[00:16] okay let's uh let's start so today we're
[00:20] going to talk about technological
[00:22] progress and economic growth
[00:25] um I mean that's it's a big topic
[00:28] certainly at MIT
[00:31] perhaps this is one of the main ways we
[00:33] contribute
[00:36] to human well-being no um but before I
[00:41] do that let me let me H do a brief
[00:43] review of of the things I did the second
[00:46] half of the the previous
[00:48] lecture for two reasons I want to do
[00:50] that Brief Review first um is as after
[00:54] spring break so I assume there is some
[00:56] depreciation of knowledge H since the
[00:58] last time and and the second is that
[01:01] that while the equations I show you at
[01:03] the end with population growth are
[01:04] correct I think I said something which
[01:07] is not correct I think I kept saying I
[01:10] don't know why but I kept saying look if
[01:12] x is small 1/ 1 plus X is approximately
[01:15] equal to Min - x no no it's
[01:17] approximately equal to 1 - x not Min - x
[01:20] but uh so I wanted to correct that that
[01:24] typle so let me remind you what what we
[01:27] had U so we had we started with a
[01:31] production function one of an important
[01:32] part of economic growth is we're going
[01:34] to capital accumulation will be sort of
[01:37] a very important variable here and so we
[01:39] hadn't talked about capital in the
[01:41] production function in the previous uh
[01:43] part of the course but now we we were
[01:46] explicit about it and we start with a
[01:47] production function that constant
[01:49] returns to scale h on Capital and labor
[01:54] H and here remember in this part of the
[01:57] course we're not talking about
[01:58] unemployment or anything like that so
[01:59] whenever I say labor I also mean
[02:02] population I mean labor force all of
[02:05] them together you know the distinction
[02:07] between each of these Concepts but
[02:08] they're not that important for growth
[02:11] matters mostly because all of those
[02:13] Aggregates sort of move in tandem over
[02:15] the long run no it's very difficult for
[02:18] for a
[02:20] population and the labor force to
[02:22] diverge for a very long period of time
[02:25] you know there may be fluctuations and
[02:26] so on but then tend to move together
[02:30] um so but we decided that we wanted to
[02:34] look at things normalized by by
[02:37] population and so output per per person
[02:41] is is an increasing function of capital
[02:43] per person but also is is increasing at
[02:46] a decreasing rate no there's decreasing
[02:48] returns with respect to uh the capital
[02:51] labor ratio and so output per capital
[02:54] grows as capital per as the economy
[02:56] becomes more Capital intensive that is
[02:58] you have more Capital per worker
[03:00] H but it grows at a decreasing rate the
[03:03] second key equation of the our model was
[03:05] that that assumed we're say in this part
[03:08] of the course we're going to assume that
[03:10] the government is not running any fiscal
[03:12] deficit or anything like that and the
[03:13] econom is closed which is an assumption
[03:15] we have maintain and we will keep
[03:18] assuming until three lectures from now
[03:20] and so in close economy no fiscal
[03:22] deficit we have that
[03:24] investment is equal to saving and we
[03:27] made an extra step to assume that the
[03:30] saving is proportional to income okay so
[03:33] s proportional to income so with all
[03:35] these things together putting this two
[03:37] things together H we got to our a very
[03:41] important equation in any growth model
[03:43] which is the capital accumulation
[03:44] equation and this equation says well the
[03:47] Capital stock tomorrow tomorrow means in
[03:50] the next unit time next year or whatever
[03:53] H H is equal to the current stock of
[03:57] capital minus the depreciation of that
[03:59] stock of capital minus Delta time KT
[04:02] plus investment but investment is equal
[04:04] to saving and saving is equal to H uh is
[04:08] proportional to to Output okay so that
[04:11] was the that was common across all the
[04:14] things we did in the previous lectur is
[04:17] there any question about these equations
[04:19] no no good okay so the next step was to
[04:22] say okay and and I did remember all the
[04:25] initial derivations I assumed that n was
[04:27] constant population was constant
[04:30] and
[04:31] so and the next step was I divided by a
[04:34] constant here so we did everything in
[04:36] terms of capital output per per person
[04:40] but actually since population was
[04:42] constant the per person part was just
[04:45] the tri we just divide it by a constant
