WEBVTT

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okay let's uh let's start so today we're

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going to talk about technological

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progress and economic growth

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um I mean that's it's a big topic

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certainly at MIT

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perhaps this is one of the main ways we

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contribute

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to human well-being no um but before I

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do that let me let me H do a brief

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review of of the things I did the second

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half of the the previous

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lecture for two reasons I want to do

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that Brief Review first um is as after

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spring break so I assume there is some

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depreciation of knowledge H since the

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last time and and the second is that

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that while the equations I show you at

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the end with population growth are

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correct I think I said something which

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is not correct I think I kept saying I

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don't know why but I kept saying look if

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x is small 1/ 1 plus X is approximately

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equal to Min - x no no it's

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approximately equal to 1 - x not Min - x

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but uh so I wanted to correct that that

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typle so let me remind you what what we

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had U so we had we started with a

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production function one of an important

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part of economic growth is we're going

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to capital accumulation will be sort of

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a very important variable here and so we

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hadn't talked about capital in the

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production function in the previous uh

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part of the course but now we we were

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explicit about it and we start with a

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production function that constant

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returns to scale h on Capital and labor

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H and here remember in this part of the

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course we're not talking about

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unemployment or anything like that so

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whenever I say labor I also mean

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population I mean labor force all of

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them together you know the distinction

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between each of these Concepts but

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they're not that important for growth

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matters mostly because all of those

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Aggregates sort of move in tandem over

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the long run no it's very difficult for

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for a

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population and the labor force to

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diverge for a very long period of time

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you know there may be fluctuations and

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so on but then tend to move together

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um so but we decided that we wanted to

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look at things normalized by by

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population and so output per per person

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is is an increasing function of capital

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per person but also is is increasing at

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a decreasing rate no there's decreasing

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returns with respect to uh the capital

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labor ratio and so output per capital

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grows as capital per as the economy

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becomes more Capital intensive that is

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you have more Capital per worker

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H but it grows at a decreasing rate the

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second key equation of the our model was

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that that assumed we're say in this part

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of the course we're going to assume that

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the government is not running any fiscal

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deficit or anything like that and the

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econom is closed which is an assumption

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we have maintain and we will keep

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assuming until three lectures from now

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and so in close economy no fiscal

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deficit we have that

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investment is equal to saving and we

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made an extra step to assume that the

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saving is proportional to income okay so

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s proportional to income so with all

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these things together putting this two

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things together H we got to our a very

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important equation in any growth model

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which is the capital accumulation

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equation and this equation says well the

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Capital stock tomorrow tomorrow means in

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the next unit time next year or whatever

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H H is equal to the current stock of

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capital minus the depreciation of that

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stock of capital minus Delta time KT

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plus investment but investment is equal

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to saving and saving is equal to H uh is

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proportional to to Output okay so that

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was the that was common across all the

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things we did in the previous lectur is

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there any question about these equations

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no no good okay so the next step was to

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say okay and and I did remember all the

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initial derivations I assumed that n was

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constant population was constant

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and

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so and the next step was I divided by a

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constant here so we did everything in

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terms of capital output per per person

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but actually since population was

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constant the per person part was just

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the tri we just divide it by a constant

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the last thing I did though in the

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previous lecture was to say okay what if

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not if that's not the case what if

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population is growing over time as well

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how does our analy change and so I did

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this no I said well okay let's try let's

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start by dividing everything by NT + one

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so then we get Capital per uh person at

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t+ one problem is I said is when I

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divide the right hand side by NT plus

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one I don't get what I want I want

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Capital at T divided by population of T

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I want output at T divide by population

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of T not at t+ one okay so what I did is

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I multiply and divide by n T both of

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these so I multiply by one NT over NT is

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one so I multiply by one everything and

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then rearrange terms so I got

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expressions like this no I got what I

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wanted here which is capital per ER

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person at the same point in time and but

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now it's multiply by NT over NT + one

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okay

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H um and the same I can do for this uh

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another expression

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here okay so so this is what I'm using

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the approximation here in which X is

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equal to GN okay this in here is just 1

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over 1 plus GN and I'm saying this is

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approximately equal I can approximate if

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GN is a small number this is

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approximately equal to 1 minus GN okay

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so that's what we have and this is a

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second

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approximation going from this line to

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this line in which we did the following

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it said okay

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you know this is equal to uh 1us

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Delta uh minus

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GN

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plus Delta * GN but the Delta time G is

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the multiplication of two small numbers

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so I said assume that is close to zero

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and the same we had here we had saving

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rate * 1 + GN you get you get the saving

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rate h plus the saving rate times GN but

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the saving rate times GN is also small

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number so we also drop okay so those are

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the more explicit steps of what I did in

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the previous lecture and I think the

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final equation I showed you was this but

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it comes from again two approximations

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the one down here which I use here and

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then the fact that I dropped the second

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order terms okay that's it and then I

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just rearrange things I move K KT over n

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to the left hand side and so we have the

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change in the stock of capital per

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person is an increasing function of

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investment uh per person which is this

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because this is saving per person and I

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can replace this by the production

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function no which is f of K Over N and

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so what I have here is a difference

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equation in capital per

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person why is this so so what so this is

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investment so the Capital stock per

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person will be growing as we

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invest the it shrinks with the passage

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of time just because of depreciation

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some things break down that reduces the

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stock of capital but the new term that

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we introduce at the end of last lecture

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is is that that now this ratio also

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declines H with population growth and so

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who can explain why we get this ter

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you know I'm saying look suppose that

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that that

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H that we have take a given amount of

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investment we take as given depreciation

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but now we I I say well if if GN Rises

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and all the rest remains constant

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then the left hand side will start

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declining or will grow less rapidly than

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what going to grow before a increase GN

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why is what do the case but

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sometimes it's counter inuitive that's

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the reason I want I I thought I rush in

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the previous lecture over that and I

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since it's going to be an important

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intermediate step into the next one

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which is when introduce technological

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progress I want us to understand why

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that GN appears with a negative sign

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there

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yep for the same amount of capital that

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increased

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inor that that

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term

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ER is going to be captured

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here and it's going to play a role but

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this one comes from something much more

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mechanical than

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that hint observe what I have on the

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left hand side I don't have on the left

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hand side the change in the stock of

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capital I have the change in the stock

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of capital per

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person so suppose I don't change the

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stock of capital at all from this period

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to the next but population grows what

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happens to this expression

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here decreases it becomes negative

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because I haven't changed the Capital

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stock but the denominator is growing

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that's the GM part and that means this

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turns negative and that's what this term

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is is here for is to capture the fact

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that the denominator now is also moving

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on the left hand side variable and and

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you say so what but I at the end of the

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day I care about the capital capital why

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why do I care about Capital per person

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well for all my analysis I told you it's

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much easier if I do it on something

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which it has a steady state that's the

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reason I'm looking for this

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normalization but once I look at the

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dynamic equation of accumulation of

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capital in

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this divided by population then I need

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to take into account the fact that my

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denominator is also moving okay so

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that's the reason that GN is there and

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and again the reason I wanted to pause

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on this is because when we introduce

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technological progress we're going to

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have a similar effect and and and so I

00:11:05.879 --> 00:11:09.399
want you to it's going to be counter

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intuitive because it sounds like

