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48:00
Transcript
0:16
okay let's uh let's start so today we're
0:20
going to talk about technological
0:22
progress and economic growth
0:25
um I mean that's it's a big topic
0:28
certainly at MIT
0:31
perhaps this is one of the main ways we
0:33
contribute
0:36
to human well-being no um but before I
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0:41
do that let me let me H do a brief
0:43
review of of the things I did the second
0:46
half of the the previous
0:48
lecture for two reasons I want to do
0:50
that Brief Review first um is as after
0:54
spring break so I assume there is some
0:56
depreciation of knowledge H since the
0:58
last time and and the second is that
1:01
that while the equations I show you at
1:03
the end with population growth are
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1:04
correct I think I said something which
1:07
is not correct I think I kept saying I
1:10
don't know why but I kept saying look if
1:12
x is small 1/ 1 plus X is approximately
1:15
equal to Min - x no no it's
1:17
approximately equal to 1 - x not Min - x
1:20
but uh so I wanted to correct that that
1:24
typle so let me remind you what what we
1:27
had U so we had we started with a
1:31
production function one of an important
1:32
part of economic growth is we're going
1:34
to capital accumulation will be sort of
1:37
a very important variable here and so we
1:39
hadn't talked about capital in the
1:41
production function in the previous uh
1:43
part of the course but now we we were
1:46
explicit about it and we start with a
1:47
production function that constant
1:49
returns to scale h on Capital and labor
1:54
H and here remember in this part of the
1:57
course we're not talking about
1:58
unemployment or anything like that so
1:59
whenever I say labor I also mean
2:02
population I mean labor force all of
2:05
them together you know the distinction
2:07
between each of these Concepts but
2:08
they're not that important for growth
2:11
matters mostly because all of those
2:13
Aggregates sort of move in tandem over
2:15
the long run no it's very difficult for
2:18
for a
2:20
population and the labor force to
2:22
diverge for a very long period of time
2:25
you know there may be fluctuations and
2:26
so on but then tend to move together
2:30
um so but we decided that we wanted to
2:34
look at things normalized by by
2:37
population and so output per per person
2:41
is is an increasing function of capital
2:43
per person but also is is increasing at
2:46
a decreasing rate no there's decreasing
2:48
returns with respect to uh the capital
2:51
labor ratio and so output per capital
2:54
grows as capital per as the economy
2:56
becomes more Capital intensive that is
2:58
you have more Capital per worker
3:00
H but it grows at a decreasing rate the
3:03
second key equation of the our model was
3:05
that that assumed we're say in this part
3:08
of the course we're going to assume that
3:10
the government is not running any fiscal
3:12
deficit or anything like that and the
3:13
econom is closed which is an assumption
3:15
we have maintain and we will keep
3:18
assuming until three lectures from now
3:20
and so in close economy no fiscal
3:22
deficit we have that
3:24
investment is equal to saving and we
3:27
made an extra step to assume that the
3:30
saving is proportional to income okay so
3:33
s proportional to income so with all
3:35
these things together putting this two
3:37
things together H we got to our a very
3:41
important equation in any growth model
3:43
which is the capital accumulation
3:44
equation and this equation says well the
3:47
Capital stock tomorrow tomorrow means in
3:50
the next unit time next year or whatever
3:53
H H is equal to the current stock of
3:57
capital minus the depreciation of that
3:59
stock of capital minus Delta time KT
4:02
plus investment but investment is equal
4:04
to saving and saving is equal to H uh is
4:08
proportional to to Output okay so that
4:11
was the that was common across all the
4:14
things we did in the previous lectur is
4:17
there any question about these equations
4:19
no no good okay so the next step was to
4:22
say okay and and I did remember all the
4:25
initial derivations I assumed that n was
4:27
constant population was constant
4:30
and
4:31
so and the next step was I divided by a
4:34
constant here so we did everything in
4:36
terms of capital output per per person
4:40
but actually since population was
4:42
constant the per person part was just
4:45
the tri we just divide it by a constant
4:48
the last thing I did though in the
4:49
previous lecture was to say okay what if
4:51
not if that's not the case what if
4:53
population is growing over time as well
4:56
how does our analy change and so I did
5:00
this no I said well okay let's try let's
5:04
start by dividing everything by NT + one
5:07
so then we get Capital per uh person at
5:10
t+ one problem is I said is when I
5:13
divide the right hand side by NT plus
5:15
one I don't get what I want I want
5:17
Capital at T divided by population of T
5:20
I want output at T divide by population
5:23