[04:48] the last thing I did though in the
[04:49] previous lecture was to say okay what if
[04:51] not if that's not the case what if
[04:53] population is growing over time as well
[04:56] how does our analy change and so I did
[05:00] this no I said well okay let's try let's
[05:04] start by dividing everything by NT + one
[05:07] so then we get Capital per uh person at
[05:10] t+ one problem is I said is when I
[05:13] divide the right hand side by NT plus
[05:15] one I don't get what I want I want
[05:17] Capital at T divided by population of T
[05:20] I want output at T divide by population
[05:23] of T not at t+ one okay so what I did is
[05:27] I multiply and divide by n T both of
[05:31] these so I multiply by one NT over NT is
[05:35] one so I multiply by one everything and
[05:38] then rearrange terms so I got
[05:40] expressions like this no I got what I
[05:43] wanted here which is capital per ER
[05:47] person at the same point in time and but
[05:50] now it's multiply by NT over NT + one
[05:55] okay
[05:56] H um and the same I can do for this uh
[05:59] another expression
[06:01] here okay so so this is what I'm using
[06:04] the approximation here in which X is
[06:06] equal to GN okay this in here is just 1
[06:10] over 1 plus GN and I'm saying this is
[06:13] approximately equal I can approximate if
[06:15] GN is a small number this is
[06:17] approximately equal to 1 minus GN okay
[06:20] so that's what we have and this is a
[06:22] second
[06:24] approximation going from this line to
[06:26] this line in which we did the following
[06:29] it said okay
[06:30] you know this is equal to uh 1us
[06:35] Delta uh minus
[06:39] GN
[06:41] plus Delta * GN but the Delta time G is
[06:46] the multiplication of two small numbers
[06:48] so I said assume that is close to zero
[06:50] and the same we had here we had saving
[06:53] rate * 1 + GN you get you get the saving
[06:58] rate h plus the saving rate times GN but
[07:02] the saving rate times GN is also small
[07:05] number so we also drop okay so those are
[07:07] the more explicit steps of what I did in
[07:10] the previous lecture and I think the
[07:11] final equation I showed you was this but
[07:14] it comes from again two approximations
[07:16] the one down here which I use here and
[07:20] then the fact that I dropped the second
[07:22] order terms okay that's it and then I
[07:26] just rearrange things I move K KT over n
[07:29] to the left hand side and so we have the
[07:31] change in the stock of capital per
[07:33] person is an increasing function of
[07:38] investment uh per person which is this
[07:41] because this is saving per person and I
[07:43] can replace this by the production
[07:45] function no which is f of K Over N and
[07:48] so what I have here is a difference
[07:50] equation in capital per
[07:55] person why is this so so what so this is
[07:59] investment so the Capital stock per
[08:01] person will be growing as we
[08:03] invest the it shrinks with the passage
[08:07] of time just because of depreciation
[08:08] some things break down that reduces the
[08:10] stock of capital but the new term that
[08:13] we introduce at the end of last lecture
[08:15] is is that that now this ratio also
[08:18] declines H with population growth and so
[08:22] who can explain why we get this ter
[08:30] you know I'm saying look suppose that
[08:33] that that
[08:35] H that we have take a given amount of
[08:38] investment we take as given depreciation
[08:41] but now we I I say well if if GN Rises
[08:44] and all the rest remains constant
[08:47] then the left hand side will start
[08:50] declining or will grow less rapidly than
[08:52] what going to grow before a increase GN
[08:55] why is what do the case but
[08:59] sometimes it's counter inuitive that's
[09:01] the reason I want I I thought I rush in
[09:03] the previous lecture over that and I
[09:06] since it's going to be an important
[09:07] intermediate step into the next one
[09:10] which is when introduce technological
[09:12] progress I want us to understand why
[09:14] that GN appears with a negative sign
[09:19] there
[09:22] yep for the same amount of capital that
[09:24] increased
[09:28] inor that that
[09:30] term
[09:32] ER is going to be captured
[09:35] here and it's going to play a role but
[09:38] this one comes from something much more
[09:40] mechanical than
[09:43] that hint observe what I have on the
[09:47] left hand side I don't have on the left
[09:49] hand side the change in the stock of
[09:53] capital I have the change in the stock
[09:55] of capital per
[09:57] person so suppose I don't change the
[09:59] 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