00:11:09.399 --> 00:11:12.159
technological progress is something

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negative no it's not

00:11:12.159 --> 00:11:19.399
negative but but in this space it turns

00:11:15.958 --> 00:11:20.838
out that if population grows very fast

00:11:19.399 --> 00:11:24.120
then you need a lot of investment to

00:11:20.839 --> 00:11:27.399
keep up the the capital labor ratio

00:11:24.120 --> 00:11:29.320
constant okay that's the idea if

00:11:27.399 --> 00:11:30.879
population is not growing I don't need

00:11:29.320 --> 00:11:32.959
need a lot of investment to keep the

00:11:30.879 --> 00:11:34.879
capital labor ratio constant but if

00:11:32.958 --> 00:11:36.879
population is growing very fast then I

00:11:34.879 --> 00:11:38.879
need a lot of investment to really keep

00:11:36.879 --> 00:11:41.799
that ratio constant that's what this is

00:11:38.879 --> 00:11:45.679
capturing there

00:11:41.799 --> 00:11:47.479
so to repeat if if this guy is is is

00:11:45.679 --> 00:11:50.319
very large then I need a lot of

00:11:47.480 --> 00:11:52.360
investment here to make this thing equal

00:11:50.320 --> 00:11:57.879
to zero so the Capital stock per person

00:11:52.360 --> 00:11:57.879
is not declining that's idea

00:11:58.240 --> 00:12:04.240
okay

00:11:59.759 --> 00:12:06.120
good okay so now ah and then I said okay

00:12:04.240 --> 00:12:09.919
this is where we finish then I said okay

00:12:06.120 --> 00:12:12.200
so let's go uh back to our diagram I can

00:12:09.919 --> 00:12:16.278
once I have everything in this space K

00:12:12.200 --> 00:12:17.959
Over N I can go back to our diagram

00:12:16.278 --> 00:12:19.639
assume that GA is equal to zero you

00:12:17.958 --> 00:12:22.278
don't even know what A is for the time

00:12:19.639 --> 00:12:24.480
being you will know in five minutes but

00:12:22.278 --> 00:12:27.600
assume GA is equal to zero then that's

00:12:24.480 --> 00:12:29.959
exactly the model we had before

00:12:27.600 --> 00:12:31.800
so and remember this this is exactly the

00:12:29.958 --> 00:12:33.278
same diagram it looked the same at least

00:12:31.799 --> 00:12:36.000
that we had when population was not

00:12:33.278 --> 00:12:39.278
growing I'm saying I can use the same

00:12:36.000 --> 00:12:42.198
diagram when population is growing as

00:12:39.278 --> 00:12:45.000
well but there is one important

00:12:42.198 --> 00:12:47.278
difference which is this this curve

00:12:45.000 --> 00:12:51.679
looks exactly the same this is just

00:12:47.278 --> 00:12:54.439
output H per per worker okay that's the

00:12:51.679 --> 00:12:57.120
Blue Line the green line looks exactly

00:12:54.440 --> 00:12:59.399
the same as in the basic model it's just

00:12:57.120 --> 00:13:02.679
little s times that the blue line so

00:12:59.399 --> 00:13:05.519
that's exactly the same but this line is

00:13:02.679 --> 00:13:09.679
different what happens to this red line

00:13:05.519 --> 00:13:12.278
as as GN goes up so what happens to this

00:13:09.679 --> 00:13:15.919
line as GN goes

00:13:12.278 --> 00:13:20.639
up becomes steeper no yeah so it rotates

00:13:15.919 --> 00:13:22.278
up okay goes up and that can sound

00:13:20.639 --> 00:13:24.799
counterintuitive sometimes because you

00:13:22.278 --> 00:13:26.039
say look look what happens here let's

00:13:24.799 --> 00:13:28.958
spend time on

00:13:26.039 --> 00:13:31.120
this suppose that we are at some St

00:13:28.958 --> 00:13:35.719
state say this

00:13:31.120 --> 00:13:35.720
one and now population growth

00:13:36.000 --> 00:13:43.360
Rises okay it sounds like Ireland in you

00:13:40.679 --> 00:13:47.198
know 2000s and

00:13:43.360 --> 00:13:49.919
so so population growth Rises a

00:13:47.198 --> 00:13:53.159
lot what happens in this diagram so

00:13:49.919 --> 00:13:57.360
suppose we're at the state state

00:13:53.159 --> 00:14:00.120
here no and that the state

00:13:57.360 --> 00:14:01.800
investment uh saving which is equal to

00:14:00.120 --> 00:14:03.959
investment is exactly what you need to

00:14:01.799 --> 00:14:06.838
maintain the stock of capital per person

00:14:03.958 --> 00:14:11.198
constant okay that's what the red line

00:14:06.839 --> 00:14:13.639
tells us no that here so that's the Gap

00:14:11.198 --> 00:14:15.278
here is this is a gap between investment

00:14:13.639 --> 00:14:18.039
and what you need to maintain the stock

00:14:15.278 --> 00:14:21.600
of capital per person constant so when

00:14:18.039 --> 00:14:23.958
the Gap is zero then then this equation

00:14:21.600 --> 00:14:26.800
this left hand side is equal to zero

00:14:23.958 --> 00:14:29.518
okay that's the red line that's the

00:14:26.799 --> 00:14:32.519
green line when this is equal to Z

00:14:29.519 --> 00:14:35.159
that's equal to that that's exactly that

00:14:32.519 --> 00:14:37.278
point okay but I'm saying suppose we are

00:14:35.159 --> 00:14:40.000
at that point and

00:14:37.278 --> 00:14:43.958
now population growth

00:14:40.000 --> 00:14:46.600
Rises so what moves in that diagram does

00:14:43.958 --> 00:14:46.599
a blue line

00:14:50.639 --> 00:14:55.919
move I don't see GN in the blue line so

00:14:53.879 --> 00:14:57.360
the Blue Line doesn't move if the Blue

00:14:55.919 --> 00:14:58.719
Line doesn't move and the saving rate

00:14:57.360 --> 00:15:00.278
hasn't changed then the green line

00:14:58.720 --> 00:15:02.879
doesn't move move

00:15:00.278 --> 00:15:05.360
either so for this diagram to be

00:15:02.879 --> 00:15:07.639
interesting what moves assum has to move

00:15:05.360 --> 00:15:10.800
so the only thing that has that can move

00:15:07.639 --> 00:15:13.079
here is the is the red line and the red

00:15:10.799 --> 00:15:15.159
line we already said if GM goes up it's

00:15:13.078 --> 00:15:16.879
going to rotate

00:15:15.159 --> 00:15:20.319
upwards that

00:15:16.879 --> 00:15:23.480
means say so now we have that line there

00:15:20.320 --> 00:15:26.120
so what happens at the at the at the

00:15:23.480 --> 00:15:29.159
previous St State stock of capital per

00:15:26.120 --> 00:15:31.959
worker at this level what happens is

00:15:29.159 --> 00:15:31.958
that a new state

00:15:32.839 --> 00:15:39.600
state no but what happens in particular

00:15:37.078 --> 00:15:41.479
what is it so I'm saying suppose that

00:15:39.600 --> 00:15:42.360
you're here and now I rotate the red

00:15:41.480 --> 00:15:45.680
line

00:15:42.360 --> 00:15:47.480
up okay so that means the red line that

00:15:45.679 --> 00:15:49.799
represents the amount of capital I need

00:15:47.480 --> 00:15:53.399
to maintain the stock of capital

00:15:49.799 --> 00:15:56.000
constant is greater than how much

00:15:53.399 --> 00:15:57.639
Society saving and therefore investing

00:15:56.000 --> 00:16:00.639
so what will happen to Capital per

00:15:57.639 --> 00:16:00.639
worker

00:16:02.278 --> 00:16:08.480
decrease exactly because you need more

00:16:05.958 --> 00:16:10.198
than you're investing so the Capital

