thing was a scheme.

06:16.519 --> 06:18.899
The guy Madoff running it knew
from the beginning what was

06:18.898 --> 06:19.648
going to happen.

06:19.649 --> 06:22.239
And so those first generation
of people, there's no reason why

06:22.242 --> 06:24.072
they deserve to make their great
returns.

06:24.069 --> 06:25.709
They benefited from the Ponzi
scheme,

06:25.709 --> 06:29.419
so the last generations suing
Madoff are effectively suing the

06:29.420 --> 06:32.220
first people as well,
and so we'll see how the courts

06:32.223 --> 06:32.703
decide it.

06:32.699 --> 06:35.759
But often the people who get
out of the Ponzi scheme early

06:35.759 --> 06:38.389
still are held liable and the
money is taken back,

06:38.391 --> 06:40.701
so we'll see what happens in
this case.

06:40.699 --> 06:43.989
But anyway, so obviously Ponzi
schemes are terrible ideas in

06:43.992 --> 06:44.552
general.

06:44.550 --> 06:47.450
But Samuelson said well,
when life is going on forever

06:47.446 --> 06:50.176
there might not have to be an
end to the scheme.

06:50.180 --> 06:51.390
It just keeps going.

06:51.389 --> 06:52.529
This guy gives to this guy.

06:52.529 --> 06:53.619
This guy gives to this guy.

06:53.620 --> 06:56.130
There's no reason for the Ponzi
scheme to end if you really

06:56.134 --> 06:58.264
think that the world's going to
go on forever,

06:58.259 --> 07:01.959
and therefore Social Security
is a great Ponzi scheme which is

07:01.963 --> 07:03.303
actually beneficial.

07:03.300 --> 07:06.650
So Samuelson even wrote this as
a journalist for

07:06.649 --> 07:09.359
Newsweek and there's
many--

07:09.360 --> 07:12.060
I happened to be a little boy
when he was writing this stuff

07:12.057 --> 07:14.707
and I remember some of the
articles and I've gone and found

07:14.708 --> 07:15.118
them.

07:15.120 --> 07:19.260
And so he describes the
benefits of Social Security as a

07:19.259 --> 07:20.389
Ponzi scheme.

07:20.389 --> 07:27.769
So this didn't turn out to be
quite right, but it certainly

07:27.771 --> 07:30.191
sounds plausible.

07:30.189 --> 07:33.569
Another thing he said was he
said that in the Social

07:33.565 --> 07:36.065
Security--
money, you could think of as a

07:36.065 --> 07:39.025
Ponzi scheme,
money too, because you have

07:39.029 --> 07:43.699
worthless pieces of paper,
but you're willing to hold them

07:43.699 --> 07:46.639
when you're young,
you'll accept them for goods

07:46.641 --> 07:49.661
because when you get old you can
find the next guy who's willing

07:49.663 --> 07:52.673
to give up goods for your money,
and that guy is willing to take

07:52.665 --> 07:55.165
the money for it because when he
gets old he can find the next

07:55.173 --> 07:57.893
generation's young who's willing
to give up good for his money.

07:57.889 --> 07:59.969
So the money,
which is a worthless piece of

07:59.973 --> 08:02.073
paper,
never gets exposed as being

08:02.069 --> 08:05.739
worthless because there's always
another generation around to

08:05.738 --> 08:09.588
take it who thinks they're going
to be able to use it later.

08:09.588 --> 08:14.668
So these are fascinating topics
that Samuelson discussed,

08:14.672 --> 08:19.122
but I don't want to discuss
them in this class.

08:19.120 --> 08:20.890
I want to discuss Social
Security,

08:20.889 --> 08:23.599
and so I'm going to do a
variant of the model that

08:23.596 --> 08:26.896
Samuelson never thought about,
which I think is a much more

08:26.899 --> 08:27.799
realistic model.

08:27.800 --> 08:32.740
So I'm going to do overlapping
generations with land,

08:32.740 --> 08:38.150
and you'll see that in this
model I'm going to add land to

08:38.154 --> 08:38.824
it.

08:38.820 --> 08:41.530
It's, I think,
a more interesting model and

08:41.529 --> 08:45.209
I'm not going to discuss the
paradoxes of infinity because

08:45.206 --> 08:48.346
once you put land,
even though time goes on

08:48.347 --> 08:50.627
forever the paradoxes disappear.

08:50.629 --> 08:53.659
So rather than spending all the
time on the paradoxes,

08:53.658 --> 08:56.048
and how they come about,
and do they make sense,

08:56.048 --> 08:58.958
I'm just going to add land from
the beginning and it will

08:58.956 --> 09:01.756
recapitulate in a nice way
almost everything we've done

09:01.760 --> 09:04.410
this semester and there won't be
any paradoxes.

09:04.409 --> 09:06.599
So what do I mean by land?

09:06.600 --> 09:14.080
I mean suppose that land
produces 1, so this is land

09:14.076 --> 09:19.056
output, produces 1 every period.

09:19.058 --> 09:22.278
So there's another output
called apples that just,

09:22.282 --> 09:25.242
you know, a tree that's going
to live forever,

09:25.241 --> 09:28.861
let's call it land,
produces 1 every single period.

09:28.860 --> 09:35.710
So here are the periods and
this is what's happening in

09:35.706 --> 09:37.606
every period.

09:37.610 --> 09:41.640
Now, land seems to make the
situation much more complicated,

09:41.643 --> 09:45.683
but in fact it will turn out
that we can analyze this pretty

09:45.677 --> 09:46.427
easily.

09:46.428 --> 09:52.048
So let me summarize,
again, the model.

09:52.048 --> 09:55.698
The model is that every
generation has 1 agent or a

09:55.702 --> 09:58.482
million identical agents,
let's say.

09:58.480 --> 10:07.670
Every generation has
endowments, so every generation

10:07.667 --> 10:10.907
t has endowment.

10:10.908 --> 10:17.348
It's generation t so it's an
endowment at time t and at time

10:17.352 --> 10:21.992
t 1 equals (3,
1) and let's say they all have

10:21.985 --> 10:26.425
utility and the utility of every
generation t,

10:26.428 --> 10:35.838
which only depends on what they
consume when they're young and

10:35.842 --> 10:42.792
old let's say is log
x_t log x_t

10:42.788 --> 10:44.638
1.

10:44.639 --> 10:47.419
So everybody cares about
consumption when they're young,

10:47.418 --> 10:49.938
consumption when they're old,
they don't care about

10:49.943 --> 10:51.513
consumption any other time.

10:51.509 --> 10:53.289
They begin with 3 apples when
they're young.

10:53.288 --> 10:55.578
They know they're going to have
1 apple when they're old.

10:55.580 --> 11:00.500
Everybody's like that for
generation t greater than or

11:00.498 --> 11:04.488
equal to 1, but generation 0
just has U^(0),

11:04.488 --> 11:07.178
so I can call that U^(t).

11:07.178 --> 11:15.198
Generation 0 only cares about
consumption when old and that's

11:15.198 --> 11:18.138
that guy at the top.

11:18.139 --> 11:21.449
But I also have to talk about
the land.

11:21.450 --> 11:29.030
Generation 0 owns the land.

11:29.028 --> 11:35.768
So that's the economy,
very simple economy,

11:35.769 --> 11:38.889
but it looks much more
complicated than anything we've

11:38.886 --> 11:40.956
done before,
but it will turn out not to be,

11:40.956 --> 11:42.216
but it looks it at first
glance.

11:42.220 --> 11:45.400
So every generation has 3
apples when young,

11:45.399 --> 11:49.859
1 apple when old except the
very first generation which has

11:49.857 --> 11:53.237
land in addition to his 1 apple
when old,

11:53.240 --> 11:58.660
and that land produces 1 apple
forever.

11:58.658 --> 12:01.678
So we have to figure out what
equilibrium is and then we have

12:01.679 --> 12:03.139
to look at Social Security.

12:03.139 --> 12:06.819
And by doing this we're going
to understand Social Security

12:06.822 --> 12:08.922
much better than we did before.

12:08.918 --> 12:13.118
So are there any questions
about this, what's going on?

12:13.120 --> 12:15.980
Then I'm going to try and write
down what equilibrium is and

12:15.980 --> 12:18.020
then solve it,
and then we're going to talk

12:18.018 --> 12:19.278
about Social Security.

12:19.279 --> 12:20.009
Yep?

12:20.009 --> 12:23.049
Student: Is U not
supposed to be

12:23.048 --> 12:25.288
>?

12:25.288 --> 12:28.418
Prof: Oh,
well if you only can eat 1 good

12:28.418 --> 12:32.478
if I put log x_1 here
it would be the same thing.

12:32.480 --> 12:36.260
Remember if I take a monotonic
transformation,

12:36.259 --> 12:38.629
if I double the utility or take
the utility,

12:38.629 --> 12:41.709
e to the utility like that,
which is just equal to

12:41.708 --> 12:44.598
x_1 it describes the
same utility.

12:44.600 --> 12:46.240
The guy's not trading anything
off.

12:46.240 --> 12:48.210
There's only 1 good,
so more of the good is better

12:48.207 --> 12:48.607
for him.

12:48.610 --> 12:51.250
It doesn't matter if we call it
log x or x_1 is the

12:51.246 --> 12:53.046
same thing, but that's a good
question.

12:53.048 --> 12:57.178
Let's call it log
x_1,

12:57.181 --> 12:59.981
make him symmetric.

12:59.980 --> 13:02.440
All right, well,
how would we define

13:02.443 --> 13:03.433
equilibrium?

13:03.428 --> 13:05.808
So there's financial
equilibrium, and then we're

13:05.812 --> 13:07.642
going to see if we can solve
this.

13:07.639 --> 13:13.029
So what's happening in
financial equilibrium?

13:13.028 --> 13:15.398
Well, it's kind of interesting
here.

13:15.399 --> 13:19.749
There's going to have to be a
price of goods every period

13:19.746 --> 13:20.986
q_t.

13:20.990 --> 13:23.710
That's the contemporaneous
price of apples.

13:23.710 --> 13:27.010
There's going to be the price
of land every period,

13:27.014 --> 13:29.334
pi, let's call it
pi_t.

13:29.330 --> 13:34.040
So this is apple price.

13:34.038 --> 13:45.608
So these are contemporaneous
prices.

13:45.610 --> 13:52.550
With contemporaneous apple
price, land price,

13:52.551 --> 13:56.181
what else do we need?

13:56.178 --> 14:00.928
Well, we have to decide what
everybody's going to consume

14:00.927 --> 14:04.397
every period,
so generation t what they're

14:04.403 --> 14:08.223
going to consume when young and
when old.

14:08.220 --> 14:11.700
Then there's generation 0,
what they're going to consume

14:11.695 --> 14:12.385
when old.

14:12.389 --> 14:22.529
What else do I need to describe
equilibrium?

14:22.529 --> 14:25.209
That's probably it.

14:25.210 --> 14:31.820
And so what's the budget set
everybody's going to face?

14:31.820 --> 14:37.390
A budget set for t greater than
or equal to 1 is the set of

14:37.386 --> 14:43.046
all--let's call it young
consumption and old consumption.

14:43.048 --> 14:46.748
So generation t because it's
going to consume something when

14:46.748 --> 14:49.128
young and when old,
such that, what?

14:49.129 --> 14:50.599
What's the budget constraint?

14:50.600 --> 14:55.600
Well, when they're young if
they want to consume goods they

14:55.604 --> 14:59.664
have to spend q_t to
consume goods.

