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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

242
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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

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want you to it's going to be counter

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intuitive because it sounds like

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technological progress is something

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negative no it's not

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negative but but in this space it turns

250
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out that if population grows very fast

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then you need a lot of investment to

252
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keep up the the capital labor ratio

253
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constant okay that's the idea if

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population is not growing I don't need

255
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need a lot of investment to keep the

256
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capital labor ratio constant but if

257
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population is growing very fast then I

258
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need a lot of investment to really keep

259
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that ratio constant that's what this is

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capturing there

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so to repeat if if this guy is is is

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very large then I need a lot of

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investment here to make this thing equal

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to zero so the Capital stock per person

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is not declining that's idea

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okay

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good okay so now ah and then I said okay

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this is where we finish then I said okay

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so let's go uh back to our diagram I can

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once I have everything in this space K

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Over N I can go back to our diagram

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assume that GA is equal to zero you

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don't even know what A is for the time

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being you will know in five minutes but

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assume GA is equal to zero then that's

276
00:12:24,480 --> 00:12:29,959
exactly the model we had before

277
00:12:27,600 --> 00:12:31,800
so and remember this this is exactly the

278
00:12:29,958 --> 00:12:33,278
same diagram it looked the same at least

279
00:12:31,799 --> 00:12:36,000
that we had when population was not

280
00:12:33,278 --> 00:12:39,278
growing I'm saying I can use the same

281
00:12:36,000 --> 00:12:42,198
diagram when population is growing as

282
00:12:39,278 --> 00:12:45,000
well but there is one important

283
00:12:42,198 --> 00:12:47,278
difference which is this this curve

284
00:12:45,000 --> 00:12:51,679
looks exactly the same this is just

285
00:12:47,278 --> 00:12:54,439
output H per per worker okay that's the

286
00:12:51,679 --> 00:12:57,120
Blue Line the green line looks exactly

287
00:12:54,440 --> 00:12:59,399
the same as in the basic model it's just

288
00:12:57,120 --> 00:13:02,679
little s times that the blue line so

289
00:12:59,399 --> 00:13:05,519
that's exactly the same but this line is

290
00:13:02,679 --> 00:13:09,679
different what happens to this red line

291
00:13:05,519 --> 00:13:12,278
as as GN goes up so what happens to this

292
00:13:09,679 --> 00:13:15,919
line as GN goes

293
00:13:12,278 --> 00:13:20,639