00:16:08.480 --> 00:16:11.759
stock has to decline and that's what

00:16:10.198 --> 00:16:14.519
will happen the new state state is going

00:16:11.759 --> 00:16:16.919
to be to the left of that point

00:16:14.519 --> 00:16:20.318
there that sounds very

00:16:16.919 --> 00:16:23.360
weird how can it be that you know after

00:16:20.318 --> 00:16:25.639
all labor contributes to Output how can

00:16:23.360 --> 00:16:28.360
it be that we end up with a

00:16:25.639 --> 00:16:30.240
lower ER output per per worker when we

00:16:28.360 --> 00:16:33.199
increase popul population growth is

00:16:30.240 --> 00:16:37.318
population growth bad in a sense for

00:16:33.198 --> 00:16:37.318
growth itself for

00:16:41.278 --> 00:16:47.439
output well the answer is no it's it's

00:16:44.919 --> 00:16:50.240
true that the new state state will have

00:16:47.440 --> 00:16:52.040
lower output per person so in that sense

00:16:50.240 --> 00:16:54.440
it's bad you have lots of population if

00:16:52.039 --> 00:16:57.000
you if if you don't change the saving

00:16:54.440 --> 00:17:00.319
rate or something then output per person

00:16:57.000 --> 00:17:02.639
will be lower but output will be higher

00:17:00.318 --> 00:17:05.438
than it used to be at any point in time

00:17:02.639 --> 00:17:08.720
it just happens that in the transition

00:17:05.439 --> 00:17:10.720
the growth of output so so the growth

00:17:08.720 --> 00:17:13.360
the growth of output in this model is

00:17:10.720 --> 00:17:16.360
going to be equal to the growth of

00:17:13.359 --> 00:17:18.479
population okay that's if you have a St

00:17:16.359 --> 00:17:20.759
state where population is growing and

00:17:18.480 --> 00:17:23.038
output per worker or per person is not

00:17:20.759 --> 00:17:25.279
growing that means output is growing at

00:17:23.038 --> 00:17:26.838
the same rate as population so that

00:17:25.279 --> 00:17:29.079
means that if I increase the rate of

00:17:26.838 --> 00:17:30.639
population growth the rate of growth

00:17:29.079 --> 00:17:32.439
output will

00:17:30.640 --> 00:17:34.440
increase together with the rate of

00:17:32.440 --> 00:17:36.640
growth of population but in the

00:17:34.440 --> 00:17:39.400
transition as the output per capita goes

00:17:36.640 --> 00:17:41.520
lower output will grow less than

00:17:39.400 --> 00:17:43.038
population that's what is happening here

00:17:41.519 --> 00:17:44.679
okay but output is growing if you

00:17:43.038 --> 00:17:46.839
population starts growing if you

00:17:44.679 --> 00:17:50.919
increase migration you're going to see

00:17:46.839 --> 00:17:53.399
output grow but output per person will

00:17:50.919 --> 00:17:56.720
start declining until you get to New

00:17:53.400 --> 00:17:59.159
State and then you'll get the same

00:17:56.720 --> 00:18:01.240
ER you'll get the higher rate of growth

00:17:59.159 --> 00:18:03.480
you continue with population growth with

00:18:01.240 --> 00:18:07.640
the high population growth but output

00:18:03.480 --> 00:18:07.640
per worker would be slightly lower rate

00:18:09.079 --> 00:18:14.319
okay anyways this may have been fast the

00:18:12.640 --> 00:18:16.520
last part but since I'm going to repeat

00:18:14.319 --> 00:18:19.879
it now in the context of technological

00:18:16.519 --> 00:18:21.759
progress we should be fine okay so if

00:18:19.880 --> 00:18:24.120
you're a little confused now it's okay

00:18:21.759 --> 00:18:25.599
if you're a little confused at the end

00:18:24.119 --> 00:18:28.079
of the lecture it's not okay because

00:18:25.599 --> 00:18:30.719
that's I'm counting with you sort of

00:18:28.079 --> 00:18:34.199
getting it in the second pass okay

00:18:30.720 --> 00:18:37.480
second try Okay so next step is is f so

00:18:34.200 --> 00:18:39.919
here we assume already population growth

00:18:37.480 --> 00:18:42.038
where we assume that technology so the

00:18:39.919 --> 00:18:44.840
production function sort of stay put for

00:18:42.038 --> 00:18:48.519
any combination of capital and labor the

00:18:44.839 --> 00:18:50.319
next step is to think what happens when

00:18:48.519 --> 00:18:53.519
the technology itself is getting better

00:18:50.319 --> 00:18:58.079
over time and that's what we call

00:18:53.519 --> 00:18:59.960
technological progress okay this is tfp

00:18:58.079 --> 00:19:03.158
let me not get into to specifics at the

00:18:59.960 --> 00:19:05.880
end I'll say a little more but P tfp

00:19:03.159 --> 00:19:08.440
stands for total Factor productivity and

00:19:05.880 --> 00:19:09.840
this index here captures the level of

00:19:08.440 --> 00:19:12.798
tfp in the

00:19:09.839 --> 00:19:14.798
US over time and it's clearly growing so

00:19:12.798 --> 00:19:17.720
technolog is getting better and better

00:19:14.798 --> 00:19:19.879
over time what that means well it I say

00:19:17.720 --> 00:19:21.079
a little more not a lot more but but

00:19:19.880 --> 00:19:25.559
it's getting

00:19:21.079 --> 00:19:27.879
better no h and so the question we have

00:19:25.558 --> 00:19:30.319
here is I'm going when to address next

00:19:27.880 --> 00:19:32.360
is how does this so now we're going to

00:19:30.319 --> 00:19:33.720
put together our entire economic growth

00:19:32.359 --> 00:19:35.678
model we're going to have population

00:19:33.720 --> 00:19:37.919
growth we're want to have also

00:19:35.679 --> 00:19:39.200
technology growing up to now the only

00:19:37.919 --> 00:19:42.559
reason you could

00:19:39.200 --> 00:19:44.519
grow a you could grow output per per

00:19:42.558 --> 00:19:46.359
worker was because you were accumulating

00:19:44.519 --> 00:19:47.918
lots of capital you were catching up

00:19:46.359 --> 00:19:49.879
with you're a steady state that's what

00:19:47.919 --> 00:19:53.120
would make you grow faster but then

00:19:49.880 --> 00:19:55.480
there was nothing else tfp is going to

00:19:53.119 --> 00:19:57.199
be the only growth in technology is

00:19:55.480 --> 00:19:59.159
going to be the only thing that will

00:19:57.200 --> 00:20:02.480
give you sustainable growth in the long

00:19:59.159 --> 00:20:07.159
run an output per person okay so this is

00:20:02.480 --> 00:20:09.319
a very important component of of H of

00:20:07.159 --> 00:20:11.720
growth again it's the only thing that

00:20:09.319 --> 00:20:15.720
will make you grow in a sustainable

00:20:11.720 --> 00:20:17.919
manner in in per person terms okay the

00:20:15.720 --> 00:20:20.480
previous model didn't have that in the

00:20:17.919 --> 00:20:24.240
previous model we had a steady

00:20:20.480 --> 00:20:26.360
state ER on on output per worker so in

00:20:24.240 --> 00:20:29.279
the previous model we didn't have growth

00:20:26.359 --> 00:20:31.479
in output per worker in the St state

00:20:29.279 --> 00:20:34.119
we could have transitional growth when

00:20:31.480 --> 00:20:35.558
we were catching up no if you if you

00:20:34.119 --> 00:20:38.959
started

00:20:35.558 --> 00:20:41.639