of T not at t+ one okay so what I did is
5:27
I multiply and divide by n T both of
5:31
these so I multiply by one NT over NT is
5:35
one so I multiply by one everything and
5:38
then rearrange terms so I got
5:40
expressions like this no I got what I
5:43
wanted here which is capital per ER
5:47
person at the same point in time and but
5:50
now it's multiply by NT over NT + one
5:55
okay
5:56
H um and the same I can do for this uh
5:59
another expression
6:01
here okay so so this is what I'm using
6:04
the approximation here in which X is
6:06
equal to GN okay this in here is just 1
6:10
over 1 plus GN and I'm saying this is
6:13
approximately equal I can approximate if
6:15
GN is a small number this is
6:17
approximately equal to 1 minus GN okay
6:20
so that's what we have and this is a
6:22
second
6:24
approximation going from this line to
6:26
this line in which we did the following
6:29
it said okay
6:30
you know this is equal to uh 1us
6:35
Delta uh minus
6:39
GN
6:41
plus Delta * GN but the Delta time G is
6:46
the multiplication of two small numbers
6:48
so I said assume that is close to zero
6:50
and the same we had here we had saving
6:53
rate * 1 + GN you get you get the saving
6:58
rate h plus the saving rate times GN but
7:02
the saving rate times GN is also small
7:05
number so we also drop okay so those are
7:07
the more explicit steps of what I did in
7:10
the previous lecture and I think the
7:11
final equation I showed you was this but
7:14
it comes from again two approximations
7:16
the one down here which I use here and
7:20
then the fact that I dropped the second
7:22
order terms okay that's it and then I
7:26
just rearrange things I move K KT over n
7:29
to the left hand side and so we have the
7:31
change in the stock of capital per
7:33
person is an increasing function of
7:38
investment uh per person which is this
7:41
because this is saving per person and I
7:43
can replace this by the production
7:45
function no which is f of K Over N and
7:48
so what I have here is a difference
7:50
equation in capital per
7:55
person why is this so so what so this is
7:59
investment so the Capital stock per
8:01
person will be growing as we
8:03
invest the it shrinks with the passage
8:07
of time just because of depreciation
8:08
some things break down that reduces the
8:10
stock of capital but the new term that
8:13
we introduce at the end of last lecture
8:15
is is that that now this ratio also
8:18
declines H with population growth and so
8:22
who can explain why we get this ter
8:30
you know I'm saying look suppose that
8:33
that that
8:35
H that we have take a given amount of
8:38
investment we take as given depreciation
8:41
but now we I I say well if if GN Rises
8:44
and all the rest remains constant
8:47
then the left hand side will start
8:50
declining or will grow less rapidly than
8:52
what going to grow before a increase GN
8:55
why is what do the case but
8:59
sometimes it's counter inuitive that's
9:01
the reason I want I I thought I rush in
9:03
the previous lecture over that and I
9:06
since it's going to be an important
9:07
intermediate step into the next one
9:10
which is when introduce technological
9:12
progress I want us to understand why
9:14
that GN appears with a negative sign
9:19
there
9:22
yep for the same amount of capital that
9:24
increased
9:28
inor that that
9:30
term
9:32
ER is going to be captured
9:35
here and it's going to play a role but
9:38
this one comes from something much more
9:40
mechanical than
9:43
that hint observe what I have on the
9:47
left hand side I don't have on the left
9:49
hand side the change in the stock of
9:53
capital I have the change in the stock
9:55
of capital per
9:57
person so suppose I don't change the
9:59
stock of capital at all from this period
10:02
to the next but population grows what
10:06
happens to this expression
10:08
here decreases it becomes negative
10:11
because I haven't changed the Capital
10:13
stock but the denominator is growing
10:15
that's the GM part and that means this
10:17
turns negative and that's what this term
10:20
is is here for is to capture the fact
10:23
that the denominator now is also moving
10:26
on the left hand side variable and and
10:28
you say so what but I at the end of the
10:30
day I care about the capital capital why
10:32
why do I care about Capital per person
10:35
well for all my analysis I told you it's
10:38
much easier if I do it on something
10:39
which it has a steady state that's the
10:42
reason I'm looking for this
10:43
normalization but once I look at the
10:46
dynamic equation of accumulation of
10:48
capital in
10:49
this divided by population then I need
10:52
to take into account the fact that my
10:54
denominator is also moving okay so
10:56
that's the reason that GN is there and
10:59
and again the reason I wanted to pause
11:00
on this is because when we introduce
11:02
technological progress we're going to
11:03
have a similar effect and and and so I
11:05
want you to it's going to be counter
11:07
intuitive because it sounds like
11:09
technological progress is something
11:10
negative no it's not
11:12
negative but but in this space it turns