up becomes steeper no yeah so it rotates

294
00:13:15,919 --> 00:13:22,278
up okay goes up and that can sound

295
00:13:20,639 --> 00:13:24,799
counterintuitive sometimes because you

296
00:13:22,278 --> 00:13:26,039
say look look what happens here let's

297
00:13:24,799 --> 00:13:28,958
spend time on

298
00:13:26,039 --> 00:13:31,120
this suppose that we are at some St

299
00:13:28,958 --> 00:13:35,719
state say this

300
00:13:31,120 --> 00:13:35,720
one and now population growth

301
00:13:36,000 --> 00:13:43,360
Rises okay it sounds like Ireland in you

302
00:13:40,679 --> 00:13:47,198
know 2000s and

303
00:13:43,360 --> 00:13:49,919
so so population growth Rises a

304
00:13:47,198 --> 00:13:53,159
lot what happens in this diagram so

305
00:13:49,919 --> 00:13:57,360
suppose we're at the state state

306
00:13:53,159 --> 00:14:00,120
here no and that the state

307
00:13:57,360 --> 00:14:01,800
investment uh saving which is equal to

308
00:14:00,120 --> 00:14:03,959
investment is exactly what you need to

309
00:14:01,799 --> 00:14:06,838
maintain the stock of capital per person

310
00:14:03,958 --> 00:14:11,198
constant okay that's what the red line

311
00:14:06,839 --> 00:14:13,639
tells us no that here so that's the Gap

312
00:14:11,198 --> 00:14:15,278
here is this is a gap between investment

313
00:14:13,639 --> 00:14:18,039
and what you need to maintain the stock

314
00:14:15,278 --> 00:14:21,600
of capital per person constant so when

315
00:14:18,039 --> 00:14:23,958
the Gap is zero then then this equation

316
00:14:21,600 --> 00:14:26,800
this left hand side is equal to zero

317
00:14:23,958 --> 00:14:29,518
okay that's the red line that's the

318
00:14:26,799 --> 00:14:32,519
green line when this is equal to Z

319
00:14:29,519 --> 00:14:35,159
that's equal to that that's exactly that

320
00:14:32,519 --> 00:14:37,278
point okay but I'm saying suppose we are

321
00:14:35,159 --> 00:14:40,000
at that point and

322
00:14:37,278 --> 00:14:43,958
now population growth

323
00:14:40,000 --> 00:14:46,600
Rises so what moves in that diagram does

324
00:14:43,958 --> 00:14:46,599
a blue line

325
00:14:50,639 --> 00:14:55,919
move I don't see GN in the blue line so

326
00:14:53,879 --> 00:14:57,360
the Blue Line doesn't move if the Blue

327
00:14:55,919 --> 00:14:58,719
Line doesn't move and the saving rate

328
00:14:57,360 --> 00:15:00,278
hasn't changed then the green line

329
00:14:58,720 --> 00:15:02,879
doesn't move move

330
00:15:00,278 --> 00:15:05,360
either so for this diagram to be

331
00:15:02,879 --> 00:15:07,639
interesting what moves assum has to move

332
00:15:05,360 --> 00:15:10,800
so the only thing that has that can move

333
00:15:07,639 --> 00:15:13,079
here is the is the red line and the red

334
00:15:10,799 --> 00:15:15,159
line we already said if GM goes up it's

335
00:15:13,078 --> 00:15:16,879
going to rotate

336
00:15:15,159 --> 00:15:20,319
upwards that

337
00:15:16,879 --> 00:15:23,480
means say so now we have that line there

338
00:15:20,320 --> 00:15:26,120
so what happens at the at the at the

339
00:15:23,480 --> 00:15:29,159
previous St State stock of capital per

340
00:15:26,120 --> 00:15:31,959
worker at this level what happens is

341
00:15:29,159 --> 00:15:31,958
that a new state

342
00:15:32,839 --> 00:15:39,600
state no but what happens in particular

343
00:15:37,078 --> 00:15:41,479
what is it so I'm saying suppose that

344
00:15:39,600 --> 00:15:42,360
you're here and now I rotate the red

345
00:15:41,480 --> 00:15:45,680
line

346
00:15:42,360 --> 00:15:47,480
up okay so that means the red line that

347
00:15:45,679 --> 00:15:49,799
represents the amount of capital I need

348
00:15:47,480 --> 00:15:53,399
to maintain the stock of capital

349
00:15:49,799 --> 00:15:56,000
constant is greater than how much

350
00:15:53,399 --> 00:15:57,639
Society saving and therefore investing

351
00:15:56,000 --> 00:16:00,639
so what will happen to Capital per

352
00:15:57,639 --> 00:16:00,639
worker

353
00:16:02,278 --> 00:16:08,480
decrease exactly because you need more

354
00:16:05,958 --> 00:16:10,198
than you're investing so the Capital

355
00:16:08,480 --> 00:16:11,759
stock has to decline and that's what

356