here then you were going to have growth

00:20:38.960 --> 00:20:45.798
fast growth but eventually will pet it

00:20:41.640 --> 00:20:48.360
out okay out work so so up to now we

00:20:45.798 --> 00:20:51.319
don't have a reason for why to to to

00:20:48.359 --> 00:20:54.798
explain why we see that output per

00:20:51.319 --> 00:20:57.480
worker grows in most economies in the

00:20:54.798 --> 00:20:59.038
world and the answer will be this this

00:20:57.480 --> 00:21:00.960
is the reason really how output per

00:20:59.038 --> 00:21:02.480
worker can grow in a sustained manner

00:21:00.960 --> 00:21:05.960
it's technolog is getting better and

00:21:02.480 --> 00:21:08.759
better over time so let's let's see so

00:21:05.960 --> 00:21:11.278
the question is let's now see what this

00:21:08.759 --> 00:21:15.240
does to the model we

00:21:11.278 --> 00:21:19.839
have now in practice technological

00:21:15.240 --> 00:21:24.120
progress takes many many forms er

00:21:19.839 --> 00:21:26.399
um it in at most basic level means that

00:21:24.119 --> 00:21:27.558
you can produce larger quantities output

00:21:26.400 --> 00:21:29.759
and that's really the meaning we're

00:21:27.558 --> 00:21:31.678
going to have here larger quantities of

00:21:29.759 --> 00:21:32.400
output for the same amount of capital

00:21:31.679 --> 00:21:35.240
and

00:21:32.400 --> 00:21:37.840
labor okay so you have 10 machines 10

00:21:35.240 --> 00:21:40.240
workers technological progress means

00:21:37.839 --> 00:21:43.240
well you used to produce 12 units now

00:21:40.240 --> 00:21:46.919
we're going to produce 12 14 15 and so

00:21:43.240 --> 00:21:49.038
on so forth that's that's a one way of

00:21:46.919 --> 00:21:51.679
techn that one of the main ways

00:21:49.038 --> 00:21:55.200
technological progress shows up we can

00:21:51.679 --> 00:21:57.679
do more with the same if you will second

00:21:55.200 --> 00:21:59.360
dimension is better product so it's not

00:21:57.679 --> 00:22:01.720
that you produce more cars but you

00:21:59.359 --> 00:22:04.038
produce better cars better computers and

00:22:01.720 --> 00:22:06.159
so on okay that's another dimension of

00:22:04.038 --> 00:22:09.158
technal prod you can produce new

00:22:06.159 --> 00:22:10.240
products things that didn't even exist

00:22:09.159 --> 00:22:13.080
but now you

00:22:10.240 --> 00:22:14.919
have that counts more than having one

00:22:13.079 --> 00:22:16.798
more unit of good it counts more because

00:22:14.919 --> 00:22:18.320
you have you know things that you

00:22:16.798 --> 00:22:20.359
couldn't even satisfy in the past you

00:22:18.319 --> 00:22:22.879
can satisfy now because you have the

00:22:20.359 --> 00:22:25.479
certain kind of goods that DNX is before

00:22:22.880 --> 00:22:28.640
that's a very important dimension of

00:22:25.480 --> 00:22:30.558
technological progress is just create no

00:22:28.640 --> 00:22:34.000
new sort of forms of inputs of

00:22:30.558 --> 00:22:36.599
production and Technologies think of AI

00:22:34.000 --> 00:22:38.960
what that will do to to technology in

00:22:36.599 --> 00:22:43.079
general and to consumption very

00:22:38.960 --> 00:22:45.079
directly ER and that's what I mean even

00:22:43.079 --> 00:22:46.960
within a product you you can get more

00:22:45.079 --> 00:22:48.839
variety and more variety you know

00:22:46.960 --> 00:22:53.120
improves welfare because you can align

00:22:48.839 --> 00:22:54.720
better the needs H with with the product

00:22:53.119 --> 00:22:57.639
and so on but we're going to make it

00:22:54.720 --> 00:22:59.120
very simple in this in this in this

00:22:57.640 --> 00:23:02.400
course we're going to we're going to

00:22:59.119 --> 00:23:03.278
model technological progress as if it

00:23:02.400 --> 00:23:06.759
was

00:23:03.278 --> 00:23:10.558
workers okay so

00:23:06.759 --> 00:23:13.879
uh we're going to capture technology

00:23:10.558 --> 00:23:15.839
with this Con with this variable a which

00:23:13.880 --> 00:23:20.559
is going to be we're going to model it

00:23:15.839 --> 00:23:23.199
as labor equivalent that is if a grows

00:23:20.558 --> 00:23:24.440
it's going to count for us as if we had

00:23:23.200 --> 00:23:26.558
more

00:23:24.440 --> 00:23:28.278
workers okay that's just one way of

00:23:26.558 --> 00:23:30.440
model it I mean I can I can do it in

00:23:28.278 --> 00:23:32.720
many different ways andan some many of

00:23:30.440 --> 00:23:34.798
these are equivalent but that's a very

00:23:32.720 --> 00:23:37.400
very nice way of modeling so we can use

00:23:34.798 --> 00:23:39.000
exactly the same diagrams we have and so

00:23:37.400 --> 00:23:40.559
okay so you can think of technological

00:23:39.000 --> 00:23:42.839
progress the way I'm going to model this

00:23:40.558 --> 00:23:45.158
here is you can think of technological

00:23:42.839 --> 00:23:46.759
progress as if this economy was

00:23:45.159 --> 00:23:50.799
receiving more

00:23:46.759 --> 00:23:53.400
workers okay or a more accurate

00:23:50.798 --> 00:23:56.839
description is with the same workers it

00:23:53.400 --> 00:23:58.960
can produce is as if he had more labor

00:23:56.839 --> 00:24:01.639
input okay that's that's one way of

00:23:58.960 --> 00:24:04.200
capturing technology technological

00:24:01.640 --> 00:24:07.679
progress so now that means that I'm

00:24:04.200 --> 00:24:11.440
going to refer to this term a n as

00:24:07.679 --> 00:24:13.919
effective labor you know so with the

00:24:11.440 --> 00:24:15.759
same number of n bodies I may get more

00:24:13.919 --> 00:24:18.159
effective label because each worker can

00:24:15.759 --> 00:24:21.839
produce more things it's a better input

00:24:18.159 --> 00:24:25.039
of production factor of production

00:24:21.839 --> 00:24:26.599
okay so it and I like to mod it this way

00:24:25.038 --> 00:24:29.079
because now I can use exactly the same

00:24:26.599 --> 00:24:32.079
diagrams we had before but rather than

00:24:29.079 --> 00:24:37.398
normalizing by population I'm going to

00:24:32.079 --> 00:24:38.918
normalize by effective labor by a n

00:24:37.398 --> 00:24:41.879
okay

00:24:38.919 --> 00:24:43.520
so let me do that so recall that we had

00:24:41.880 --> 00:24:46.278
our production function with constant

00:24:43.519 --> 00:24:50.240
return so this hold I'm going to set

00:24:46.278 --> 00:24:53.480
this x now as 1/ a n we used to have 1/

00:24:50.240 --> 00:24:56.640
n I'm going to have 1/ a n and so I'm

00:24:53.480 --> 00:24:59.038
going to now have output per effective

00:24:56.640 --> 00:25:02.120
worker is going to be also the same

00:24:59.038 --> 00:25:03.240
little function f of capital per

00:25:02.119 --> 00:25:06.719
effective

00:25:03.240 --> 00:25:08.480
worker okay and what is nice of this is

00:25:06.720 --> 00:25:12.200
that now here rather than plotting y

00:25:08.480 --> 00:25:13.960
Over N I'm going to PL plot y over a n

00:25:12.200 --> 00:25:16.840
rather than plotting K Over N here I'm