11:15
out that if population grows very fast
11:19
then you need a lot of investment to
11:20
keep up the the capital labor ratio
11:24
constant okay that's the idea if
11:27
population is not growing I don't need
11:29
need a lot of investment to keep the
11:30
capital labor ratio constant but if
11:32
population is growing very fast then I
11:34
need a lot of investment to really keep
11:36
that ratio constant that's what this is
11:38
capturing there
11:41
so to repeat if if this guy is is is
11:45
very large then I need a lot of
11:47
investment here to make this thing equal
11:50
to zero so the Capital stock per person
11:52
is not declining that's idea
11:58
okay
11:59
good okay so now ah and then I said okay
12:04
this is where we finish then I said okay
12:06
so let's go uh back to our diagram I can
12:09
once I have everything in this space K
12:12
Over N I can go back to our diagram
12:16
assume that GA is equal to zero you
12:17
don't even know what A is for the time
12:19
being you will know in five minutes but
12:22
assume GA is equal to zero then that's
12:24
exactly the model we had before
12:27
so and remember this this is exactly the
12:29
same diagram it looked the same at least
12:31
that we had when population was not
12:33
growing I'm saying I can use the same
12:36
diagram when population is growing as
12:39
well but there is one important
12:42
difference which is this this curve
12:45
looks exactly the same this is just
12:47
output H per per worker okay that's the
12:51
Blue Line the green line looks exactly
12:54
the same as in the basic model it's just
12:57
little s times that the blue line so
12:59
that's exactly the same but this line is
13:02
different what happens to this red line
13:05
as as GN goes up so what happens to this
13:09
line as GN goes
13:12
up becomes steeper no yeah so it rotates
13:15
up okay goes up and that can sound
13:20
counterintuitive sometimes because you
13:22
say look look what happens here let's
13:24
spend time on
13:26
this suppose that we are at some St
13:28
state say this
13:31
one and now population growth
13:36
Rises okay it sounds like Ireland in you
13:40
know 2000s and
13:43
so so population growth Rises a
13:47
lot what happens in this diagram so
13:49
suppose we're at the state state
13:53
here no and that the state
13:57
investment uh saving which is equal to
14:00
investment is exactly what you need to
14:01
maintain the stock of capital per person
14:03
constant okay that's what the red line
14:06
tells us no that here so that's the Gap
14:11
here is this is a gap between investment
14:13
and what you need to maintain the stock
14:15
of capital per person constant so when
14:18
the Gap is zero then then this equation
14:21
this left hand side is equal to zero
14:23
okay that's the red line that's the
14:26
green line when this is equal to Z
14:29
that's equal to that that's exactly that
14:32
point okay but I'm saying suppose we are
14:35
at that point and
14:37
now population growth
14:40
Rises so what moves in that diagram does
14:43
a blue line
14:50
move I don't see GN in the blue line so
14:53
the Blue Line doesn't move if the Blue
14:55
Line doesn't move and the saving rate
14:57
hasn't changed then the green line
14:58
doesn't move move
15:00
either so for this diagram to be
15:02
interesting what moves assum has to move
15:05
so the only thing that has that can move
15:07
here is the is the red line and the red
15:10
line we already said if GM goes up it's
15:13
going to rotate
15:15
upwards that
15:16
means say so now we have that line there
15:20
so what happens at the at the at the
15:23
previous St State stock of capital per
15:26
worker at this level what happens is
15:29
that a new state
15:32
state no but what happens in particular
15:37
what is it so I'm saying suppose that
15:39
you're here and now I rotate the red
15:41
line
15:42
up okay so that means the red line that
15:45
represents the amount of capital I need
15:47
to maintain the stock of capital
15:49
constant is greater than how much
15:53
Society saving and therefore investing
15:56
so what will happen to Capital per
15:57
worker
16:02
decrease exactly because you need more
16:05
than you're investing so the Capital
16:08
stock has to decline and that's what
16:10
will happen the new state state is going
16:11
to be to the left of that point
16:14
there that sounds very
16:16
weird how can it be that you know after
16:20
all labor contributes to Output how can
16:23
it be that we end up with a
16:25
lower ER output per per worker when we
16:28
increase popul population growth is
16:30
population growth bad in a sense for
16:33
growth itself for
16:41
output well the answer is no it's it's
16:44
true that the new state state will have
16:47
lower output per person so in that sense
16:50
it's bad you have lots of population if
16:52
you if if you don't change the saving
16:54
rate or something then output per person
16:57
will be lower but output will be higher
17:00
than it used to be at any point in time
17:02
it just happens that in the transition
17:05
the growth of output so so the growth
17:08