14:59.659 --> 15:03.609
So this is young, call that Y.

15:03.610 --> 15:07.040
And when they're old they're
going to have to consume,

15:07.038 --> 15:10.468
sorry, when they're young
they're consuming--what else

15:10.466 --> 15:12.146
would they want to do?

15:12.149 --> 15:16.749
They might want to hold land so
we could call that

15:16.754 --> 15:22.494
pi_t and I better add
a theta here for their holding

15:22.488 --> 15:25.278
of land,
pi_t theta,

15:25.283 --> 15:27.683
that's how much land they hold.

15:27.679 --> 15:28.749
Remember how we did this?

15:28.750 --> 15:31.760
And then what have they got?

15:31.759 --> 15:36.359
We'll they've got their
endowment, time t.

15:36.360 --> 15:38.500
This is time t, let's say.

15:38.500 --> 15:39.680
This is generation t.

15:39.678 --> 15:44.638
So their endowment is going to
be e^(t)_t,

15:44.644 --> 15:48.254
but that's 3,
so I might as well write

15:48.245 --> 15:51.355
e^(t)_t just as 3.

15:51.360 --> 15:57.830
And what else have they got?

15:57.830 --> 16:01.100
Nothing?

16:01.100 --> 16:04.430
Everybody comes into the world
with just apples when young and

16:04.426 --> 16:06.876
apples when old,
so when they're young they've

16:06.879 --> 16:08.569
got 3 apples they can sell.

16:08.570 --> 16:11.720
They can consume something,
so 3 - q.

16:11.720 --> 16:14.810
The stuff they don't consume
they sell and they can buy land

16:14.806 --> 16:15.326
with it.

16:15.330 --> 16:22.760
Ah, god all this time this
never happened.

16:22.759 --> 16:32.399
Sorry about that.

16:32.399 --> 16:34.289
And when they're old what can
they do?

16:34.288 --> 16:37.668
Well, when they're old at
q_t 1,

16:37.666 --> 16:40.876
times Z now,
are they going to bother to

16:40.876 --> 16:43.756
hold the land when they're old?

16:43.759 --> 16:46.549
No, because they're going to be
dead and they don't care about

16:46.551 --> 16:47.331
their children.

16:47.330 --> 16:49.240
All they care about is eating
as much as they can.

16:49.240 --> 16:52.860
So they're going to sell all
their land, so that's got to be

16:52.859 --> 16:54.699
less than or equal to,
what?

16:54.700 --> 16:58.160
And so here's the--what are
they going to get when they're

16:58.155 --> 16:58.515
old?

16:58.519 --> 17:03.539
Well, they have q_t 1
when they're old,

17:03.544 --> 17:07.004
and their endowment,
of 1 what?

17:07.000 --> 17:14.170
They can sell their land
pi_t 1 times theta.

17:14.170 --> 17:16.610
Whatever they bought the first
time they can now sell when

17:16.609 --> 17:17.209
they're old.

17:17.210 --> 17:28.110
Plus what else do they have?

17:28.108 --> 17:30.198
So one last term,
what else is it?

17:30.200 --> 17:31.260
So see what they do.

17:31.259 --> 17:33.069
Why would you buy land?

17:33.068 --> 17:35.768
Well, because when you're young
you're so rich you don't want to

17:35.767 --> 17:37.477
consume everything when you're
young,

17:37.480 --> 17:39.430
so instead of consuming your
whole 3,

17:39.430 --> 17:40.410
you consume less.

17:40.410 --> 17:42.610
You buy the land because the
land's going to be worth

17:42.613 --> 17:43.633
something next period.

17:43.630 --> 17:47.450
So what is it going to give for
you next period?

17:47.450 --> 17:50.410
What do you get next period
from the land?

17:50.410 --> 17:53.640
Well, if you own the land you
get what?

17:53.640 --> 17:56.220
You get the dividend.

17:56.220 --> 17:59.380
So the dividend we have to
multiply by the price,

17:59.377 --> 18:02.337
which on one of the early
classes I forgot.

18:02.338 --> 18:04.808
And the dividend is 1,
that's the dividend,

18:04.806 --> 18:06.916
but how many dividends do you
get?

18:06.920 --> 18:07.580
How many apples?

18:07.578 --> 18:09.928
It depends on how much of the
land you had.

18:09.930 --> 18:12.860
So if you had theta units of
the land you get,

18:12.864 --> 18:16.914
you know, if you had 3 acres of
land you get 3 apples which you

18:16.905 --> 18:19.575
can sell for a price q_t
1.

18:19.578 --> 18:23.388
You also still have the 3 acres
of land which you can sell off

18:23.394 --> 18:24.524
when you're old.

18:24.519 --> 18:27.909
So that's the revenue you get
by selling off the land and you

18:27.910 --> 18:30.170
also sell off some of your
endowment,

18:30.170 --> 18:32.540
maybe, and that's how you can
buy when you're old.

18:32.538 --> 18:36.048
So that's what the budget set
is of the young,

18:36.051 --> 18:37.771
of every generation.

18:37.769 --> 18:44.679
And the budget set for
generation t=0 is simply

18:44.676 --> 18:48.576
x_1,
is simply Z,

18:48.580 --> 18:56.390
we'll call it Z such that what
does this guy do?

18:56.390 --> 19:00.430
Well, q_1Z has to be
less than or equal to,

19:00.426 --> 19:01.976
what does he have?

19:01.980 --> 19:07.050
q_1 times 1,
plus he's got all the land.

19:07.049 --> 19:10.599
So he's got 1 acre of land.

19:10.598 --> 19:16.208
That's all the land there was,
so he's got pi

19:16.210 --> 19:19.270
times--pi_1.

19:19.269 --> 19:22.449
He's got all the land,
so I've normalized the land to

19:22.453 --> 19:23.193
be 1 acre.

19:23.190 --> 19:29.580
So pi 1 times all land.

19:29.579 --> 19:34.669
That's what that guy can do.

19:34.670 --> 19:44.140
So equilibrium is,
x_t is best for

19:44.143 --> 19:55.163
generation t in budget set t and
x_1,

19:55.160 --> 20:02.380
so this is this and theta,
and x_1--

20:02.380 --> 20:03.130
did I write theta?

20:03.130 --> 20:06.240
Oh, I forgot to write theta in
the definition of equilibrium

20:06.238 --> 20:09.008
here,
so I have to write a theta t

20:09.006 --> 20:14.116
there also having to keep track
of how much land they're going

20:14.117 --> 20:15.037
to have.

20:15.039 --> 20:18.909
This is t = 1 to infinity.

20:18.910 --> 20:22.040
So the equilibrium is what are
the prices every period of

20:22.041 --> 20:23.051
apples and land?

20:23.048 --> 20:27.328
What does every generation do
in terms of their consumption

20:27.327 --> 20:31.747
and how much land they hold and
how much does that very first

20:31.752 --> 20:33.452
generation consume.

20:33.450 --> 20:36.070
It's obvious they're going to
sell all their land to consume

20:36.071 --> 20:37.051
as much as they can.

20:37.048 --> 20:42.608
So the budget set,
so x_1 solves.

20:42.608 --> 20:50.218
So Z = x_1 and y Z
theta equals that,

20:50.220 --> 20:52.800
best for generation t in this
budget set,

20:52.798 --> 21:03.548
and Z = x_1 is best
for generation 0 in this budget

21:03.554 --> 21:04.634
set.

21:04.630 --> 21:07.840
So to say it in words it's very
simple in words,

21:07.838 --> 21:09.928
and then we have this
mathematics and it looks

21:09.933 --> 21:12.733
complicated but we're just going
to say it's going to be very

21:12.727 --> 21:15.517
short to solve it even though it
looks very complicated.

21:15.519 --> 21:17.969
So the problem is this.

21:17.970 --> 21:21.060
We've got generations who are
rich when young,

21:21.057 --> 21:23.597
poor when old,
there's land that lasts

21:23.596 --> 21:24.416
forever.

21:24.420 --> 21:27.580
The only way people can save is
by holding the land.

21:27.579 --> 21:28.709
That's like holding stock.

21:28.710 --> 21:30.150
That's holding something real.

21:30.150 --> 21:33.020
So when they're young they're
going to take some of their

21:33.023 --> 21:35.103
extra endowment,
because they're so rich when

21:35.104 --> 21:36.514
young,
they've got 3 when young,

21:36.513 --> 21:38.313
and they're going to use it to
buy land.

21:38.308 --> 21:42.278
And when they get old they're
going to sell the land,

21:42.279 --> 21:44.369
and eat the endowment from the
land,

21:44.368 --> 21:47.618
the dividend from the land,
and sell the land and use that

21:47.622 --> 21:50.992
sale proceed to also increase
their consumption when old.

21:50.990 --> 21:53.540
So they'll be taken care of
when they're old because they're

21:53.540 --> 21:54.580
able to hold the land.

21:54.578 --> 21:57.168
And the question is how do we
solve for this equilibrium?

21:57.170 --> 22:00.770
And so why is it--so just to go
back to Samuelson and all that,

22:00.770 --> 22:02.340
why is it so interesting?

22:02.338 --> 22:06.068
Well, one of the reasons it's
interesting is that people when

22:06.065 --> 22:09.475
they're young have to think
about the price of land next

22:09.480 --> 22:13.140
period when they're old because
they know they're buying the

22:13.144 --> 22:14.204
land today.

22:14.200 --> 22:17.360
They can see the price today,
but when they get old they have

22:17.363 --> 22:18.513
to,
you know, why are they buying

22:18.505 --> 22:20.315
the land today,
partly for the dividend next

22:20.321 --> 22:23.141
period when they're old,
but also for the resale value

22:23.141 --> 22:23.851
of the land.

22:23.848 --> 22:26.558
So everybody is thinking to
himself, what's the value of

22:26.555 --> 22:28.075
land going to be next period?

22:28.078 --> 22:31.038
And of course the value of land
next period depends on what the

22:31.038 --> 22:33.088
young in that period are willing
to pay,

22:33.088 --> 22:35.328
but they're thinking about what
they're willing to pay on the

22:35.333 --> 22:37.393
basis of what they expect to
happen the period after.

22:37.390 --> 22:39.710
So everybody has to think about
the guy after him,

22:39.710 --> 22:41.640
and what the guy after him is
thinking about what the guy

22:41.637 --> 22:45.037
after him is thinking,
and it looks very complicated.

22:45.038 --> 22:47.738
And we want to solve for an
equilibrium which everybody can

22:47.737 --> 22:50.577
rationally anticipate what the
guy in front of him is going to

22:50.575 --> 22:52.985
do which means rationally
anticipate what that guy is

22:52.992 --> 22:56.252
rationally anticipating the guy
in front of him is going to do,

22:56.250 --> 22:59.780
and you have to solve for the
whole equilibrium and see how it

22:59.784 --> 23:00.484
turns out.

23:00.480 --> 23:04.310
Any questions about this?

23:04.308 --> 23:06.738
It looks very hard,
but it's going to turn out to

23:06.742 --> 23:07.912
be very, very simple.

23:07.910 --> 23:09.950
Yes?

23:09.950 --> 23:17.520
Student: For generation
0 why haven't we added the

23:17.518 --> 23:25.758
dividend that he would get from
holding the land in the second

23:25.762 --> 23:27.252
period?

23:27.250 --> 23:29.800
Prof: By the way,
I haven't said what happens to

23:29.796 --> 23:31.066
the dividend in period 0.