00:25:13.960 --> 00:25:19.038
going to plot K over a n and I have the

00:25:16.839 --> 00:25:21.959
blue line looks exactly like it used to

00:25:19.038 --> 00:25:24.200
look it's just I'm dividing by a Over N

00:25:21.960 --> 00:25:26.079
remember the trick in all these models

00:25:24.200 --> 00:25:28.319
is to find the right normalization that

00:25:26.079 --> 00:25:30.678
is to find the right X so I can find

00:25:28.319 --> 00:25:32.038
find a steady state in my diagram I

00:25:30.679 --> 00:25:34.720
don't want these curves to be moving

00:25:32.038 --> 00:25:36.359
around I want this to have a a steady

00:25:34.720 --> 00:25:38.839
state something a point that that we're

00:25:36.359 --> 00:25:42.079
going to converge to after enough time

00:25:38.839 --> 00:25:43.480
has passed okay and I know that that the

00:25:42.079 --> 00:25:45.439
thing that will do it in a model in

00:25:43.480 --> 00:25:47.480
which I have popul effective workers

00:25:45.440 --> 00:25:50.240
growing is one in which I divide

00:25:47.480 --> 00:25:52.720
everything by effective

00:25:50.240 --> 00:25:54.278
workers okay so that's what I'm doing

00:25:52.720 --> 00:25:55.720
here I'm going to build a diagram that

00:25:54.278 --> 00:25:58.440
looks like the other one that has a nice

00:25:55.720 --> 00:26:00.720
steady state as the previous one had

00:25:58.440 --> 00:26:02.558
okay so I have my blue line you I have

00:26:00.720 --> 00:26:03.919
my blue line I know I have my green line

00:26:02.558 --> 00:26:06.480
no because the green line was just

00:26:03.919 --> 00:26:09.679
little s times the blue line so I have

00:26:06.480 --> 00:26:11.440
that the last thing I need and I already

00:26:09.679 --> 00:26:14.919
show you that but I'm going to show it

00:26:11.440 --> 00:26:17.038
again is is the is the red line okay but

00:26:14.919 --> 00:26:19.440
for the red line I need to find this

00:26:17.038 --> 00:26:21.919
term the term remember the red line

00:26:19.440 --> 00:26:24.080
represents the capital we need to

00:26:21.919 --> 00:26:26.799
maintain the current stock of capital

00:26:24.079 --> 00:26:29.480
per effective worker constant that's

00:26:26.798 --> 00:26:31.038
what I need my red line for so let's get

00:26:29.480 --> 00:26:32.720
there and it always start from this

00:26:31.038 --> 00:26:34.158
equation so this equation is still the

00:26:32.720 --> 00:26:36.600
same as it used to be that doesn't

00:26:34.159 --> 00:26:39.000
change but what I'm going to do now is

00:26:36.599 --> 00:26:43.319
rather than dividing by n I'm going to

00:26:39.000 --> 00:26:45.480
divide by a * n so the same as I did

00:26:43.319 --> 00:26:48.960
earlier in this lecture I now want to

00:26:45.480 --> 00:26:51.319
divide by a Over N so I get Capital per

00:26:48.960 --> 00:26:53.200
effective work on the left hand side I

00:26:51.319 --> 00:26:57.000
don't like what I get here but you know

00:26:53.200 --> 00:27:00.200
that I can divide and multiply by a n n

00:26:57.000 --> 00:27:03.200
over a n so I can write the right hand

00:27:00.200 --> 00:27:04.840
side after do all my substitutions as

00:27:03.200 --> 00:27:08.720
this

00:27:04.839 --> 00:27:13.000
okay you know so I first step one I

00:27:08.720 --> 00:27:16.159
divided everything by a t + 1 * NT + 1

00:27:13.000 --> 00:27:19.839
step two I multiply each of these terms

00:27:16.159 --> 00:27:22.919
by a and t i multiply by AT and T divide

00:27:19.839 --> 00:27:25.918
by AT and T and T okay and then I

00:27:22.919 --> 00:27:27.799
regroup things so I end up with that

00:27:25.919 --> 00:27:31.480
well this using the approximation we

00:27:27.798 --> 00:27:33.679
have here here is equal to approximately

00:27:31.480 --> 00:27:37.240
equal to 1 minus g

00:27:33.679 --> 00:27:37.240
n and g

00:27:41.798 --> 00:27:48.519
n is equal to

00:27:45.278 --> 00:27:48.519
GA plus

00:27:48.599 --> 00:27:53.918
GN okay so I already show you that that

00:27:51.839 --> 00:27:57.839
case for the case in which GA was equal

00:27:53.919 --> 00:27:59.840
to zero I'm doing now the same thing but

00:27:57.839 --> 00:28:03.158
but you know since I renormalize things

00:27:59.839 --> 00:28:06.639
by effective workers effective labor

00:28:03.159 --> 00:28:08.480
rather than actual label I need to use a

00:28:06.640 --> 00:28:10.720
n rather than

00:28:08.480 --> 00:28:12.679
n okay and then by the same

00:28:10.720 --> 00:28:15.240
approximation I had before which is that

00:28:12.679 --> 00:28:18.240
you know these products are close to

00:28:15.240 --> 00:28:20.720
zero then I get to the equation I want

00:28:18.240 --> 00:28:22.679
and if I write it in first difference

00:28:20.720 --> 00:28:24.480
then I get my Red Line This is my red

00:28:22.679 --> 00:28:28.278
line

00:28:24.480 --> 00:28:29.720
here okay

00:28:28.278 --> 00:28:35.679
good

00:28:29.720 --> 00:28:38.600
so H in um this tells me that when the

00:28:35.679 --> 00:28:42.240
ER the green line green line is equal to

00:28:38.599 --> 00:28:44.158
the red line then I have a steady state

00:28:42.240 --> 00:28:45.839
capital perfective worker is constant

00:28:44.159 --> 00:28:47.960
that this this is equal to zero that's

00:28:45.839 --> 00:28:49.839
the way I find my steady state if I ask

00:28:47.960 --> 00:28:51.720
you a question find the steady state of

00:28:49.839 --> 00:28:54.158
this economy what you'll do is you'll

00:28:51.720 --> 00:28:56.480
set this equal to zero and find the

00:28:54.159 --> 00:29:00.640
Capital stock that gives you this equal

00:28:56.480 --> 00:29:04.079
to zero that's the way you do it okay

00:29:00.640 --> 00:29:06.880
so so that's that's that and then we get

00:29:04.079 --> 00:29:09.398
back to

00:29:06.880 --> 00:29:10.760
um well this is this is the same as we

00:29:09.398 --> 00:29:13.038
had

00:29:10.759 --> 00:29:16.839
before that's what I just said that's

00:29:13.038 --> 00:29:18.640
the way you find the stud State okay and

00:29:16.839 --> 00:29:21.240
then we get back to the diagram I

00:29:18.640 --> 00:29:25.440
started with in this lecture okay but

00:29:21.240 --> 00:29:28.200
now we have here a a n and now in in in

00:29:25.440 --> 00:29:32.240
the first part I said assume this G ga

00:29:28.200 --> 00:29:36.240
GA is equal to zero now the main actor

00:29:32.240 --> 00:29:38.120
is GA positive okay and and we get this

00:29:36.240 --> 00:29:39.960
diagram so now I can ask you the

00:29:38.119 --> 00:29:42.479
question that that that I asked you

00:29:39.960 --> 00:29:45.600
before with population growth and see

00:29:42.480 --> 00:29:48.079
how much I can confuse you suppose that

00:29:45.599 --> 00:29:50.839
GA goes up that sounds like a good thing

00:29:48.079 --> 00:29:54.278
no I mean ER suppose that we're at the

00:29:50.839 --> 00:29:59.000
steady state here and I mean this

00:29:54.278 --> 00:29:59.000
diagram has too much stuff let me

00:29:59.329 --> 00:30:02.529
[Music]