the growth of output in this model is
17:10
going to be equal to the growth of
17:13
population okay that's if you have a St
17:16
state where population is growing and
17:18
output per worker or per person is not
17:20
growing that means output is growing at
17:23
the same rate as population so that
17:25
means that if I increase the rate of
17:26
population growth the rate of growth
17:29
output will
17:30
increase together with the rate of
17:32
growth of population but in the
17:34
transition as the output per capita goes
17:36
lower output will grow less than
17:39
population that's what is happening here
17:41
okay but output is growing if you
17:43
population starts growing if you
17:44
increase migration you're going to see
17:46
output grow but output per person will
17:50
start declining until you get to New
17:53
State and then you'll get the same
17:56
ER you'll get the higher rate of growth
17:59
you continue with population growth with
18:01
the high population growth but output
18:03
per worker would be slightly lower rate
18:09
okay anyways this may have been fast the
18:12
last part but since I'm going to repeat
18:14
it now in the context of technological
18:16
progress we should be fine okay so if
18:19
you're a little confused now it's okay
18:21
if you're a little confused at the end
18:24
of the lecture it's not okay because
18:25
that's I'm counting with you sort of
18:28
getting it in the second pass okay
18:30
second try Okay so next step is is f so
18:34
here we assume already population growth
18:37
where we assume that technology so the
18:39
production function sort of stay put for
18:42
any combination of capital and labor the
18:44
next step is to think what happens when
18:48
the technology itself is getting better
18:50
over time and that's what we call
18:53
technological progress okay this is tfp
18:58
let me not get into to specifics at the
18:59
end I'll say a little more but P tfp
19:03
stands for total Factor productivity and
19:05
this index here captures the level of
19:08
tfp in the
19:09
US over time and it's clearly growing so
19:12
technolog is getting better and better
19:14
over time what that means well it I say
19:17
a little more not a lot more but but
19:19
it's getting
19:21
better no h and so the question we have
19:25
here is I'm going when to address next
19:27
is how does this so now we're going to
19:30
put together our entire economic growth
19:32
model we're going to have population
19:33
growth we're want to have also
19:35
technology growing up to now the only
19:37
reason you could
19:39
grow a you could grow output per per
19:42
worker was because you were accumulating
19:44
lots of capital you were catching up
19:46
with you're a steady state that's what
19:47
would make you grow faster but then
19:49
there was nothing else tfp is going to
19:53
be the only growth in technology is
19:55
going to be the only thing that will
19:57
give you sustainable growth in the long
19:59
run an output per person okay so this is
20:02
a very important component of of H of
20:07
growth again it's the only thing that
20:09
will make you grow in a sustainable
20:11
manner in in per person terms okay the
20:15
previous model didn't have that in the
20:17
previous model we had a steady
20:20
state ER on on output per worker so in
20:24
the previous model we didn't have growth
20:26
in output per worker in the St state
20:29
we could have transitional growth when
20:31
we were catching up no if you if you
20:34
started
20:35
here then you were going to have growth
20:38
fast growth but eventually will pet it
20:41
out okay out work so so up to now we
20:45
don't have a reason for why to to to
20:48
explain why we see that output per
20:51
worker grows in most economies in the
20:54
world and the answer will be this this
20:57
is the reason really how output per
20:59
worker can grow in a sustained manner
21:00
it's technolog is getting better and
21:02
better over time so let's let's see so
21:05
the question is let's now see what this
21:08
does to the model we
21:11
have now in practice technological
21:15
progress takes many many forms er
21:19
um it in at most basic level means that
21:24
you can produce larger quantities output
21:26
and that's really the meaning we're
21:27
going to have here larger quantities of
21:29
output for the same amount of capital
21:31
and
21:32
labor okay so you have 10 machines 10
21:35
workers technological progress means
21:37
well you used to produce 12 units now
21:40
we're going to produce 12 14 15 and so
21:43
on so forth that's that's a one way of
21:46
techn that one of the main ways
21:49
technological progress shows up we can
21:51
do more with the same if you will second
21:55
dimension is better product so it's not
21:57
that you produce more cars but you
21:59
produce better cars better computers and
22:01
so on okay that's another dimension of
22:04
technal prod you can produce new
22:06
products things that didn't even exist
22:09
but now you
22:10
have that counts more than having one
22:13
more unit of good it counts more because
22:14
you have you know things that you
22:16