23:31.068 --> 23:33.778
So actually I think that was a
good point.

23:33.779 --> 23:35.879
So he gets 1.

23:35.880 --> 23:42.720
He also gets the dividend in
period 0, so I'm glad you asked

23:42.715 --> 23:44.565
that question.

23:44.568 --> 23:48.458
So to answer your question,
remember the convention that

23:48.459 --> 23:52.349
we've made which holds in the
market and it's one of the

23:52.347 --> 23:55.457
reasons for the breakdown of the
market.

23:55.460 --> 23:59.840
One of the reasons why the
market seized up in the last

23:59.842 --> 24:02.112
year or two,
or the last year,

24:02.107 --> 24:05.807
is because when you buy a stock
like the land somebody has to

24:05.810 --> 24:09.760
give the money and the other guy
has to give back the stock,

24:09.759 --> 24:13.379
and the people buying and
selling are not actually meeting

24:13.382 --> 24:16.882
each other and simultaneously
transferring money for the

24:16.876 --> 24:18.526
ownership of the land.

24:18.528 --> 24:21.548
One guy's in San Francisco and
the other guy's in New York and

24:21.553 --> 24:24.133
they're doing it through some
screen or something.

24:24.130 --> 24:26.390
So the physical asset isn't
quite changing hands.

24:26.390 --> 24:29.640
So you have to make a
convention about when do you say

24:29.643 --> 24:31.733
the deal has actually concluded.

24:31.730 --> 24:34.150
So the convention is,
that we always use,

24:34.150 --> 24:36.870
is that if you buy the land at
time 0 you don't get the

24:36.874 --> 24:39.434
dividends--
at time t, if you buy the land

24:39.434 --> 24:43.064
at time t you don't start
getting the dividends until time

24:43.055 --> 24:43.495
t 1.

24:43.500 --> 24:49.300
So if the young generation buys
the land at time 1 they don't

24:49.298 --> 24:53.548
get the dividend until starting
at time 2.

24:53.548 --> 24:57.858
So the very first dividend at
time 1 is going to go to the old

24:57.861 --> 25:00.901
guy at time 1,
which I had left out here.

25:00.900 --> 25:03.510
So the old guy does get a
dividend, it's the dividend at

25:03.512 --> 25:05.512
time 1 because he began owning
the land.

25:05.509 --> 25:08.219
So he had it before,
so he gets that piece of land.

25:08.220 --> 25:13.770
Even though he's selling the
land at time 1 he still gets the

25:13.766 --> 25:17.476
dividend at time 1,
and the generation that bought

25:17.484 --> 25:20.804
it at time 1 doesn't start
getting dividends until time 2.

25:20.798 --> 25:23.948
So that was an excellent
question, and it was an

25:23.945 --> 25:26.485
oversight of mine,
so exactly right.

25:26.490 --> 25:28.020
And that's how it happens in
real life.

25:28.019 --> 25:31.469
Of course, the length of time
might be 3 days or it might be 1

25:31.467 --> 25:31.917
month.

25:31.920 --> 25:35.530
It depends on the security,
what the settlement rules are,

25:35.529 --> 25:38.509
but there's always got to be a
break between when you buy the

25:38.512 --> 25:41.552
stuff and when you start getting
the dividends because it just

25:41.545 --> 25:44.325
takes time for the whole
physical process to happen.

25:44.328 --> 25:51.338
So they say t 3 is a very
common kind of settlement,

25:51.342 --> 25:52.582
or t 1.

25:52.578 --> 25:55.248
That means that in 3 days or in
1 day,

25:55.250 --> 25:58.210
and so if you're desperate for
cash and you have to give--

25:58.210 --> 26:00.520
so anyway, I won't get
into--we'll come back to this

26:00.517 --> 26:02.777
when we talk about the crisis
and what happened.

26:02.778 --> 26:07.208
So people who are desperate to
get stuff, it doesn't start

26:07.211 --> 26:09.701
coming for a little while,
so.

26:09.700 --> 26:10.280
Any other questions?

26:10.279 --> 26:11.079
Yes?

26:11.078 --> 26:14.488
Student: Should we
multiply the price of apples by

26:14.493 --> 26:15.473
q_1?

26:15.470 --> 26:16.470
Prof: Should I what?

26:16.470 --> 26:18.820
Student: Should we
multiply what

26:18.824 --> 26:20.564
>?

26:20.559 --> 26:28.429
Prof: Absolutely.

26:28.430 --> 26:29.340
Very good.

26:29.339 --> 26:38.249
Any other comments?

26:38.250 --> 26:39.860
All right, now how do you solve
this?

26:39.858 --> 26:42.138
Well, let's figure out how to
solve this.

26:42.140 --> 26:45.910
So the first thing you could
notice is that--so Fisher never

26:45.914 --> 26:49.824
thought of having infinite time
and never thought about Social

26:49.817 --> 26:50.647
Security.

26:50.650 --> 26:51.710
Maybe he thought about Social
Security.

26:51.710 --> 26:54.250
I'm not aware that he had any
thoughts about Social Security.

26:54.250 --> 26:57.370
We didn't have Social Security
so it's unlikely he had been

26:57.365 --> 26:58.435
thinking about it.

26:58.440 --> 27:01.840
So I don't think he thought
about time going on forever,

27:01.838 --> 27:05.048
but that doesn't mean his
methods aren't--

27:05.048 --> 27:09.188
he died, by the way,
in 1947, I think,

27:09.190 --> 27:11.910
something like that,
so right around the time Allais

27:11.910 --> 27:12.870
wrote his paper.

27:12.869 --> 27:19.069
So what is it that he said?

27:19.068 --> 27:20.678
All his lessons are going to
hold true.

27:20.680 --> 27:26.120
The first thing he said is that
look, in every period there are

27:26.115 --> 27:28.655
qs on every side of things.

27:28.660 --> 27:30.570
Here are q_t,
q_t,

27:30.571 --> 27:32.231
q_t 1,
q_t 1,

27:32.226 --> 27:33.256
q_t 1.

27:33.259 --> 27:37.829
So if you just double--there's
no loss in generality by taking

27:37.827 --> 27:40.297
all the q_ts to be 1.

27:40.298 --> 27:43.018
We have no theory of inflation
yet, because there's no money or

27:43.017 --> 27:43.497
anything.

27:43.500 --> 27:46.280
So you might as well assume
we're measuring everything in

27:46.284 --> 27:48.724
terms of apples and take
q_t to be 1.

27:48.720 --> 27:51.820
So without loss of generality,
as they say,

27:51.818 --> 27:55.438
q_t = 1,
and of course that means we can

27:55.435 --> 27:58.605
divide every equation by
q_t.

27:58.608 --> 28:01.218
So pi_t divided by
q_t would go here and

28:01.224 --> 28:02.294
we'd have a 1 and a 1.

28:02.288 --> 28:05.798
We divide this one by q_t
1, still it's an equation.

28:05.798 --> 28:10.348
We have Z less than or equal to
1 pi_t 1 over

28:10.348 --> 28:15.488
q_t 1 1 times 1 times
theta, so we just re-normalize

28:15.489 --> 28:17.089
all the prices.

28:17.088 --> 28:38.148
So, re-normalize all nominal
prices in terms of apples.

28:38.150 --> 28:41.310
So one simplifying thing is we
can get rid of--so think of

28:41.305 --> 28:44.455
pi_t as the price of
land in terms of apples.

28:44.460 --> 28:47.820
So we just get rid of all the
qs here.

28:47.818 --> 28:52.568
Just assume that they're 1,
and so we have this equation.

28:52.568 --> 29:05.548
And now that means that
pi_t = price of land

29:05.548 --> 29:15.588
at time t in terms of apples at
time t.

29:15.588 --> 29:18.748
So that was a normalization we
did many times before.

29:18.750 --> 29:21.940
We said that we might as well
assume the contemporaneous

29:21.944 --> 29:22.414
price.

29:22.410 --> 29:24.140
We can't figure out what
inflation is,

29:24.137 --> 29:25.957
so let's figure there's no
inflation.

29:25.960 --> 29:29.230
The price of apples is always 1
and we're going to measure the

29:29.231 --> 29:31.111
price of land in terms of
apples.

29:31.108 --> 29:34.058
So we get the same equation
that now looks a lot simpler.

29:34.058 --> 29:36.168
So the qs, we don't have to
really worry about.

29:36.170 --> 29:41.500
We're just worrying about the
pis every period.

29:41.500 --> 29:44.200
So what did Fisher say to do?

29:44.200 --> 29:47.390
So we've got to worry
about--what did Fisher say to

29:47.390 --> 29:47.710
do?

29:47.710 --> 29:53.000
What was his--whenever you have
an economy, a stock market

29:52.999 --> 29:56.989
economy like this,
what did he say to do?

29:56.990 --> 29:59.360
What was his advice?

29:59.358 --> 30:01.038
He said turn it into general
equilibrium.

30:01.039 --> 30:06.299
How?

30:06.299 --> 30:07.019
By doing what?

30:07.019 --> 30:07.789
Yeah?

30:07.788 --> 30:09.428
Student: Adjust the
endowments.

30:09.430 --> 30:21.900
Prof: So Fisher said,
Fisher's lesson,

30:21.896 --> 30:37.196
forget about assets by putting
their dividends into the

30:37.199 --> 30:41.449
endowments.

30:41.450 --> 30:44.390
That's his first lesson.

30:44.390 --> 30:51.820
So you see this is a good
summary of what we've learned so

30:51.818 --> 30:59.638
far, and a second lesson was
look at present value prices.

30:59.640 --> 31:02.980
So he says forget all these pis
and things like that.

31:02.980 --> 31:05.680
Just look at the present value.

31:05.680 --> 31:08.130
So we're looking at
p_1,

31:08.132 --> 31:10.662
p_2,
p_3 ...

31:10.660 --> 31:17.940
where p_t,
price at time 0,

31:17.936 --> 31:25.616
let's say or time 1,
it doesn't matter,

31:25.618 --> 31:34.108
price at time 1 of an apple at
time t.

31:34.108 --> 31:36.358
So once you knew the presence
of the endowment then,

31:36.358 --> 31:38.878
I'm not going to write all
this, the endowment of all

31:38.884 --> 31:41.074
generations 1 and above it stays
the same,

31:41.068 --> 31:44.808
(3,1), (3,1),
(3,1), but the endowment of

31:44.805 --> 31:51.195
generation 0 is now 1,
1,1, 1,1, 1,1 forever.

31:51.200 --> 31:55.470
And the budget set,
everybody's going to have a

31:55.471 --> 31:58.631
budget set determined by the ps.

31:58.630 --> 32:02.210
So now we're just one step from
solving this.

32:02.210 --> 32:06.840
So there's one more thing to
notice before we can solve it,

32:06.838 --> 32:19.898
so by symmetry,
so observe that by symmetry we

32:19.896 --> 32:36.146
can hope to find an equilibrium
with p_t 1 over

32:36.145 --> 32:48.525
p_t = p,
a constant.

32:48.529 --> 32:52.939
So every generation is the same.

32:52.940 --> 32:55.490
The only relevant price for a
generation is the tradeoff

32:55.486 --> 32:58.306
between the price of goods when
they're young and the price of

32:58.309 --> 32:59.559
goods when they're old.

32:59.559 --> 33:00.789
That's what Fisher said.