00:30:19.640 --> 00:30:22.720
okay so we're

00:30:22.919 --> 00:30:29.960
here that's our initial

00:30:26.519 --> 00:30:29.960
State um

00:30:37.798 --> 00:30:44.679
zero and and this line here is Delta

00:30:42.240 --> 00:30:48.000
plus

00:30:44.679 --> 00:30:48.000
GA plus

00:30:49.079 --> 00:30:59.480
GN * K over a n okay

00:30:55.599 --> 00:31:03.359
so the question well first let's let's

00:30:59.480 --> 00:31:03.360
so suppose we're at the say

00:31:03.720 --> 00:31:11.600
state is output constant there I mean

00:31:08.480 --> 00:31:14.480
that's it's a state state it's output

00:31:11.599 --> 00:31:16.839
output constant there so suppose we are

00:31:14.480 --> 00:31:16.839
at that

00:31:17.638 --> 00:31:24.599
point here here we know that investment

00:31:21.359 --> 00:31:26.558
exactly how much we need to maintain the

00:31:24.599 --> 00:31:28.359
stock of capital per effective worker

00:31:26.558 --> 00:31:29.158
constant that's what what the state

00:31:28.359 --> 00:31:33.719
state

00:31:29.159 --> 00:31:37.120
means question is output constant

00:31:33.720 --> 00:31:37.120
there state

00:31:48.798 --> 00:31:54.879
state

00:31:51.359 --> 00:31:58.638
no this only says

00:31:54.880 --> 00:32:01.919
that Capital per effective work

00:31:58.638 --> 00:32:05.398
is constant that means that if effective

00:32:01.919 --> 00:32:07.679
workers or labor is growing then capital

00:32:05.398 --> 00:32:10.119
is growing at the same rate and

00:32:07.679 --> 00:32:15.278
therefore output is growing at the same

00:32:10.119 --> 00:32:17.278
rate as effective workers okay that's

00:32:15.278 --> 00:32:19.000
the reason remember the whole trick so

00:32:17.278 --> 00:32:21.079
the curves would not be moving around is

00:32:19.000 --> 00:32:23.000
I find the right normalization so

00:32:21.079 --> 00:32:24.319
everything is growing at the same rate

00:32:23.000 --> 00:32:28.319
in that St

00:32:24.319 --> 00:32:28.319
State okay

00:32:29.119 --> 00:32:33.479
so let me actually show you that and

00:32:30.839 --> 00:32:35.558
then I'm going to go over the experiment

00:32:33.480 --> 00:32:37.480
I want to have so this is what is

00:32:35.558 --> 00:32:42.079
happening in that steady

00:32:37.480 --> 00:32:45.519
state so Capital per effective worker at

00:32:42.079 --> 00:32:49.199
the steady state so at that point

00:32:45.519 --> 00:32:52.319
there is zero no that's a stady that's

00:32:49.200 --> 00:32:55.519
my definition of a steady state okay

00:32:52.319 --> 00:32:58.079
output effective worker is also growing

00:32:55.519 --> 00:33:01.480
at at at the rate zero that's that one

00:32:58.079 --> 00:33:05.480
over there

00:33:01.480 --> 00:33:09.240
sorry that's my state level of output

00:33:05.480 --> 00:33:09.240
per effective worker

00:33:11.798 --> 00:33:18.319
okay so these are constant that's a say

00:33:14.759 --> 00:33:21.119
State those are constant this ratio is

00:33:18.319 --> 00:33:22.960
constant each of those components is

00:33:21.119 --> 00:33:25.558
not

00:33:22.960 --> 00:33:30.480
so that's what I'm plotting there so

00:33:25.558 --> 00:33:33.759
that's those are not growing Capital per

00:33:30.480 --> 00:33:37.720
worker what about that well you you see

00:33:33.759 --> 00:33:41.359
there explain why why so claim Capital

00:33:37.720 --> 00:33:44.880
per worker is growing at the rate GA how

00:33:41.359 --> 00:33:44.879
do I know that

00:33:54.250 --> 00:33:57.608
[Music]