couldn't even satisfy in the past you
22:18
can satisfy now because you have the
22:20
certain kind of goods that DNX is before
22:22
that's a very important dimension of
22:25
technological progress is just create no
22:28
new sort of forms of inputs of
22:30
production and Technologies think of AI
22:34
what that will do to to technology in
22:36
general and to consumption very
22:38
directly ER and that's what I mean even
22:43
within a product you you can get more
22:45
variety and more variety you know
22:46
improves welfare because you can align
22:48
better the needs H with with the product
22:53
and so on but we're going to make it
22:54
very simple in this in this in this
22:57
course we're going to we're going to
22:59
model technological progress as if it
23:02
was
23:03
workers okay so
23:06
uh we're going to capture technology
23:10
with this Con with this variable a which
23:13
is going to be we're going to model it
23:15
as labor equivalent that is if a grows
23:20
it's going to count for us as if we had
23:23
more
23:24
workers okay that's just one way of
23:26
model it I mean I can I can do it in
23:28
many different ways andan some many of
23:30
these are equivalent but that's a very
23:32
very nice way of modeling so we can use
23:34
exactly the same diagrams we have and so
23:37
okay so you can think of technological
23:39
progress the way I'm going to model this
23:40
here is you can think of technological
23:42
progress as if this economy was
23:45
receiving more
23:46
workers okay or a more accurate
23:50
description is with the same workers it
23:53
can produce is as if he had more labor
23:56
input okay that's that's one way of
23:58
capturing technology technological
24:01
progress so now that means that I'm
24:04
going to refer to this term a n as
24:07
effective labor you know so with the
24:11
same number of n bodies I may get more
24:13
effective label because each worker can
24:15
produce more things it's a better input
24:18
of production factor of production
24:21
okay so it and I like to mod it this way
24:25
because now I can use exactly the same
24:26
diagrams we had before but rather than
24:29
normalizing by population I'm going to
24:32
normalize by effective labor by a n
24:37
okay
24:38
so let me do that so recall that we had
24:41
our production function with constant
24:43
return so this hold I'm going to set
24:46
this x now as 1/ a n we used to have 1/
24:50
n I'm going to have 1/ a n and so I'm
24:53
going to now have output per effective
24:56
worker is going to be also the same
24:59
little function f of capital per
25:02
effective
25:03
worker okay and what is nice of this is
25:06
that now here rather than plotting y
25:08
Over N I'm going to PL plot y over a n
25:12
rather than plotting K Over N here I'm
25:13
going to plot K over a n and I have the
25:16
blue line looks exactly like it used to
25:19
look it's just I'm dividing by a Over N
25:21
remember the trick in all these models
25:24
is to find the right normalization that
25:26
is to find the right X so I can find
25:28
find a steady state in my diagram I
25:30
don't want these curves to be moving
25:32
around I want this to have a a steady
25:34
state something a point that that we're
25:36
going to converge to after enough time
25:38
has passed okay and I know that that the
25:42
thing that will do it in a model in
25:43
which I have popul effective workers
25:45
growing is one in which I divide
25:47
everything by effective
25:50
workers okay so that's what I'm doing
25:52
here I'm going to build a diagram that
25:54
looks like the other one that has a nice
25:55
steady state as the previous one had
25:58
okay so I have my blue line you I have
26:00
my blue line I know I have my green line
26:02
no because the green line was just
26:03
little s times the blue line so I have
26:06
that the last thing I need and I already
26:09
show you that but I'm going to show it
26:11
again is is the is the red line okay but
26:14
for the red line I need to find this
26:17
term the term remember the red line
26:19
represents the capital we need to
26:21
maintain the current stock of capital
26:24
per effective worker constant that's
26:26
what I need my red line for so let's get
26:29
there and it always start from this
26:31
equation so this equation is still the
26:32
same as it used to be that doesn't
26:34
change but what I'm going to do now is
26:36
rather than dividing by n I'm going to
26:39
divide by a * n so the same as I did
26:43
earlier in this lecture I now want to
26:45
divide by a Over N so I get Capital per
26:48
effective work on the left hand side I
26:51
don't like what I get here but you know
26:53
that I can divide and multiply by a n n
26:57
over a n so I can write the right hand
27:00
side after do all my substitutions as
27:03
this
27:04
okay you know so I first step one I
27:08
divided everything by a t + 1 * NT + 1
27:13
step two I multiply each of these terms
27:16
by a and t i multiply by AT and T divide
27:19
by AT and T and T okay and then I
27:22
regroup things so I end up with that
27:25
well this using the approximation we
27:27
have here here is equal to approximately