33:00.788 --> 33:04.678
The veil of the stock market is
just a means of transferring

33:04.682 --> 33:08.382
wealth between when you're young
and when you're old,

33:08.380 --> 33:10.570
and really you should
calculate--all these guys have

33:10.566 --> 33:11.206
to calculate.

33:11.210 --> 33:13.940
If I buy the stock now when I'm
young it's going to cost me a

33:13.940 --> 33:16.490
certain amount of money and I'm
going to be able to get a

33:16.489 --> 33:16.989
return.

33:16.990 --> 33:21.980
So the real rate of return,
right, that they're all going

33:21.980 --> 33:26.970
to calculate is going to equal--
we'll, by putting in

33:26.967 --> 33:32.547
pi_t dollars today
they get out pi_t 1

33:32.546 --> 33:36.146
the dividend,
1, tomorrow, right?

33:36.150 --> 33:38.820
So tomorrow they're going to
get pi_t 1 1.

33:38.818 --> 33:43.308
So if they buy 1 share of stock
it costs them pi_t and

33:43.307 --> 33:46.367
tomorrow they get pi_t
apples,

33:46.368 --> 33:47.728
we're measuring in terms of
apples,

33:47.730 --> 33:50.480
and in the future they get
pi_t 1 1 apple in the

33:50.483 --> 33:50.923
future.

33:50.920 --> 33:52.990
So that's the real rate of
return.

33:52.990 --> 33:55.390
That's like 1 r,
1 r_t,

33:55.387 --> 33:59.207
but we're going to assume that
that's a constant.

33:59.210 --> 34:03.970
1 r we're going to guess it's a
constant and that's just 1 over

34:03.970 --> 34:08.040
this p that I told you about
before, the ratio p_t

34:08.039 --> 34:10.419
1, the present value.

34:10.420 --> 34:15.950
So this ratio is just the
interest rate between time t and

34:15.952 --> 34:17.022
time t 1.

34:17.018 --> 34:19.638
So Fisher says you don't have
to think about all the stock

34:19.637 --> 34:22.387
market and what the return on
the stock market and all that's

34:22.393 --> 34:23.133
going to be.

34:23.130 --> 34:24.450
Really you're just trading off.

34:24.449 --> 34:27.579
By doing all that calculation
you're figuring out what's the

34:27.577 --> 34:30.277
tradeoff between time t goods
and time t 1 goods.

34:30.280 --> 34:33.030
In the Fisher economy you don't
look at the stock market.

34:33.030 --> 34:36.060
You assume that everybody knows
the present value prices and

34:36.063 --> 34:39.153
therefore the tradeoff between
time t and time t 1 goods,

34:39.150 --> 34:42.990
and we're going to assume
that's a constant because the

34:42.987 --> 34:46.897
thing's so symmetric how else
could it turn out except a

34:46.896 --> 34:47.816
constant.

34:47.820 --> 34:49.220
So now we're ready to solve it.

34:49.219 --> 34:53.199
We've done all the tricks,
almost, to solve it.

34:53.199 --> 34:59.199
So what is equilibrium going to
be?

34:59.199 --> 35:00.149
So here's equilibrium.

35:00.150 --> 35:08.880
It's going to be a very simple
equation.

35:08.880 --> 35:11.770
At every generation you're
going to have an old and a

35:11.766 --> 35:12.206
young.

35:12.210 --> 35:17.590
So what is the total supply of
goods in every generation?

35:17.590 --> 35:19.680
How much goods are there?

35:19.679 --> 35:25.499
There's 1 for the old apple.

35:25.500 --> 35:28.380
All right, if you look at any
generation like this one at time

35:28.378 --> 35:30.028
2 there's that one,
no not that one,

35:30.030 --> 35:30.880
a little less.

35:30.880 --> 35:34.390
The one in the middle that's
the 1 for the old guy,

35:34.389 --> 35:37.409
then there's the young guy who
has 3, right,

35:37.407 --> 35:41.197
and then there's the apple that
the land produces.

35:41.199 --> 35:53.029
So this is young apples and
this is the dividend of apples.

35:53.030 --> 35:55.280
So that's how many apples there
are in the economy.

35:55.280 --> 35:58.730
So who's going to be eating
them?

35:58.730 --> 36:01.790
Well, there's going to be an
old guy eating apples and

36:01.793 --> 36:04.573
there's going to be a young guy
eating apples.

36:04.570 --> 36:07.980
So how much is the old guy
going to eat?

36:07.980 --> 36:11.850
Well, the old guy's going to
spend half his money,

36:11.846 --> 36:14.526
and how much money does he
have?

36:14.530 --> 36:18.480
Well, from his point of view
he's just trading off when he's

36:18.481 --> 36:20.491
young against when he's old.

36:20.489 --> 36:24.609
So from his point of view he's
got 3 apples when he's young

36:24.608 --> 36:28.258
plus 1 apple when he's old,
but that's worth,

36:28.262 --> 36:33.542
to him, the tradeoff between
apples when he's young and when

36:33.543 --> 36:38.143
he's old is just given by p,
divided by p.

36:38.139 --> 36:40.569
All right, so this is the whole
trick.

36:40.570 --> 36:44.720
So we have to spend a minute
until this dawns on you why this

36:44.717 --> 36:45.407
is true.

36:45.409 --> 36:47.159
And now what's the young going
to do?

36:47.159 --> 36:49.799
The young generation,
what's their income?

36:49.800 --> 36:53.670
Well, they only care about the
tradeoff between prices when

36:53.670 --> 36:56.140
they're young and when they're
old.

36:56.139 --> 36:58.689
So when they're young and when
they're old they don't care

36:58.686 --> 37:00.156
about land according to Fisher.

37:00.159 --> 37:01.299
They don't have to think about
that.

37:01.300 --> 37:04.390
They just have to know the
price, which we're assuming is p

37:04.393 --> 37:06.533
for everybody,
the tradeoff between young

37:06.527 --> 37:09.087
apples which are worth more than
old apples.

37:09.090 --> 37:15.320
So to them they have the same
income 3 1 p.

37:15.320 --> 37:17.530
Now, these ps refer to
different time periods,

37:17.534 --> 37:19.014
but we're assuming the same.

37:19.010 --> 37:21.000
Here's the young.

37:21.000 --> 37:27.610
This is the young,
so this is divided by 1.

37:27.610 --> 37:32.920
So this is the young and this
is the old.

37:32.920 --> 37:35.640
And once I solve this equation
we'll have the whole

37:35.643 --> 37:37.113
equilibrium,
but we need to understand this

37:37.110 --> 37:37.780
equation [note:
the equation is:

37:37.782 --> 37:39.132
(1 half times (3 1 p) over p 1
half times (3 1 p) over 1) = 1 3

37:39.128 --> 37:39.388
1 = 5].

37:39.389 --> 37:41.349
So where did I get this
equation?

37:41.349 --> 37:46.869
So let's take any time period 2
like T = 2 for example.

37:46.869 --> 37:50.119
We know the total apples around
that can be eaten are 5.

37:50.119 --> 37:51.339
That's on the right hand side.

37:51.340 --> 37:55.600
The old guy's apple,
the young guy's 3 apples and

37:55.603 --> 37:59.693
the land producing 1 apple,
5 apples in all.

37:59.690 --> 38:01.540
Now who's going to be eating
the apples?

38:01.539 --> 38:04.099
There are going to be old guys
and there are going to be young

38:04.103 --> 38:05.033
guys, eating apples.

38:05.030 --> 38:09.760
So the old will be the
generation 1 guys.

38:09.760 --> 38:12.490
They're going to be eating
apples, and then the generation

38:12.485 --> 38:14.345
2 guys are going to be eating
apples.

38:14.349 --> 38:17.929
Now, the generation 2 people
they've got 3 apples at time 2,

38:17.925 --> 38:21.255
so they're looking at 3,
but they've got expectations in

38:21.260 --> 38:22.170
their head.

38:22.170 --> 38:23.360
They're going to think ahead.

38:23.360 --> 38:26.230
What's the price of stock
market today versus tomorrow?

38:26.230 --> 38:28.410
Fisher says they do all that
thinking,

38:28.409 --> 38:31.849
they realize the tradeoff
between consumption at time t

38:31.851 --> 38:35.041
when they're young and
consumption at time t 1 when

38:35.039 --> 38:36.059
they're old.

38:36.059 --> 38:37.429
That's given by the price p.

38:37.429 --> 38:39.219
We've assumed there's a price p.

38:39.219 --> 38:40.939
So they're going to say to
themselves,

38:40.940 --> 38:42.850
"Okay, I've got 3 apples
when I'm young,

38:42.849 --> 38:45.769
1 apple when I'm old is not
worth the same in present value

38:45.766 --> 38:48.196
terms--
it's just 3 1 P because the old

38:48.197 --> 38:51.767
apple's not worth as much at
time t as it as time t 1,

38:51.769 --> 38:52.869
it's 3 1p.

38:52.869 --> 38:56.079
I'm going to spend half of my
income and the price when I'm

38:56.077 --> 38:58.177
young I've assumed that's
one."

38:58.179 --> 38:59.579
So that's what the young are
doing.

38:59.579 --> 39:02.109
The old guys,
now the old guys what they're

39:02.110 --> 39:06.030
doing at time t depended on what
they did when they were young.

39:06.030 --> 39:08.920
But when they were young at
time 1,

39:08.920 --> 39:12.830
they knew there was a tradeoff
between time 1 and time 2

39:12.829 --> 39:14.969
apples,
but we've assumed it's the same

39:14.972 --> 39:17.362
price tradeoff,
so we've assumed it's the same

39:17.364 --> 39:19.564
p, and so they did the same
calculation.

39:19.559 --> 39:22.089
When they were young they were
going to spend half their money,

39:22.090 --> 39:25.040
this time 1 generation is going
to spend half its money when

39:25.039 --> 39:28.279
it's young,
half its present value when

39:28.278 --> 39:31.258
young, divided by--
so when they were young they

39:31.257 --> 39:33.397
were going to do that,
but when they're old now

39:33.396 --> 39:36.036
they're looking forward to
spending half their present

39:36.041 --> 39:38.831
value when they're old,
and the price of apples when

39:38.829 --> 39:41.809
they're old is given by p
relative to when they're young.

39:41.809 --> 39:44.719
So they're going to spend 1
half times the present value of

39:44.717 --> 39:47.147
their income,
divided by the present value of

39:47.148 --> 39:50.508
the price of the old apple which
is the apple we're talking about

39:50.512 --> 39:53.142
because they're consuming when
they're old now.

39:53.139 --> 39:56.499
So their consumption plus this
consumption equals 5.

39:56.500 --> 40:00.810
Now, at least half of you must
be baffled, so ask me a question

40:00.811 --> 40:03.941
to see if we can get to the
bottom of this.

40:03.940 --> 40:04.390
That's it.

40:04.389 --> 40:05.229
That's the whole equation.

40:05.230 --> 40:08.410
As soon as we solve this we'll
figure out all the prices and

40:08.414 --> 40:10.254
everything in the whole economy.

40:10.250 --> 40:15.170
And so we're at the end,
but this requires a little bit

40:15.170 --> 40:17.540
of thought, so go ahead.

40:17.539 --> 40:22.609
Student: Shouldn't it be
4 1 p because there's the

40:22.610 --> 40:25.510
dividend, or maybe like 3 2 p?

40:25.510 --> 40:26.220
Prof: No.

40:26.219 --> 40:28.139
Student: I mean,
where does the dividend fit in?

40:28.139 --> 40:29.789
Prof: That's a good
question.