00:33:58.960 --> 00:34:05.038
so the question I'm asking

00:34:01.278 --> 00:34:10.239
there is what is the rate of

00:34:05.038 --> 00:34:10.239
growth of k/

00:34:14.039 --> 00:34:24.358
n Pro given that I already know that the

00:34:18.760 --> 00:34:24.359
rate of growth of K over a

00:34:24.760 --> 00:34:29.440
n is equal to zero

00:34:34.239 --> 00:34:45.439
well this the rate of growth of K Over N

00:34:38.119 --> 00:34:47.599
is the rate of growth of K over a n plus

00:34:45.440 --> 00:34:49.240
the rate of growth of

00:34:47.599 --> 00:34:53.679
a

00:34:49.239 --> 00:34:54.479
no I mean if a is growing and this ratio

00:34:53.679 --> 00:34:57.358
is

00:34:54.480 --> 00:34:59.199
constant that means that k/ n must be

00:34:57.358 --> 00:35:00.960
growing

00:34:59.199 --> 00:35:04.679
and it has to be growing at exactly the

00:35:00.960 --> 00:35:05.800
same rate as this a is growing otherwise

00:35:04.679 --> 00:35:07.000
I wouldn't be able to maintain that

00:35:05.800 --> 00:35:09.440
ratio

00:35:07.000 --> 00:35:12.679
constant

00:35:09.440 --> 00:35:15.400
okay and the same logic applies

00:35:12.679 --> 00:35:18.358
to Output per worker because in that

00:35:15.400 --> 00:35:19.320
steady state output per effective worker

00:35:18.358 --> 00:35:23.239
is

00:35:19.320 --> 00:35:26.160
constant but a is growing so output per

00:35:23.239 --> 00:35:28.479
worker must be growing at the same rate

00:35:26.159 --> 00:35:31.598
as a is growing and that's

00:35:28.480 --> 00:35:34.358
G okay

00:35:31.599 --> 00:35:36.880
good labor well labor is exogenous which

00:35:34.358 --> 00:35:40.119
say population is growing at the rate n

00:35:36.880 --> 00:35:44.599
that's given what about

00:35:40.119 --> 00:35:49.160
Capital an output well claim capital and

00:35:44.599 --> 00:35:49.160
output are growing at the rate GA plus

00:35:49.800 --> 00:35:56.079
GN and I can do the same as I was in

00:35:52.400 --> 00:35:58.680
here I'm asking you the question GK what

00:35:56.079 --> 00:36:01.760
is the rate of growth of GK

00:35:58.679 --> 00:36:03.838
well is going to be equal to the rate of

00:36:01.760 --> 00:36:09.040
growth of k/

00:36:03.838 --> 00:36:09.039
n plus the rate of growth of

00:36:09.159 --> 00:36:13.879
n okay this is equal to

00:36:14.239 --> 00:36:22.039
GA so it's G Plus

00:36:16.960 --> 00:36:24.318
GN and the same happens for uh

00:36:22.039 --> 00:36:25.838
um for

00:36:24.318 --> 00:36:28.159
output

00:36:25.838 --> 00:36:30.039
okay so that's what is remember I said

00:36:28.159 --> 00:36:32.440
earlier on that

00:36:30.039 --> 00:36:34.960
that if an economy has more population

00:36:32.440 --> 00:36:38.599
growth it will grow

00:36:34.960 --> 00:36:40.440
more okay there's no doubt of that

00:36:38.599 --> 00:36:42.599
obviously output per worker will not

00:36:40.440 --> 00:36:44.920
grow more because population growth

00:36:42.599 --> 00:36:46.160
grows more in the new state G doesn't

00:36:44.920 --> 00:36:48.920
show up

00:36:46.159 --> 00:36:51.159
there okay but the only thing that will

00:36:48.920 --> 00:36:54.639
make output per

00:36:51.159 --> 00:36:55.598
worker grow is technological progress so

00:36:54.639 --> 00:37:00.400
it's

00:36:55.599 --> 00:37:00.400
G that was my claim

00:37:01.639 --> 00:37:07.879
earlier there's another we're going to

00:37:04.440 --> 00:37:07.880
use this later

00:37:09.838 --> 00:37:12.838
but

00:37:13.000 --> 00:37:19.119
um

00:37:15.920 --> 00:37:21.318
um no I'm not going to do this myself

00:37:19.119 --> 00:37:23.480
now we're I'm going to get back to what

00:37:21.318 --> 00:37:24.519
I wanted to do now because I need to

00:37:23.480 --> 00:37:26.480
tell you a little bit more about the

00:37:24.519 --> 00:37:29.838
production function to do growth

00:37:26.480 --> 00:37:34.119
accounting um which is what I wanted to

00:37:29.838 --> 00:37:36.239
do so but this is clear I mean this is

00:37:34.119 --> 00:37:38.079
important

00:37:36.239 --> 00:37:40.919
okay

00:37:38.079 --> 00:37:43.720
good so this is the reason GA is such an

00:37:40.920 --> 00:37:46.200
important variable what you guys do here

00:37:43.719 --> 00:37:48.000
at MIT is very important afterwards very

00:37:46.199 --> 00:37:49.919
important

00:37:48.000 --> 00:37:52.440
okay that's the only thing that can

00:37:49.920 --> 00:37:54.639
drive really growth in the long run in

00:37:52.440 --> 00:37:54.639
per

00:37:54.880 --> 00:38:00.800
capita this GM plays also role I mean

00:37:58.318 --> 00:38:02.800
you look at countries not only the

00:38:00.800 --> 00:38:05.880
growth in per capita output you'll tend

00:38:02.800 --> 00:38:07.920
to look at growth a total growth one of

00:38:05.880 --> 00:38:10.880
the big concerns in big parts of Asia

00:38:07.920 --> 00:38:13.519
now in Europe as well as I said earlier

00:38:10.880 --> 00:38:15.640
in the course is that g is turning

00:38:13.519 --> 00:38:18.358
negative that's not going to affect

00:38:15.639 --> 00:38:23.199
output per worker growth but it does

00:38:18.358 --> 00:38:26.400
affect output growth in general okay and

00:38:23.199 --> 00:38:29.159
you can see it here so if G goes down

00:38:26.400 --> 00:38:31.639
that will reduce the rate of growth of

00:38:29.159 --> 00:38:33.118
output doesn't reduce the rate of growth

00:38:31.639 --> 00:38:34.598
output of worker but it does reduce the

00:38:33.119 --> 00:38:37.599
rate of growth of

00:38:34.599 --> 00:38:37.599
output

00:38:37.920 --> 00:38:42.800
good so what happens remember we did in

00:38:40.639 --> 00:38:44.960
the in the in the in the basic model we

00:38:42.800 --> 00:38:48.079
did an experiment in which we increase

00:38:44.960 --> 00:38:49.880
the saving rate so we can do the same

00:38:48.079 --> 00:38:53.359
here what happens if we get an increase

00:38:49.880 --> 00:38:55.480
in the saving rate do we get more growth

00:38:53.358 --> 00:38:58.000
in the long run and the answer is for

00:38:55.480 --> 00:38:59.679
the same reasons we had before no

00:38:58.000 --> 00:39:02.599
if we increase the saving rate in this

00:38:59.679 --> 00:39:04.960
now this full model all that happens is

00:39:02.599 --> 00:39:06.960
that this green line moves up it means

00:39:04.960 --> 00:39:08.240
that at initial St State now we have

00:39:06.960 --> 00:39:09.720
more saving and therefore more

00:39:08.239 --> 00:39:11.679
investment than we need to maintain the

00:39:09.719 --> 00:39:13.598
stock of capital per effective worker

00:39:11.679 --> 00:39:16.559
constant which means that we're going to

00:39:13.599 --> 00:39:18.680
get transitional growth Capital per

00:39:16.559 --> 00:39:21.759
effective worker will start growing for

00:39:18.679 --> 00:39:24.118
a while and as that happens output per

00:39:21.760 --> 00:39:27.359
effective worker will also start

00:39:24.119 --> 00:39:29.400
growing okay but eventually the

00:39:27.358 --> 00:39:31.440
increasing returns will kick in here as

00:39:29.400 --> 00:39:35.160
well and we are going to that

00:39:31.440 --> 00:39:38.200
transitional growth will stop and H will

00:39:35.159 --> 00:39:40.000
end up at a higher level of output per

00:39:38.199 --> 00:39:41.879
effective worker and a higher level of

00:39:40.000 --> 00:39:44.880
capital per effective worker but the

00:39:41.880 --> 00:39:46.838
rate of growth in the long run will not

00:39:44.880 --> 00:39:50.000
be affected by the saving rate we'll get

00:39:46.838 --> 00:39:54.599
more transitional growth but we will not

00:39:50.000 --> 00:39:58.000
get a faster long-term

00:39:54.599 --> 00:39:59.599
growth a lot of the Asian Miracle that's

00:39:58.000 --> 00:40:02.079
that the Southeast Asian milon in

00:39:59.599 --> 00:40:05.000
particular we saw very fast rates of

00:40:02.079 --> 00:40:08.920
growth in many economies of

00:40:05.000 --> 00:40:11.039
Asia was a lot of that kind meaning was

00:40:08.920 --> 00:40:13.800
a combination of what we had before

00:40:11.039 --> 00:40:16.559
economies that were relatively poor had

00:40:13.800 --> 00:40:18.519
low Capital per work early on in which a

00:40:16.559 --> 00:40:20.480
saving rate increased enormously and

00:40:18.519 --> 00:40:23.358
that combination gave them

00:40:20.480 --> 00:40:26.240
enormous a transitional growth so rate

00:40:23.358 --> 00:40:29.000
of growth of 10 12% that was Japan and

00:40:26.239 --> 00:40:30.959
then it was Korea Taiwan and so on all

00:40:29.000 --> 00:40:33.599
those economies had very fast rates of

00:40:30.960 --> 00:40:35.318
growth as a result of that China later

00:40:33.599 --> 00:40:37.119
on and China was a big thing for the

00:40:35.318 --> 00:40:39.519
world because it was much bigger at the

00:40:37.119 --> 00:40:41.800
same time but it was mostly a

00:40:39.519 --> 00:40:43.440
combination of those two things it was

00:40:41.800 --> 00:40:47.359
being having a low stock of capital

00:40:43.440 --> 00:40:49.720
early on combined with for a variety of

00:40:47.358 --> 00:40:51.759
reasons and increasing the saving rate

00:40:49.719 --> 00:40:54.199
and that combination so gave them very

00:40:51.760 --> 00:40:56.160