27:31
equal to 1 minus g
27:33
n and g
27:41
n is equal to
27:45
GA plus
27:48
GN okay so I already show you that that
27:51
case for the case in which GA was equal
27:53
to zero I'm doing now the same thing but
27:57
but you know since I renormalize things
27:59
by effective workers effective labor
28:03
rather than actual label I need to use a
28:06
n rather than
28:08
n okay and then by the same
28:10
approximation I had before which is that
28:12
you know these products are close to
28:15
zero then I get to the equation I want
28:18
and if I write it in first difference
28:20
then I get my Red Line This is my red
28:22
line
28:24
here okay
28:28
good
28:29
so H in um this tells me that when the
28:35
ER the green line green line is equal to
28:38
the red line then I have a steady state
28:42
capital perfective worker is constant
28:44
that this this is equal to zero that's
28:45
the way I find my steady state if I ask
28:47
you a question find the steady state of
28:49
this economy what you'll do is you'll
28:51
set this equal to zero and find the
28:54
Capital stock that gives you this equal
28:56
to zero that's the way you do it okay
29:00
so so that's that's that and then we get
29:04
back to
29:06
um well this is this is the same as we
29:09
had
29:10
before that's what I just said that's
29:13
the way you find the stud State okay and
29:16
then we get back to the diagram I
29:18
started with in this lecture okay but
29:21
now we have here a a n and now in in in
29:25
the first part I said assume this G ga
29:28
GA is equal to zero now the main actor
29:32
is GA positive okay and and we get this
29:36
diagram so now I can ask you the
29:38
question that that that I asked you
29:39
before with population growth and see
29:42
how much I can confuse you suppose that
29:45
GA goes up that sounds like a good thing
29:48
no I mean ER suppose that we're at the
29:50
steady state here and I mean this
29:54
diagram has too much stuff let me
29:59
[Music]
30:19
okay so we're
30:22
here that's our initial
30:26
State um
30:37
zero and and this line here is Delta
30:42
plus
30:44
GA plus
30:49
GN * K over a n okay
30:55
so the question well first let's let's
30:59
so suppose we're at the say
31:03
state is output constant there I mean
31:08
that's it's a state state it's output
31:11
output constant there so suppose we are
31:14
at that
31:17
point here here we know that investment
31:21
exactly how much we need to maintain the
31:24
stock of capital per effective worker
31:26
constant that's what what the state
31:28
state
31:29
means question is output constant
31:33
there state
31:48
state
31:51
no this only says
31:54
that Capital per effective work
31:58
is constant that means that if effective
32:01
workers or labor is growing then capital
32:05
is growing at the same rate and
32:07
therefore output is growing at the same
32:10
rate as effective workers okay that's
32:15
the reason remember the whole trick so
32:17
the curves would not be moving around is
32:19
I find the right normalization so
32:21
everything is growing at the same rate
32:23
in that St
32:24
State okay
32:29
so let me actually show you that and
32:30
then I'm going to go over the experiment
32:33
I want to have so this is what is
32:35
happening in that steady
32:37
state so Capital per effective worker at
32:42
the steady state so at that point
32:45
there is zero no that's a stady that's
32:49
my definition of a steady state okay
32:52
output effective worker is also growing
32:55
at at at the rate zero that's that one
32:58
over there
33:01
sorry that's my state level of output
33:05
per effective worker
33:11
okay so these are constant that's a say
33:14
State those are constant this ratio is
33:18
constant each of those components is
33:21
not
33:22
so that's what I'm plotting there so
33:25
that's those are not growing Capital per
33:30
worker what about that well you you see
33:33
there explain why why so claim Capital
33:37
per worker is growing at the rate GA how
33:41
do I know that
33:54
[Music]
33:58
so the question I'm asking
34:01
there is what is the rate of
34:05
growth of k/
34:14
n Pro given that I already know that the
34:18
rate of growth of K over a
34:24
n is equal to zero
34:34
well this the rate of growth of K Over N
34:38
is the rate of growth of K over a n plus
34:45
the rate of growth of
34:47
a
34:49
no I mean if a is growing and this ratio
34:53
is
34:54
constant that means that k/ n must be
34:57
growing
34:59
and it has to be growing at exactly the
35:00
same rate as this a is growing otherwise
35:04
I wouldn't be able to maintain that
35:05
ratio
35:07
constant
35:09
okay and the same logic applies
35:12
to Output per worker because in that
35:15
steady state output per effective worker
35:18
is
35:19
constant but a is growing so output per
35:23
worker must be growing at the same rate
35:26
as a is growing and that's
35:28
G okay
35:31
good labor well labor is exogenous which
35:34
say population is growing at the rate n
35:36
that's given what about
35:40
Capital an output well claim capital and
35:44
output are growing at the rate GA plus
35:49