40:29.789 --> 40:31.789
The dividend fit in here
because, yes,

40:31.793 --> 40:32.933
there's a dividend.

40:32.929 --> 40:36.369
Here's the dividend that got
produced, so there's an apple to

40:36.367 --> 40:38.427
be eaten from the dividend,
right?

40:38.429 --> 40:42.349
Now, you're saying--so it's a
very important question you're

40:42.351 --> 40:42.951
asking.

40:42.949 --> 40:46.159
So it's correct what I wrote,
but it doesn't sound correct.

40:46.159 --> 40:47.649
So what he's saying,
the question is,

40:47.652 --> 40:48.982
what happened to the dividend.

40:48.980 --> 40:52.620
This generation,
say, this young generation,

40:52.623 --> 40:55.763
either one, say the old
generation.

40:55.760 --> 40:59.220
The old generation,
when they were young at time 1

40:59.219 --> 41:02.889
they bought land looking forward
to their old age.

41:02.889 --> 41:05.469
They sold the land,
and they got the dividend.

41:05.469 --> 41:09.949
How come that's not factoring
in to their demand?

41:09.949 --> 41:11.379
That's his question, right?

41:11.380 --> 41:15.190
The answer is because that's
precisely the point of what

41:15.188 --> 41:16.088
Fisher did.

41:16.090 --> 41:17.900
Fisher said,
yes, in the real world

41:17.898 --> 41:20.768
everybody is thinking to
themselves, like generation 1,

41:20.771 --> 41:22.051
"I'm young now.

41:22.050 --> 41:24.420
I'm buying the land because
when I get old I'll be able to

41:24.420 --> 41:26.460
resell it and I'll also get the
dividend."

41:26.460 --> 41:28.830
But Fisher has thought ahead.

41:28.829 --> 41:31.679
Fisher's saying if the guy's
going to think about pi_t

41:31.679 --> 41:33.359
1,
that's what he'll be able to

41:33.355 --> 41:35.895
sell the land for,
and he's going to think about

41:35.900 --> 41:39.320
the dividend he's going to get,
and his rate of return is

41:39.320 --> 41:43.010
therefore divided by how much he
had to pay for the land today.

41:43.010 --> 41:44.230
That's his rate of return.

41:44.230 --> 41:47.870
But see, the bottom thing is
how many apples he had to give

41:47.871 --> 41:51.201
up, pi_t there,
is how many apples he had to

41:51.201 --> 41:52.961
give up to get the land.

41:52.960 --> 41:56.520
The numerator is how many
apples he gets next period after

41:56.516 --> 41:59.196
selling the land and taking the
dividend.

41:59.199 --> 42:03.299
So that ratio is the tradeoff
between apples today and apples

42:03.300 --> 42:04.940
in the future for him.

42:04.940 --> 42:07.300
So if he says to himself,
what Fisher says,

42:07.295 --> 42:09.985
the only thing the guy cares
about is that ratio,

42:09.987 --> 42:12.007
that tradeoff,
which we're calling p,

42:12.007 --> 42:12.847
1 over p.

42:12.849 --> 42:15.919
That's the tradeoff he's going
to have in his mind.

42:15.920 --> 42:20.080
And so what is his income?

42:20.079 --> 42:22.509
This guy began with no land.

42:22.510 --> 42:24.210
Only 0 began with the land.

42:24.210 --> 42:27.790
Everybody else buys the land
only as a means of getting to

42:27.789 --> 42:30.049
more consumption when they're
old.

42:30.050 --> 42:33.490
So the whole point of Fisher's
insight is you don't have to

42:33.494 --> 42:36.944
keep track of how the guy's
managing to get the payoff when

42:36.938 --> 42:37.708
he's old.

42:37.710 --> 42:43.120
All he's doing is he's
recognizing a tradeoff of 1 r or

42:43.117 --> 42:45.337
1 over p,
that tradeoff between

42:45.338 --> 42:48.098
consumption when young and
consumption when old and all he

42:48.103 --> 42:50.723
can do is turn his endowment
when he is young into more

42:50.724 --> 42:52.864
endowment when he's old at that
ratio,

42:52.860 --> 42:56.030
and it doesn't matter how he
does it as long as we have the

42:56.025 --> 42:56.785
right ratio.

42:56.789 --> 42:58.689
So Fisher says forget about the
assets.

42:58.690 --> 43:02.260
Just keep track of the present
value prices and these will tell

43:02.257 --> 43:05.817
you the ratio of transformation
of goods when young to when old

43:05.824 --> 43:08.994
and that's all you need to know
to make a decision.

43:08.989 --> 43:10.139
That's the whole point of
Fisher.

43:10.139 --> 43:12.019
You don't need to think about
the assets.

43:12.018 --> 43:16.378
Now, after we get the ps we'll
go back and figure out what the

43:16.380 --> 43:17.740
price of land is.

43:17.739 --> 43:20.979
Any other questions?

43:20.980 --> 43:22.280
Yes?

43:22.280 --> 43:25.800
Student: Can you explain
again why the price of the

43:25.797 --> 43:27.277
second part is just 1?

43:27.280 --> 43:30.640
Why can you use 1
>?

43:30.639 --> 43:34.149
Prof: Yes,
because I'm taking p as the

43:34.150 --> 43:34.790
ratio.

43:34.789 --> 43:41.889
So p, this p is here,
so it says if I had 1 apple at

43:41.889 --> 43:48.849
time t how many apples could I
get at time t 1,

43:48.849 --> 43:50.039
[correction:
1 over]

43:50.043 --> 43:53.533
p of them, right,
because this ratio--so for

43:53.534 --> 43:57.834
every apple I have down here I
can get [correction:

43:57.829 --> 44:00.579
1 over]
p apples at time t 1.

44:00.579 --> 44:03.159
If the ratio of two prices is p
it doesn't matter what their

44:03.157 --> 44:05.857
levels are--so I might as well
as think of one of them as 1 and

44:05.864 --> 44:06.874
the other one as p.

44:06.869 --> 44:10.339
I could think of the first one
as 2 and the second one as 2 p.

44:10.340 --> 44:13.960
That would be the same thing,
right?

44:13.960 --> 44:18.450
So if I thought of the first
price as 2 and this price as 2 p

44:18.447 --> 44:21.887
I'd put a 2 here,
a 2 here, and a 2 here and it

44:21.889 --> 44:24.059
wouldn't change anything.

44:24.059 --> 44:26.849
Remember, we learned this the
very--

44:26.849 --> 44:29.089
this is why the lessons of
general equilibrium they seem so

44:29.092 --> 44:31.572
obvious and then you put them in
a slightly different context and

44:31.568 --> 44:33.038
you realize how clever Fisher
was.

44:33.039 --> 44:36.399
If you double all the prices
you're not going to change

44:36.404 --> 44:37.094
anything.

44:37.090 --> 44:39.140
It's the price ratios that
matter.

44:39.139 --> 44:41.759
So it's the tradeoff between
apples when young and apples

44:41.762 --> 44:42.842
when old that matter.

44:42.840 --> 44:45.670
If you assume that tradeoff is
given by p you might as well

44:45.672 --> 44:48.082
assume that the first guy,
for all we care,

44:48.081 --> 44:51.671
he might as well assume that
he's measuring the prices when

44:51.672 --> 44:58.212
he's young in terms of 1,
and the prices when he's old in

44:58.206 --> 45:00.036
terms of p.

45:00.039 --> 45:01.849
Those were very good questions.

45:01.849 --> 45:06.209
This is a little confusing but
when we go back to the original

45:06.210 --> 45:09.070
equilibrium it'll be clearer,
I think.

45:09.070 --> 45:12.790
But so that's the only equation
that we have to satisfy.

45:12.789 --> 45:15.019
So we can solve that equation
now.

45:15.019 --> 45:23.489
Any other questions?

45:23.489 --> 45:25.929
Let's solve that equation.

45:25.929 --> 45:29.179
That equation is I'm going to
multiply by 2 p,

45:29.177 --> 45:32.567
so I'm going to get 10 p on the
right-hand side,

45:32.568 --> 45:33.288
right?

45:33.289 --> 45:36.679
Because if I multiply by 2 p I
get 5 times 2 p is 10 p.

45:36.679 --> 45:47.239
On the left-hand side I'm just
going to get 3 1 p 3 p p

45:47.242 --> 45:49.202
squared.

45:49.199 --> 45:54.009
So if I rearrange I just get p
squared--uh-oh,

45:54.014 --> 45:56.694
my usual problems here.

45:56.690 --> 46:04.470
p squared - 6 p 3 = 0.

46:04.469 --> 46:10.599
p squared - 6 p 3 = 0,
so p = 6 (and I'm using the

46:10.599 --> 46:18.479
quadratic formula which I assume
you know) - b squared - 4--.

46:18.480 --> 46:28.010
So 6 squared - 4 times 1 times
3, minus 12, over 2 = 6 - the

46:28.009 --> 46:32.369
square root of 24 over 2.

46:32.369 --> 46:36.329
So the square root of 24 is a
little bit less than 5,

46:36.329 --> 46:39.059
so this is going to be a little
bit more than 1,

46:39.059 --> 46:42.469
sorry a little bit less than 5,
so this will be a little bit

46:42.472 --> 46:44.452
more than 1,
so the whole thing will be a

46:44.449 --> 46:45.599
little bit more than a half.

46:45.599 --> 46:50.779
So let's say it's .55.

46:50.780 --> 46:53.290
So here's a crucial step.

46:53.289 --> 46:56.719
How did I know when I said 6
plus or minus,

46:56.715 --> 46:58.915
why did I take the minus?

46:58.920 --> 47:02.360
Because if I had taken 6 plus
this I would have gotten a

47:02.360 --> 47:04.990
gigantic--well,
let's come back to that.

47:04.989 --> 47:07.919
So how did I know to take 6
minus that instead of 6 plus

47:07.916 --> 47:08.286
this?

47:08.289 --> 47:11.119
So if this is the p then what
are the prices?

47:11.119 --> 47:12.609
What are Fisher's prices?

47:12.610 --> 47:19.410
We've just solved for
equilibrium and these prices are

47:19.413 --> 47:26.223
going to be--we call this 1,1,
maybe .55, .55 squared,

47:26.217 --> 47:29.167
.55 cubed etcetera.

47:29.170 --> 47:33.040
That's what Fisher says the
prices are.

47:33.039 --> 47:36.019
And we can now figure out
everybody's consumption.

47:36.018 --> 47:39.548
Y and Z, what's Y going to
equal?

47:39.550 --> 47:44.000
Y is this thing on the right,
1 half 3 1 p,

47:44.001 --> 47:46.971
so it's .355 divided by 2.

47:46.969 --> 47:53.269
So that's 1.775.

47:53.269 --> 47:55.699
And what's Z?

47:55.699 --> 47:56.249
You should check.

47:56.250 --> 47:58.050
I'm going a little fast here
for myself.

47:58.050 --> 48:04.130
3.55 divided by 2 is 1.775,
so what is Z?

48:04.130 --> 48:19.530
It's going to be 1 and a half
plus--no, it's 3.5 divided by

48:19.527 --> 48:21.117
1.1.

48:21.119 --> 48:22.079
Student:
>

48:22.083 --> 48:23.173
are those numbers
>

48:23.170 --> 48:26.140
Prof: p is .5--I'm going
too fast for you,

48:26.143 --> 48:26.643
ah ha!

48:26.639 --> 48:28.509
p is .55, right?