fast transitional growth but they're all

00:40:54.199 --> 00:40:58.358
getting a little stuck now and they're

00:40:56.159 --> 00:41:01.118
very concerned with that well they're

00:40:58.358 --> 00:41:02.719
fighting against this model there's lots

00:41:01.119 --> 00:41:05.280
of concerns of what is happening to

00:41:02.719 --> 00:41:07.199
China are we going to follow the Japan

00:41:05.280 --> 00:41:09.680
path and so on well they're following

00:41:07.199 --> 00:41:12.039
this model that's what's happening to

00:41:09.679 --> 00:41:12.039
aair

00:41:12.599 --> 00:41:18.480
order I I'll say a little bit more later

00:41:15.880 --> 00:41:21.838
on about that so in this particular case

00:41:18.480 --> 00:41:23.838
no what what what I have done is in log

00:41:21.838 --> 00:41:27.000
space so I can have linear things when

00:41:23.838 --> 00:41:29.480
it's growing in log space this economy

00:41:27.000 --> 00:41:33.239
with the the low saving rate was

00:41:29.480 --> 00:41:35.960
growing here the slope of this was this

00:41:33.239 --> 00:41:38.559
is output so the slope of this was GA

00:41:35.960 --> 00:41:41.800
plus GN remember in a stady state output

00:41:38.559 --> 00:41:44.039
is growing at GA plus GN if the saving

00:41:41.800 --> 00:41:46.200
rate now increases then output starts

00:41:44.039 --> 00:41:49.119
growing transitionally faster than GA

00:41:46.199 --> 00:41:51.480
plus GN that's the reason sort of output

00:41:49.119 --> 00:41:54.760
grows faster than G here is all is

00:41:51.480 --> 00:41:56.440
growing faster than G here is very fast

00:41:54.760 --> 00:41:58.440
okay this is when we saw in Asia the

00:41:56.440 --> 00:42:02.480
rate of growth of 12% and stuff like

00:41:58.440 --> 00:42:04.599
that we were there moving there and and

00:42:02.480 --> 00:42:06.400
and but eventually it sort of PS out you

00:42:04.599 --> 00:42:08.400
end up with a higher level of output per

00:42:06.400 --> 00:42:12.440
capita per

00:42:08.400 --> 00:42:15.200
worker a higher sort of path no it's an

00:42:12.440 --> 00:42:16.720
entire path the rate of growth goes back

00:42:15.199 --> 00:42:19.960
to GA plus

00:42:16.719 --> 00:42:22.279
GN er uh but but you get this

00:42:19.960 --> 00:42:25.440
transitional growth which is very

00:42:22.280 --> 00:42:27.400
strong and once you're here once you all

00:42:25.440 --> 00:42:29.720
you run out of sort of the high saving

00:42:27.400 --> 00:42:31.440
and the catching up growth and so on

00:42:29.719 --> 00:42:33.159
there is little the only way you're

00:42:31.440 --> 00:42:37.000
going to really change your rate of

00:42:33.159 --> 00:42:37.000
growth in a sustained manner is doing

00:42:39.039 --> 00:42:45.920
what once you have used the tool of you

00:42:42.358 --> 00:42:48.358
know of catching up with the world of

00:42:45.920 --> 00:42:51.880
increasing your saving rate sometimes to

00:42:48.358 --> 00:42:54.239
levels incredibly High you still want to

00:42:51.880 --> 00:42:59.039
keep growing very fast what is the only

00:42:54.239 --> 00:42:59.039
option you have according to this model

00:43:06.639 --> 00:43:13.558
particularly let me bring even more ER

00:43:11.199 --> 00:43:15.519
realism to the story particular if GN is

00:43:13.559 --> 00:43:18.720
dropping and you still want to keep your

00:43:15.519 --> 00:43:21.199
growth high and your GN now you sort of

00:43:18.719 --> 00:43:22.959
use the catching up growth you use the

00:43:21.199 --> 00:43:24.439
higher saving rate which gives you

00:43:22.960 --> 00:43:26.400
transitional growth but it doesn't give

00:43:24.440 --> 00:43:27.920
you permanently higher rate of growth

00:43:26.400 --> 00:43:29.760
and on top of that for reasons you don't

00:43:27.920 --> 00:43:32.559
control population growth is declining

00:43:29.760 --> 00:43:34.920
even turning negative in some

00:43:32.559 --> 00:43:36.559
cases but suppose you still want to keep

00:43:34.920 --> 00:43:39.280
the rate of growth very high what is the

00:43:36.559 --> 00:43:39.280
only option you

00:43:41.159 --> 00:43:46.480
have increase G exactly technological

00:43:44.480 --> 00:43:48.159
progress that's the only option you have

00:43:46.480 --> 00:43:49.599
so it makes sense you see that you know

00:43:48.159 --> 00:43:51.838
in the case of china they're obsessed

00:43:49.599 --> 00:43:54.160
about technology and so on they

00:43:51.838 --> 00:43:56.880
understand the solo model okay if you

00:43:54.159 --> 00:43:58.799
want to maintain growth at a high Pace

00:43:56.880 --> 00:44:01.680
you you're going to need to work on that

00:43:58.800 --> 00:44:03.240
side a lot now it doesn't have to be you

00:44:01.679 --> 00:44:05.440
necessarily it's the world as a whole

00:44:03.239 --> 00:44:08.439
because technology you know moves around

00:44:05.440 --> 00:44:12.519
the world but but GA is at the end what

00:44:08.440 --> 00:44:12.519
puts the limits of what we can

00:44:12.639 --> 00:44:17.279
do ah what I what I was going to do is

00:44:15.760 --> 00:44:20.119
that's what I was drawing this diagram

00:44:17.280 --> 00:44:22.480
for is say well suppose that in this D

00:44:20.119 --> 00:44:24.920
this situation we are in a state state

00:44:22.480 --> 00:44:27.838
and we do increase

00:44:24.920 --> 00:44:29.358
GA what happens if we increase ga a well

00:44:27.838 --> 00:44:34.318
this

00:44:29.358 --> 00:44:37.199
curve rotates up no and at that point

00:44:34.318 --> 00:44:38.199
it's clear that that if if GA grows

00:44:37.199 --> 00:44:41.199
you're going to start growing at a

00:44:38.199 --> 00:44:43.078
faster rate but transitionally actually

00:44:41.199 --> 00:44:46.960
you're going to grow less than in your

00:44:43.079 --> 00:44:46.960
long-term rate of growth why is that the

00:44:47.519 --> 00:44:55.960
case so my claim is suppose we manage to

00:44:51.400 --> 00:45:00.559
increase GA so now we know that this

00:44:55.960 --> 00:45:03.358
line here now going to a um be steeper

00:45:00.559 --> 00:45:05.480
or say this we were in this line

00:45:03.358 --> 00:45:06.960
whatever we were in this line and now we

00:45:05.480 --> 00:45:09.159
make it a steeper so we're want to start

00:45:06.960 --> 00:45:11.400
growing faster eventually in the new

00:45:09.159 --> 00:45:12.318
state state and my claim now is that in

00:45:11.400 --> 00:45:15.039
the

00:45:12.318 --> 00:45:16.920
transition growth is less than the new

00:45:15.039 --> 00:45:18.440
rate of growth in the new in the new

00:45:16.920 --> 00:45:21.800
state state rate of

00:45:18.440 --> 00:45:24.358
growth is higher than the rate of growth

00:45:21.800 --> 00:45:27.599
of the previous St state but it's lower

00:45:24.358 --> 00:45:30.759
than the long run how do I see that I

00:45:27.599 --> 00:45:30.760
need another diagram you

00:45:36.639 --> 00:45:44.799
think so let me

00:45:39.599 --> 00:45:44.800
just put the the s y curve

00:45:45.159 --> 00:45:54.199
here so we were

00:45:48.800 --> 00:45:55.480
here at this state if I increase GA the

00:45:54.199 --> 00:45:57.239
only thing that will move here and

00:45:55.480 --> 00:45:58.800
remember the output equation is there

00:45:57.239 --> 00:46:02.719
but I don't want to put it the only

00:45:58.800 --> 00:46:07.039
thing I do is I rotate this curve

00:46:02.719 --> 00:46:07.039
up okay so this moves

00:46:07.199 --> 00:46:12.519
up do you see yes so this curves moves

00:46:11.519 --> 00:46:16.838
up when

00:46:12.519 --> 00:46:19.239
GA goes up so at the oldest steady state

00:46:16.838 --> 00:46:21.679
what I have now is a gap between the

00:46:19.239 --> 00:46:24.719
saving this economy investment and how

00:46:21.679 --> 00:46:27.558
much I need in order to maintain Capital

00:46:24.719 --> 00:46:29.879
per effective worker constant

00:46:27.559 --> 00:46:33.079
which means that I'm going to start

00:46:29.880 --> 00:46:34.640
moving in this direction until I reach

00:46:33.079 --> 00:46:37.800
the new stady

00:46:34.639 --> 00:46:40.679
state okay during this transition I'm

00:46:37.800 --> 00:46:43.318
growing at a lower Pace than in the new

00:46:40.679 --> 00:46:45.440
steady state in this new steady state I

00:46:43.318 --> 00:46:45.440
be

00:46:46.079 --> 00:46:51.960
growing much faster than in this state

00:46:48.559 --> 00:46:53.760
how much faster well equal to Delta GA

00:46:51.960 --> 00:46:55.960
but in the transition I will grow faster

00:46:53.760 --> 00:46:59.400
than that but not as fast as in the new

00:46:55.960 --> 00:46:59.400
today St that's the name was

00:47:06.480 --> 00:47:11.440
making H okay

00:47:15.119 --> 00:47:20.440
good do I you know i' rather discuss

00:47:18.760 --> 00:47:24.240
this with more time so questions about

00:47:20.440 --> 00:47:24.240
what we have done up to now

00:47:31.199 --> 00:47:37.078
is it clear or is it very unclear and

00:47:34.599 --> 00:47:37.079
probably

00:47:38.239 --> 00:47:43.679
both so let me I I I want to let me keep

00:47:42.239 --> 00:47:45.519
this for the next the next lecture

00:47:43.679 --> 00:47:49.519
because going to take a little time just

00:47:45.519 --> 00:47:49.519
play okay