GN and I can do the same as I was in
35:52
here I'm asking you the question GK what
35:56
is the rate of growth of GK
35:58
well is going to be equal to the rate of
36:01
growth of k/
36:03
n plus the rate of growth of
36:09
n okay this is equal to
36:14
GA so it's G Plus
36:16
GN and the same happens for uh
36:22
um for
36:24
output
36:25
okay so that's what is remember I said
36:28
earlier on that
36:30
that if an economy has more population
36:32
growth it will grow
36:34
more okay there's no doubt of that
36:38
obviously output per worker will not
36:40
grow more because population growth
36:42
grows more in the new state G doesn't
36:44
show up
36:46
there okay but the only thing that will
36:48
make output per
36:51
worker grow is technological progress so
36:54
it's
36:55
G that was my claim
37:01
earlier there's another we're going to
37:04
use this later
37:09
but
37:13
um
37:15
um no I'm not going to do this myself
37:19
now we're I'm going to get back to what
37:21
I wanted to do now because I need to
37:23
tell you a little bit more about the
37:24
production function to do growth
37:26
accounting um which is what I wanted to
37:29
do so but this is clear I mean this is
37:34
important
37:36
okay
37:38
good so this is the reason GA is such an
37:40
important variable what you guys do here
37:43
at MIT is very important afterwards very
37:46
important
37:48
okay that's the only thing that can
37:49
drive really growth in the long run in
37:52
per
37:54
capita this GM plays also role I mean
37:58
you look at countries not only the
38:00
growth in per capita output you'll tend
38:02
to look at growth a total growth one of
38:05
the big concerns in big parts of Asia
38:07
now in Europe as well as I said earlier
38:10
in the course is that g is turning
38:13
negative that's not going to affect
38:15
output per worker growth but it does
38:18
affect output growth in general okay and
38:23
you can see it here so if G goes down
38:26
that will reduce the rate of growth of
38:29
output doesn't reduce the rate of growth
38:31
output of worker but it does reduce the
38:33
rate of growth of
38:34
output
38:37
good so what happens remember we did in
38:40
the in the in the in the basic model we
38:42
did an experiment in which we increase
38:44
the saving rate so we can do the same
38:48
here what happens if we get an increase
38:49
in the saving rate do we get more growth
38:53
in the long run and the answer is for
38:55
the same reasons we had before no
38:58
if we increase the saving rate in this
38:59
now this full model all that happens is
39:02
that this green line moves up it means
39:04
that at initial St State now we have
39:06
more saving and therefore more
39:08
investment than we need to maintain the
39:09
stock of capital per effective worker
39:11
constant which means that we're going to
39:13
get transitional growth Capital per
39:16
effective worker will start growing for
39:18
a while and as that happens output per
39:21
effective worker will also start
39:24
growing okay but eventually the
39:27
increasing returns will kick in here as
39:29
well and we are going to that
39:31
transitional growth will stop and H will
39:35
end up at a higher level of output per
39:38
effective worker and a higher level of
39:40
capital per effective worker but the
39:41
rate of growth in the long run will not
39:44
be affected by the saving rate we'll get
39:46
more transitional growth but we will not
39:50
get a faster long-term
39:54
growth a lot of the Asian Miracle that's
39:58
that the Southeast Asian milon in
39:59
particular we saw very fast rates of
40:02
growth in many economies of
40:05
Asia was a lot of that kind meaning was
40:08
a combination of what we had before
40:11
economies that were relatively poor had
40:13
low Capital per work early on in which a
40:16
saving rate increased enormously and
40:18
that combination gave them
40:20
enormous a transitional growth so rate
40:23
of growth of 10 12% that was Japan and
40:26
then it was Korea Taiwan and so on all
40:29
those economies had very fast rates of
40:30
growth as a result of that China later
40:33
on and China was a big thing for the
40:35
world because it was much bigger at the
40:37
same time but it was mostly a
40:39
combination of those two things it was
40:41
being having a low stock of capital
40:43
early on combined with for a variety of
40:47
reasons and increasing the saving rate
40:49
and that combination so gave them very
40:51
fast transitional growth but they're all
40:54
getting a little stuck now and they're
40:56
very concerned with that well they're
40:58
fighting against this model there's lots
41:01
of concerns of what is happening to
41:02
China are we going to follow the Japan
41:05
path and so on well they're following
41:07
this model that's what's happening to
41:09
aair
41:12
order I I'll say a little bit more later
41:15
on about that so in this particular case
41:18
no what what what I have done is in log
41:21
space so I can have linear things when
41:23
it's growing in log space this economy
41:27
with the the low saving rate was
41:29
growing here the slope of this was this
41:33