48:28.510 --> 48:30.490
I just got p.

48:30.489 --> 48:32.509
So if I want a C now,
go back to consumption,

48:32.507 --> 48:35.027
what's the consumption going to
be when you're young?

48:35.030 --> 48:41.170
It's going to be,
Y is going to be 3 .55 divided

48:41.172 --> 48:47.002
by 2 which equals that,
right, 3 .55 that's the guy's

48:46.998 --> 48:51.018
income and he consumes a half
when he's young,

48:51.019 --> 48:53.569
so that's 1.775.

48:53.570 --> 49:01.680
And when he's old he's going to
have the same income,

49:01.679 --> 49:11.459
so 1.775 divided by p,
so it's going to be 1.775

49:11.456 --> 49:19.606
divided by .55,
and that you can see--no,

49:19.610 --> 49:24.020
that doesn't look right.

49:24.018 --> 49:31.278
Yeah, that divided by p and
that's going to be a little bit

49:31.277 --> 49:37.537
more than 3 and so,
in fact, if you solve it out it

49:37.536 --> 49:40.786
turns out to be 3.225.

49:40.789 --> 49:42.779
Did I go too fast there?

49:42.780 --> 49:45.320
I'm plugging in .55 there.

49:45.320 --> 49:48.310
So it's 3.55 divided by a half.

49:48.309 --> 49:52.329
That was that number,
1.775 divided by p which was

49:52.326 --> 49:54.026
.55,
so you can see it's a little

49:54.025 --> 49:56.965
bit more than 3,
because .55 into 1.7 is a

49:56.974 --> 49:59.114
little bit more than 3.

49:59.110 --> 50:08.180
In fact, if you solve it out to
some decimal places it's that.

50:08.179 --> 50:10.319
So we've solved what everybody
does.

50:10.320 --> 50:12.270
Now we know what everyone's
going to do.

50:12.268 --> 50:19.478
The young are going to spend
1.775, are going to consume

50:19.480 --> 50:25.380
1.775, they're going to consume
1.775 here.

50:25.380 --> 50:26.570
They have an endowment of 3
apples.

50:26.570 --> 50:27.950
They're not going to eat them
all.

50:27.949 --> 50:30.639
They're going to consume 1.775
of them.

50:30.639 --> 50:33.569
And then the old,
at the same time,

50:33.565 --> 50:35.455
what are they doing?

50:35.460 --> 50:39.390
They're consuming 3.225,
but you notice that those

50:39.393 --> 50:42.653
things add up to 5,
so the consumption when they're

50:42.648 --> 50:44.858
young plus the consumption when
they're old--

50:44.860 --> 50:48.550
so the consumption of this old
guy there is 3.225 and you add

50:48.548 --> 50:51.758
the consumption of that,
yeah, I went too high there,

50:51.757 --> 50:55.017
the consumption of the young
guy just under him is 1.775,

50:55.019 --> 50:56.399
the two of them add up to 5.

50:56.400 --> 50:58.170
That exactly clears the market.

50:58.170 --> 51:02.020
So at time 2 you repeat the
same thing, at time 3,

51:02.023 --> 51:02.893
etcetera.

51:02.889 --> 51:07.649
So you see we've already
cleared all the markets except

51:07.648 --> 51:11.698
the one at time 1 which looks
more complicated,

51:11.701 --> 51:15.051
but we've cleared all the
markets.

51:15.050 --> 51:19.330
Now, what's the price of land
going to be?

51:19.329 --> 51:22.009
What's the price of land?

51:22.010 --> 51:22.880
Nowhere to write that.

51:22.880 --> 51:25.650
Let's write it here.

51:25.650 --> 51:29.160
What's the price of land which
is going to be a constant?

51:29.159 --> 51:31.669
How do we figure that out?

51:31.670 --> 51:38.580
How would Fisher say you figure
out the price of land?

51:38.579 --> 51:42.739
So the price of land at time 1,
say, what would Fisher say?

51:42.739 --> 51:43.419
Yep?

51:43.420 --> 51:46.820
Student: Whatever the
young guy would pay for it?

51:46.820 --> 51:49.850
Prof: That's one way of
getting it.

51:49.849 --> 51:51.969
So what's he paying for it?

51:51.969 --> 51:54.349
Student: Whatever he
doesn't spend on his

51:54.349 --> 51:55.059
consumption.

51:55.059 --> 52:01.679
Prof: Right,
so from this equation he spent

52:01.679 --> 52:02.759
1.775.

52:02.760 --> 52:08.520
His income was 3,
so what's left over?

52:08.518 --> 52:10.618
What did he spend on land
therefore?

52:10.619 --> 52:12.159
Student: 1.225.

52:12.159 --> 52:15.499
Prof: So the price of
land has to be 1.225.

52:15.500 --> 52:18.190
Now, that's not the way Fisher
suggested finding out the price

52:18.188 --> 52:18.628
of land.

52:18.630 --> 52:21.080
What did he say you should do?

52:21.079 --> 52:22.819
What's the fundamental theorem?

52:22.820 --> 52:24.230
Student: Present value
of all the payments.

52:24.230 --> 52:26.820
Prof: And what is that?

52:26.820 --> 52:28.950
So the land pays 1 apple every
period.

52:28.949 --> 52:30.169
Student:
>

52:30.170 --> 52:32.810
Student: So it's paying
1.

52:32.809 --> 52:37.289
Prof: So it's paying 1 p
1 times p squared 1 times p

52:37.289 --> 52:41.159
cubed 1 times p to the fourth,
right, because looked at from

52:41.159 --> 52:43.659
the point of view of time 1 you
get an apple next period

52:43.663 --> 52:45.123
relative to the apples today.

52:45.119 --> 52:46.439
That's worth p.

52:46.440 --> 52:50.380
An apple in 2 periods is worth
p squared at time 1 because an

52:50.375 --> 52:53.915
apple at time 2 is worth p
apples at time 1 and worth p

52:53.916 --> 52:55.816
squared apples at time 0.

52:55.820 --> 52:59.910
So you just keep doing this,
but this is a perpetuity and so

52:59.907 --> 53:01.707
therefore it's equal to?

53:01.710 --> 53:03.330
Student: 1 over r.

53:03.329 --> 53:06.219
Student: We're going to
>.

53:06.219 --> 53:08.829
Prof: Yeah, 1 over r.

53:08.829 --> 53:13.449
So it's equal to 1 over r,
and so what's r?

53:13.449 --> 53:15.689
So what's r?

53:15.690 --> 53:17.470
How do we figure out what r is?

53:17.469 --> 53:21.489
Student: If we know p
then we can find r.

53:21.489 --> 53:31.299
Prof: 1 over 1 r = p,
right, = .55,

53:31.304 --> 53:44.954
so therefore 1 r = 1 over .55
and r = (1 over .55) - 1.

53:44.949 --> 53:52.739
And so this is a little less
than 2 - 1 is going to be like

53:52.739 --> 53:59.189
.81 or something,
and you take 1 over .81 and you

53:59.186 --> 54:02.406
get the same number.

54:02.409 --> 54:03.729
So Fisher solved everything.

54:03.730 --> 54:09.030
I mean, the Fisher method
solves it all.

54:09.030 --> 54:12.040
Let's worry about time 1.

54:12.039 --> 54:12.659
We haven't done that.

54:12.659 --> 54:14.509
So what happens every period?

54:14.510 --> 54:18.160
Every period like from 2
onwards, the young guys says,

54:18.155 --> 54:19.115
"Ah ha!

54:19.119 --> 54:21.379
I've got 3 apples.

54:21.380 --> 54:22.540
What am I going to do with
them?"

54:22.539 --> 54:25.589
He says to himself,
"Well, the price of the

54:25.590 --> 54:29.290
land is 1.225 so I could eat
some of the apples or I could

54:29.291 --> 54:30.851
buy some land."

54:30.849 --> 54:32.219
And what does he decide to do?

54:32.219 --> 54:37.039
He says, "Let me eat 1.775
apples and spend the rest of my

54:37.038 --> 54:39.368
money buying 1 acre of land.

54:39.369 --> 54:40.659
Now, why am I doing that?

54:40.659 --> 54:45.099
Because next period I know the
price of land's going to be the

54:45.103 --> 54:48.823
same 1.225 and I'm going to get
a dividend of 1,

54:48.820 --> 54:52.600
so I'm going to be getting a
rate of return (we just

54:52.599 --> 54:55.119
calculated) of 81 percent."

54:55.119 --> 55:02.099
So this ratio up here,
this is another thing,

55:02.101 --> 55:11.781
this also this number is equal
to 1.225 1 divided by 1.225.

55:11.780 --> 55:16.560
That's also equal to 1.81.

55:16.559 --> 55:20.259
Remember r we just calculated
over here.

55:20.260 --> 55:21.500
Where did I do r?

55:21.500 --> 55:23.410
r was 81 percent.

55:23.409 --> 55:27.109
That's the same number here,
81 percent.

55:27.110 --> 55:30.210
So everybody says to himself,
"Given that there's an 81

55:30.213 --> 55:33.323
percent rate of interest I'm
happy to hold the whole unit of

55:33.317 --> 55:36.317
land because at that rate of
interest I'm just trading off

55:36.315 --> 55:39.045
consumption today for
consumption when I'm old at the

55:39.050 --> 55:40.840
rate that I want to."

55:40.840 --> 55:44.320
And at time 0 the market clears
also.

55:44.320 --> 55:48.970
So we cleared the market for
every time 2 through infinity,

55:48.972 --> 55:51.542
and that was by this equation.

55:51.539 --> 55:52.159
That was up here.

55:52.159 --> 55:56.039
By picking the right p we know
every market from T = 2 onwards

55:56.043 --> 55:57.003
was clearing.

55:57.000 --> 56:00.600
And Fisher would say by Walras'
Law we don't have to worry about

56:00.601 --> 56:04.261
time 1, that's going to clear as
well and sure enough it does.

56:04.260 --> 56:05.950
It's a little bit different now.

56:05.949 --> 56:10.269
It's just the old guy,
but the old guy with his land

56:10.268 --> 56:13.738
which is 1.225 plus his dividend
of 1--

56:13.739 --> 56:25.329
his land which is worth 1.225
and his dividend of--

56:25.329 --> 56:33.169
hope I wrote down the right
price of land all this time.

56:33.170 --> 56:37.120
Oh, that would be bad.

56:37.119 --> 56:39.019
So the old guy, what does he do?

56:39.018 --> 56:45.298
He has his 1 apple plus he has
the land so he's going to

56:45.302 --> 56:50.102
consume--the old guy has
his--oh, I see.

56:50.099 --> 56:53.639
So what happens at time 1?

56:53.639 --> 56:56.809
The old guy has his dividend
that he had before,

56:56.806 --> 57:01.046
so he's got the dividend of the
land because he's owned the land

57:01.050 --> 57:01.860
forever.

57:01.860 --> 57:04.610
So he gets the dividend of 1,
so that's 1,

57:04.610 --> 57:08.570
plus he has an endowment of
one, so he's consuming 2 now.

57:08.570 --> 57:11.710
Plus he sells the land for
1.225.

57:11.710 --> 57:15.960
So that all adds up to 3.225,
and then if you add the young

57:15.960 --> 57:20.430
generation's 1.775 that indeed
clears the market at time 1.

