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