is output so the slope of this was GA
41:35
plus GN remember in a stady state output
41:38
is growing at GA plus GN if the saving
41:41
rate now increases then output starts
41:44
growing transitionally faster than GA
41:46
plus GN that's the reason sort of output
41:49
grows faster than G here is all is
41:51
growing faster than G here is very fast
41:54
okay this is when we saw in Asia the
41:56
rate of growth of 12% and stuff like
41:58
that we were there moving there and and
42:02
and but eventually it sort of PS out you
42:04
end up with a higher level of output per
42:06
capita per
42:08
worker a higher sort of path no it's an
42:12
entire path the rate of growth goes back
42:15
to GA plus
42:16
GN er uh but but you get this
42:19
transitional growth which is very
42:22
strong and once you're here once you all
42:25
you run out of sort of the high saving
42:27
and the catching up growth and so on
42:29
there is little the only way you're
42:31
going to really change your rate of
42:33
growth in a sustained manner is doing
42:39
what once you have used the tool of you
42:42
know of catching up with the world of
42:45
increasing your saving rate sometimes to
42:48
levels incredibly High you still want to
42:51
keep growing very fast what is the only
42:54
option you have according to this model
43:06
particularly let me bring even more ER
43:11
realism to the story particular if GN is
43:13
dropping and you still want to keep your
43:15
growth high and your GN now you sort of
43:18
use the catching up growth you use the
43:21
higher saving rate which gives you
43:22
transitional growth but it doesn't give
43:24
you permanently higher rate of growth
43:26
and on top of that for reasons you don't
43:27
control population growth is declining
43:29
even turning negative in some
43:32
cases but suppose you still want to keep
43:34
the rate of growth very high what is the
43:36
only option you
43:41
have increase G exactly technological
43:44
progress that's the only option you have
43:46
so it makes sense you see that you know
43:48
in the case of china they're obsessed
43:49
about technology and so on they
43:51
understand the solo model okay if you
43:54
want to maintain growth at a high Pace
43:56
you you're going to need to work on that
43:58
side a lot now it doesn't have to be you
44:01
necessarily it's the world as a whole
44:03
because technology you know moves around
44:05
the world but but GA is at the end what
44:08
puts the limits of what we can
44:12
do ah what I what I was going to do is
44:15
that's what I was drawing this diagram
44:17
for is say well suppose that in this D
44:20
this situation we are in a state state
44:22
and we do increase
44:24
GA what happens if we increase ga a well
44:27
this
44:29
curve rotates up no and at that point
44:34
it's clear that that if if GA grows
44:37
you're going to start growing at a
44:38
faster rate but transitionally actually
44:41
you're going to grow less than in your
44:43
long-term rate of growth why is that the
44:47
case so my claim is suppose we manage to
44:51
increase GA so now we know that this
44:55
line here now going to a um be steeper
45:00
or say this we were in this line
45:03
whatever we were in this line and now we
45:05
make it a steeper so we're want to start
45:06
growing faster eventually in the new
45:09
state state and my claim now is that in
45:11
the
45:12
transition growth is less than the new
45:15
rate of growth in the new in the new
45:16
state state rate of
45:18
growth is higher than the rate of growth
45:21
of the previous St state but it's lower
45:24
than the long run how do I see that I
45:27
need another diagram you
45:36
think so let me
45:39
just put the the s y curve
45:45
here so we were
45:48
here at this state if I increase GA the
45:54
only thing that will move here and
45:55
remember the output equation is there
45:57
but I don't want to put it the only
45:58
thing I do is I rotate this curve
46:02
up okay so this moves
46:07
up do you see yes so this curves moves
46:11
up when
46:12
GA goes up so at the oldest steady state
46:16
what I have now is a gap between the
46:19
saving this economy investment and how
46:21
much I need in order to maintain Capital
46:24
per effective worker constant
46:27
which means that I'm going to start
46:29
moving in this direction until I reach
46:33
the new stady
46:34
state okay during this transition I'm
46:37
growing at a lower Pace than in the new
46:40
steady state in this new steady state I
46:43
be
46:46
growing much faster than in this state
46:48
how much faster well equal to Delta GA
46:51
but in the transition I will grow faster
46:53
than that but not as fast as in the new
46:55
today St that's the name was
47:06
making H okay
47:15
good do I you know i' rather discuss
47:18
this with more time so questions about
47:20
what we have done up to now
47:31
is it clear or is it very unclear and
47:34
probably
47:38
both so let me I I I want to let me keep
47:42
this for the next the next lecture
47:43
because going to take a little time just
47:45
play okay
— end of transcript —
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