57:20.429 --> 57:27.619
So the market's going to clear
in every single period,

57:27.619 --> 57:31.269
but we only had to solve it for
periods 2 and onwards which were

57:31.269 --> 57:33.529
all symmetric because by Walras
Law,

57:33.530 --> 57:36.050
according to Fisher,
once it clears from time 2

57:36.048 --> 57:39.338
onwards without even bothering
to check we know it would have

57:39.335 --> 57:42.015
had to work at time 1 and sure
enough it did.

57:42.018 --> 57:44.108
So as I said,
let's summarize now what we've

57:44.108 --> 57:46.438
done and then we can start
drawing the lesson.

57:46.440 --> 57:49.130
So what we did is we started
with a complicated model with

57:49.130 --> 57:51.820
land and people having to look
forward and expect what the

57:51.822 --> 57:54.422
price of land was going to be
depending on what the next

57:54.420 --> 57:57.280
generation wanted to hold,
which depended on what they

57:57.280 --> 57:59.930
were going to think the
generation of that were going to

57:59.929 --> 58:00.749
hold etcetera.

58:00.750 --> 58:05.210
Very complicated stuff.

58:05.210 --> 58:07.390
And we saw that to solve it was
very simple.

58:07.389 --> 58:08.849
You just do the Fisher thing.

58:08.849 --> 58:13.229
If everybody's rational you can
forget about the assets and the

58:13.233 --> 58:17.553
land and turn everything into
present value prices and put the

58:17.547 --> 58:20.467
endowments--
so you forget about all the

58:20.474 --> 58:23.534
assets and just put the
dividends into people's

58:23.534 --> 58:27.264
endowments and look at all the
present value prices,

58:27.260 --> 58:30.170
and the present values prices
by symmetry,

58:30.170 --> 58:32.190
we're assuming,
just grow exponentially,

58:32.190 --> 58:33.990
decline exponentially.

58:33.989 --> 58:37.659
And then we can solve the one
equation and figure out what

58:37.659 --> 58:41.449
that price was,
the exponential number p that's

58:41.454 --> 58:44.774
to the nth power gives the nth
price,

58:44.768 --> 58:48.228
the present value price,
so solving for that p we then

58:48.231 --> 58:49.671
cleared the markets.

58:49.670 --> 58:52.210
We found out what everyone's
going to do when young and when

58:52.208 --> 58:55.068
old,
and by plugging in now Fisher's

58:55.072 --> 58:57.592
formula,
the price of every asset is the

58:57.590 --> 59:01.910
present value of its dividends,
we figured out what the price

59:01.911 --> 59:05.451
of land was every period,
so we've solved for the whole

59:05.454 --> 59:07.064
equilibrium and sure enough it
clears.

59:07.059 --> 59:09.699
And in equilibrium everybody's
doing this calculation.

59:09.699 --> 59:13.139
If I buy land today I'm going
to get that rate of return on

59:13.143 --> 59:15.403
the land which corresponds to
the p.

59:15.400 --> 59:24.860
It's going to be 81 percent,
and so everything works out.

59:24.860 --> 59:28.540
So what's this got to do with
Social Security?

59:28.539 --> 59:29.619
Are there any questions about
this?

59:29.619 --> 59:35.279
I sense a little bit of
puzzlement still.

59:35.280 --> 59:40.120
You shouldn't be that far away
from understanding it,

59:40.117 --> 59:42.627
so let's hear a question.

59:42.630 --> 59:44.470
What don't you don't understand?

59:44.469 --> 59:47.479
Just point to an equation you
don't understand.

59:47.480 --> 59:47.950
Yes.

59:47.949 --> 59:49.699
Good, brave of you.

59:49.699 --> 59:53.199
Student: How do we show
that theta should equal 1?

59:53.199 --> 59:58.219
Prof: So Fisher says
that--the way I solved it is I

59:58.219 --> 1:00:00.069
ignored the assets.

1:00:00.070 --> 1:00:02.160
So I didn't pay attention to
what the assets were.

1:00:02.159 --> 1:00:03.979
I just put the dividends in the
endowment.

1:00:03.980 --> 1:00:07.270
I didn't pay any attention to
what people were holding of the

1:00:07.268 --> 1:00:10.558
assets because Fisher says
forget the assets all together.

1:00:10.559 --> 1:00:13.019
Just do the present value
prices and augment the

1:00:13.018 --> 1:00:13.698
endowments.

1:00:13.699 --> 1:00:17.009
And I found the present value
prices by getting this factor p,

1:00:17.012 --> 1:00:20.272
and then it was just p to the n
and I found what everyone was

1:00:20.268 --> 1:00:21.408
going to consume.

1:00:21.409 --> 1:00:23.769
That was it as far as Fisher's
concerned,

1:00:23.768 --> 1:00:27.478
but then Fisher says once we've
found general equilibrium we can

1:00:27.478 --> 1:00:31.238
go back to financial equilibrium
and figure out what the price of

1:00:31.244 --> 1:00:34.384
land is,
which is the present value of

1:00:34.382 --> 1:00:37.572
the dividend,
so it's price is 1.225,

1:00:37.572 --> 1:00:41.282
and the step I left out,
which you're asking about,

1:00:41.280 --> 1:00:44.550
you can also figure out what
assets everybody's holding.

1:00:44.550 --> 1:00:48.110
So Fisher's saying--what assets
are they holding?

1:00:48.110 --> 1:00:53.320
Well, the guy,
he's consuming 1.775 here.

1:00:53.320 --> 1:00:57.930
We figured out the price there
of 1.225 so it must be that he's

1:00:57.931 --> 1:01:02.321
holding exactly 1 unit of the
asset, and so the asset market

1:01:02.322 --> 1:01:03.812
is clearing too.

1:01:03.809 --> 1:01:04.889
But that's no accident.

1:01:04.889 --> 1:01:07.889
Fisher's saying if you clear
all the markets doing the

1:01:07.894 --> 1:01:10.684
present value general
equilibrium stuff and you go

1:01:10.675 --> 1:01:13.675
back to the financial
equilibrium you're automatically

1:01:13.679 --> 1:01:16.459
going to be clearing all those
markets too.

1:01:16.460 --> 1:01:21.560
So I left out the step because
somebody anticipated all that

1:01:21.561 --> 1:01:26.751
and got me to calculate the
price of 1 in a cheating way,

1:01:26.750 --> 1:01:29.550
he said assume theta's 1 then
figure out how much money you're

1:01:29.550 --> 1:01:32.140
spending on the asset,
so we did that.

1:01:32.139 --> 1:01:35.259
What I should have done is done
Fisher's trick of figuring out

1:01:35.260 --> 1:01:38.160
the price of the asset,
which is 1.225 and then,

1:01:38.163 --> 1:01:40.403
of course,
we know the guy must have

1:01:40.396 --> 1:01:43.346
bought 1 asset in order to use
up his budget set,

1:01:43.349 --> 1:01:45.739
but that clears the market for
assets.

1:01:45.739 --> 1:01:46.979
But Fisher knew that was going
to happen.

1:01:46.980 --> 1:01:47.850
It always has to happen.

1:01:47.849 --> 1:01:51.169
That's the beauty of what he
did.

1:01:51.170 --> 1:01:52.060
Yes?

1:01:52.059 --> 1:01:54.449
Student: So in that
equation over there we have to

1:01:54.449 --> 1:01:55.559
assume p is less than 1?

1:01:55.559 --> 1:01:57.359
Prof: Yes,
so the point is,

1:01:57.358 --> 1:02:00.138
thank you, I'm coming back to
exactly that point.

1:02:00.139 --> 1:02:03.819
So the point is when you look
at the present value of land

1:02:03.815 --> 1:02:07.615
it's going to be p p squared p
cubed p to the fourth ....

1:02:07.619 --> 1:02:10.389
The present value of land had
better be finite,

1:02:10.389 --> 1:02:14.089
so in other words p has to be
less than 1 otherwise the value

1:02:14.088 --> 1:02:17.968
of land would be infinite and it
wouldn't make any sense because

1:02:17.971 --> 1:02:21.731
in the very first old guy with
an infinite value of land would

1:02:21.731 --> 1:02:25.431
buy more apples than there
possibly were in the world.

1:02:25.429 --> 1:02:29.339
So you know that the real
interest rate has to be

1:02:29.335 --> 1:02:30.225
positive.

1:02:30.230 --> 1:02:34.920
If the real interest rate were
less than 0, and you had some

1:02:34.920 --> 1:02:38.340
asset that paid a constant
dividend forever,

1:02:38.340 --> 1:02:41.840
that asset would have an
infinite value.

1:02:41.840 --> 1:02:46.630
So the presence of land,
which pays a constant asset

1:02:46.628 --> 1:02:52.168
forever, forces the real rate of
interest to be positive.

1:02:52.170 --> 1:02:54.730
So Samuelson and all his talk
of negative real interest rates,

1:02:54.730 --> 1:02:55.780
it can't really happen.

1:02:55.780 --> 1:03:00.410
Land's going to pay some
dividend probably forever,

1:03:00.409 --> 1:03:05.779
so there's going to be a
positive real rate of interest.

1:03:05.780 --> 1:03:07.940
And so it means in Social
Security,

1:03:07.940 --> 1:03:11.570
if the young give up 1 to get 1
back when they're old they're

1:03:11.570 --> 1:03:14.960
always going to be losing
because there's a positive real

1:03:14.958 --> 1:03:17.678
rate of interest,
and so every generation has to

1:03:17.681 --> 1:03:17.961
lose.

1:03:17.960 --> 1:03:22.280
So it's precisely the point.

1:03:22.280 --> 1:03:25.320
Because of the presence of land
you know that the real rate of

1:03:25.318 --> 1:03:27.458
interest is going to have to be
positive.

1:03:27.460 --> 1:03:29.180
Fisher never made this argument.

1:03:29.179 --> 1:03:31.889
He said it's impatience and
maybe if people are incredibly

1:03:31.889 --> 1:03:34.219
patient it could even turn out
to be negative,

1:03:34.219 --> 1:03:35.949
or if output was bigger
[correction: smaller]

1:03:35.949 --> 1:03:38.109
next period than it is this
period you could even have a

1:03:38.110 --> 1:03:41.060
negative rate of interest,
but not so when you have land

1:03:41.056 --> 1:03:43.076
with a constant dividend
forever.

1:03:43.079 --> 1:03:46.339
Then if the interest rate is
constant it'd better be

1:03:46.342 --> 1:03:49.992
positive, otherwise the land
would have infinite value.

1:03:49.989 --> 1:03:52.659
So it's a new argument for a
positive rate of interest.

1:03:52.659 --> 1:03:59.009
The land has to have a finite
value.

1:03:59.010 --> 1:04:04.270
Any other questions?

1:04:04.268 --> 1:04:07.668
So when you solve for a couple
of these you're going to do it

1:04:07.670 --> 1:04:10.100
very easily,
I mean, after you've done it a

1:04:10.097 --> 1:04:12.517
couple times this will seem very
easy to you.

1:04:12.518 --> 1:04:14.248
I know it seems a little
confusing now,

1:04:14.250 --> 1:04:16.710
but let's just do a couple more
thought experiments.

1:04:16.710 --> 1:04:18.440
Suppose we do Social Security?

1:04:18.440 --> 1:04:20.590
What will happen with Social
Security?

1:04:20.590 --> 1:04:22.320
How does that work?

1:04:22.320 --> 1:04:25.380
What does Social Security mean?

1:04:25.380 --> 1:04:29.410
Well, Social Security means the
young give the old something and

1:04:29.407 --> 1:04:33.367
until now we talked about it as
if the young could give the old

1:04:33.369 --> 1:04:35.159
part of their endowment.

1:04:35.159 --> 1:04:37.879
The young pay taxes and the
taxes get handed over to the old

1:04:37.882 --> 1:04:38.162
guy.

1:04:38.159 --> 1:04:41.109
That's pay as you go and we
talked as if it wouldn't change

1:04:41.105 --> 1:04:44.555
the equilibrium,
but we said at the same time

1:04:44.559 --> 1:04:49.279
that Social Security was the
most gigantic program any

1:04:49.275 --> 1:04:54.255
government anywhere in the world
has ever adopted and the

1:04:54.257 --> 1:04:58.347
giveaway was bigger than GNP for
a year,

1:04:58.349 --> 1:05:01.149
17 trillion compared to 12 or
14 trillion.

1:05:01.150 --> 1:05:04.340
So clearly it's going to have
an effect on the interest rate.

1:05:04.340 --> 1:05:07.610
So we ought to take that into
account if we're doing a more

1:05:07.608 --> 1:05:09.748
careful analysis of Social
Security.

1:05:09.750 --> 1:05:11.640
So what would Social Security
do?

1:05:11.639 --> 1:05:14.029
How would I take into account
Social Security?

1:05:14.030 --> 1:05:18.430
Suppose every young person gave
1 apple to the old guy at the

1:05:18.429 --> 1:05:19.309
same time?

1:05:19.309 --> 1:05:23.959
How would I figure out what
happened in the new equilibrium?

1:05:23.960 --> 1:05:33.410
How would the economy change?

1:05:33.409 --> 1:05:36.089
What would I change and solve
differently?

1:05:36.090 --> 1:05:55.090


1:05:55.090 --> 1:05:58.970
Well, all I would do is I would
change this to a 2.

1:05:58.969 --> 1:06:01.969
Every young guy now only has 2
apples when he's young because

1:06:01.974 --> 1:06:04.934
he's given 1 of them to the old
and the old would have 2.

1:06:04.929 --> 1:06:14.839
So all the way through here I
would just change all this to

1:06:14.842 --> 1:06:18.092
2,2, 2,2, 2,2,
2.

1:06:18.090 --> 1:06:19.120
That's what I would do.

1:06:19.119 --> 1:06:21.319
That's the change.

1:06:21.320 --> 1:06:23.110
Then I have to re-solve the
equilibrium.

1:06:23.110 --> 1:06:25.140
So how would that change?

1:06:25.139 --> 1:06:31.279
What would I change in my one
equation?

1:06:31.280 --> 1:06:35.090
Well, the apples in the
economy, the young apples,

1:06:35.090 --> 1:06:39.200
the guy's only got 2,
but the old's got 2 and there's

1:06:39.202 --> 1:06:42.212
still 1 apple coming from the
land,

1:06:42.210 --> 1:06:43.490
so that's still 5.

1:06:43.489 --> 1:06:45.579
But now every generation's
going to be behaving a little

1:06:45.583 --> 1:06:46.273
bit differently.

1:06:46.268 --> 1:06:50.008
They're going to have 2 when
they're young and 2 when they're

1:06:50.014 --> 1:06:50.394
old.

1:06:50.389 --> 1:06:53.659
This guy will have 2 when he's
young and 2 when he's old and

1:06:53.664 --> 1:06:55.444
otherwise it's the same thing.

1:06:55.440 --> 1:06:59.770
So I just re-solve for the
equilibrium.

1:06:59.768 --> 1:07:10.548
So if I re-solve for the
equilibrium multiplying by 2 p

1:07:10.547 --> 1:07:18.727
I'll have 2 2 p 4 p multiplying
by 2 p.

1:07:18.730 --> 1:07:21.780
Sorry, I just confused myself.

1:07:21.780 --> 1:07:23.650
I multiplied by 2 p.

1:07:23.650 --> 1:07:28.850
I've got 2 2 p multiplying by 2
p.

1:07:28.849 --> 1:07:34.939
I have 2 p here,
plus multiplying by 2 p I have

1:07:34.936 --> 1:07:37.446
2 p squared here.

1:07:37.449 --> 1:07:39.919
Hope I'm doing this right.

1:07:39.920 --> 1:07:42.860
And I've got 10 p on the right
like I had before.

1:07:42.860 --> 1:07:49.950
So now I've got 2 p squared -
10 p and that's 4 p,

1:07:49.945 --> 1:07:56.015
so it's still 6 p (it looks
like) 2 = 0.

1:07:56.019 --> 1:08:08.159
And so p = 6 or - 36 - 8 over 4.

1:08:08.159 --> 1:08:13.179
And so that,
I hope I did that right,

1:08:13.182 --> 1:08:17.092
I hope you're checking it.

1:08:17.090 --> 1:08:27.950
So that turns out to be p is
2.8, no.

1:08:27.949 --> 1:08:31.549
Social Security, p is .38 now.

1:08:31.550 --> 1:08:43.290
So now it equals .38.

1:08:43.288 --> 1:08:51.658
So 6 - square root of 28 so
it's working out pretty much,

1:08:51.659 --> 1:08:59.729
so .38 is the new price,
so therefore the interest rate

1:08:59.730 --> 1:09:02.870
1 over 1 r = .38.

1:09:02.868 --> 1:09:04.798
So what do you think happens to
the interest rate?

1:09:04.800 --> 1:09:08.160
So r now equals--before I write
it you can figure out what it is

1:09:08.162 --> 1:09:09.392
yourself in a second.

1:09:09.390 --> 1:09:12.710
Do you think the interest rate
went up or down in the new

1:09:12.707 --> 1:09:13.297
economy?

1:09:13.300 --> 1:09:15.500
What would Fisher have said?

1:09:15.500 --> 1:09:16.740
Student: Up.

1:09:16.738 --> 1:09:21.668
Prof: Up,
it went way up,

1:09:21.671 --> 1:09:27.241
and so it's actually 347
percent.

1:09:27.238 --> 1:09:31.628
So the interest rate went from
81 percent to--no that can't be

1:09:31.632 --> 1:09:32.212
right.

1:09:32.210 --> 1:09:39.190
It went to 161 percent.

1:09:39.189 --> 1:09:40.589
So the interest rate went up.

1:09:40.590 --> 1:09:43.920
So the loss is even worse than
it seemed before.

1:09:43.920 --> 1:09:46.470
Remember, in present value
terms, when you're young you

1:09:46.474 --> 1:09:49.224
give up 1 and when you're old
you get 1 and so you lose the

1:09:49.217 --> 1:09:50.067
present value.

1:09:50.069 --> 1:09:54.629
So the present value of that
trade is this plus that over 1

1:09:54.625 --> 1:09:54.935
r.

1:09:54.939 --> 1:09:57.419
Well, now that r has gone up
you're losing even more.

1:09:57.420 --> 1:10:00.630
So Social Security at the
current interest rates looks bad

1:10:00.626 --> 1:10:01.916
for every generation.

1:10:01.920 --> 1:10:04.070
After you do the Social
Security and everybody

1:10:04.070 --> 1:10:07.030
understands it's happening it's
going to be even worse in terms

1:10:07.034 --> 1:10:08.044
of present value.

1:10:08.038 --> 1:10:11.838
So Social Security,
again, everybody is giving

1:10:11.836 --> 1:10:15.376
something when they're young to
the old.

1:10:15.380 --> 1:10:18.590
So the guy at the very
beginning, at the very top,

1:10:18.591 --> 1:10:19.511
gains a lot.

1:10:19.510 --> 1:10:22.180
Everybody else,
every other generation loses

1:10:22.175 --> 1:10:25.945
and you can compute the utility
after Social Security compared

1:10:25.954 --> 1:10:29.864
to before Social Security and it
goes from something like 2.7 to

1:10:29.859 --> 1:10:30.479
2.3.

1:10:30.479 --> 1:10:34.089
So there's a substantial loss
for everyone's utility except

1:10:34.088 --> 1:10:35.768
for the first generation.

1:10:35.770 --> 1:10:38.650
On the other hand we rescued
the first generation.

1:10:38.649 --> 1:10:40.779
Now, there are two more
experiments.

1:10:40.779 --> 1:10:42.449
I'm not going to be able to
finish today,

1:10:42.445 --> 1:10:43.775
but I'm going to mention them.

1:10:43.779 --> 1:10:48.789
Experiment one is suppose we
had more and more children every

1:10:48.792 --> 1:10:49.882
generation?

1:10:49.880 --> 1:10:52.970
How would we take that into
account?

1:10:52.970 --> 1:10:56.200
Well, it's very simple to take
into account.

1:10:56.198 --> 1:11:00.938
The same thing with the trivial
change you can figure out what

1:11:00.944 --> 1:11:03.904
happens with more and more
children.

1:11:03.899 --> 1:11:05.069
So I'm going to go back to
(3,1).

1:11:05.069 --> 1:11:06.259
This will only take me one
minute.

1:11:06.260 --> 1:11:06.880
Sorry about this.

1:11:06.880 --> 1:11:12.750
I know time's running out,
but let me just finish this

1:11:12.752 --> 1:11:13.642
story.

1:11:13.640 --> 1:11:16.040
So if we had more and more
children in every generation,

1:11:16.038 --> 1:11:19.608
so every 30 years let's say the
population doubled,

1:11:19.609 --> 1:11:22.299
that's not such a high growth
rate per year,

1:11:22.300 --> 1:11:29.950
you'd have 6 and 2 here and
then it'd go up to 12 and 4.

1:11:29.948 --> 1:11:33.068
But, again, it's all
exponentially growing and the

1:11:33.067 --> 1:11:35.227
dividends would also be growing.

1:11:35.229 --> 1:11:39.859
So this would be 2 and 4 and 8
and 16 etcetera.

1:11:39.859 --> 1:11:43.409
But as you will see in a
second--I won't do it this time.

1:11:43.408 --> 1:11:46.168
Next time you'll see that it's
very easy to solve for the new

1:11:46.173 --> 1:11:46.823
equilibrium.

1:11:46.819 --> 1:11:49.179
You put a double here thing
because the young,

1:11:49.175 --> 1:11:50.845
there are twice as many young.

1:11:50.850 --> 1:11:53.060
You just solve it and you do
the whole thing.

1:11:53.060 --> 1:11:57.290
And what happens is Social
Security isn't solved.

1:11:57.288 --> 1:12:00.528
Samuelson was in a way wrong
again.

1:12:00.529 --> 1:12:04.879
Even though there are two young
people for every old person--so

1:12:04.880 --> 1:12:08.740
every young person only has to
give up half an apple.

1:12:08.738 --> 1:12:12.348
You only have to give up half
an apple when you're young and

1:12:12.349 --> 1:12:15.469
when you're old you still get a
whole apple back.

1:12:15.470 --> 1:12:18.330
It sounds like now surely you
should gain, but the point is

1:12:18.328 --> 1:12:20.938
you don't because the rate of
interest gets higher.

1:12:20.939 --> 1:12:23.479
And then we're going to have
generations that alternate in

1:12:23.475 --> 1:12:26.005
size, but all these are very
easy to solve once you figure

1:12:26.011 --> 1:12:26.591
this out.

1:12:26.590 --> 1:12:29.720
So on Thursday you have to
solve a problem just like that

1:12:29.717 --> 1:12:32.617
so you get the hang of it,
just one problem to do for

1:12:32.622 --> 1:12:33.352
Thursday.

1:12:33.350 --> 1:12:38.000