00:16:10,198 --> 00:16:14,519
will happen the new state state is going

357
00:16:11,759 --> 00:16:16,919
to be to the left of that point

358
00:16:14,519 --> 00:16:20,318
there that sounds very

359
00:16:16,919 --> 00:16:23,360
weird how can it be that you know after

360
00:16:20,318 --> 00:16:25,639
all labor contributes to Output how can

361
00:16:23,360 --> 00:16:28,360
it be that we end up with a

362
00:16:25,639 --> 00:16:30,240
lower ER output per per worker when we

363
00:16:28,360 --> 00:16:33,199
increase popul population growth is

364
00:16:30,240 --> 00:16:37,318
population growth bad in a sense for

365
00:16:33,198 --> 00:16:37,318
growth itself for

366
00:16:41,278 --> 00:16:47,439
output well the answer is no it's it's

367
00:16:44,919 --> 00:16:50,240
true that the new state state will have

368
00:16:47,440 --> 00:16:52,040
lower output per person so in that sense

369
00:16:50,240 --> 00:16:54,440
it's bad you have lots of population if

370
00:16:52,039 --> 00:16:57,000
you if if you don't change the saving

371
00:16:54,440 --> 00:17:00,319
rate or something then output per person

372
00:16:57,000 --> 00:17:02,639
will be lower but output will be higher

373
00:17:00,318 --> 00:17:05,438
than it used to be at any point in time

374
00:17:02,639 --> 00:17:08,720
it just happens that in the transition

375
00:17:05,439 --> 00:17:10,720
the growth of output so so the growth

376
00:17:08,720 --> 00:17:13,360
the growth of output in this model is

377
00:17:10,720 --> 00:17:16,360
going to be equal to the growth of

378
00:17:13,359 --> 00:17:18,479
population okay that's if you have a St

379
00:17:16,359 --> 00:17:20,759
state where population is growing and

380
00:17:18,480 --> 00:17:23,038
output per worker or per person is not

381
00:17:20,759 --> 00:17:25,279
growing that means output is growing at

382
00:17:23,038 --> 00:17:26,838
the same rate as population so that

383
00:17:25,279 --> 00:17:29,079
means that if I increase the rate of

384
00:17:26,838 --> 00:17:30,639
population growth the rate of growth

385
00:17:29,079 --> 00:17:32,439
output will

386
00:17:30,640 --> 00:17:34,440
increase together with the rate of

387
00:17:32,440 --> 00:17:36,640
growth of population but in the

388
00:17:34,440 --> 00:17:39,400
transition as the output per capita goes

389
00:17:36,640 --> 00:17:41,520
lower output will grow less than

390
00:17:39,400 --> 00:17:43,038
population that's what is happening here

391
00:17:41,519 --> 00:17:44,679
okay but output is growing if you

392
00:17:43,038 --> 00:17:46,839
population starts growing if you

393
00:17:44,679 --> 00:17:50,919
increase migration you're going to see

394
00:17:46,839 --> 00:17:53,399
output grow but output per person will

395
00:17:50,919 --> 00:17:56,720
start declining until you get to New

396
00:17:53,400 --> 00:17:59,159
State and then you'll get the same

397
00:17:56,720 --> 00:18:01,240
ER you'll get the higher rate of growth

398
00:17:59,159 --> 00:18:03,480
you continue with population growth with

399
00:18:01,240 --> 00:18:07,640
the high population growth but output

400
00:18:03,480 --> 00:18:07,640
per worker would be slightly lower rate

401
00:18:09,079 --> 00:18:14,319
okay anyways this may have been fast the

402
00:18:12,640 --> 00:18:16,520
last part but since I'm going to repeat

403
00:18:14,319 --> 00:18:19,879
it now in the context of technological

404
00:18:16,519 --> 00:18:21,759
progress we should be fine okay so if

405
00:18:19,880 --> 00:18:24,120
you're a little confused now it's okay

406
00:18:21,759 --> 00:18:25,599
if you're a little confused at the end

407
00:18:24,119 --> 00:18:28,079
of the lecture it's not okay because

408
00:18:25,599 --> 00:18:30,719
that's I'm counting with you sort of

409
00:18:28,079 --> 00:18:34,199
getting it in the second pass okay

410
00:18:30,720 --> 00:18:37,480
second try Okay so next step is is f so

411
00:18:34,200 --> 00:18:39,919
here we assume already population growth

412
00:18:37,480 --> 00:18:42,038
where we assume that technology so the

413
00:18:39,919 --> 00:18:44,840
production function sort of stay put for

414
00:18:42,038 --> 00:18:48,519
any combination of capital and labor the

415
00:18:44,839 --> 00:18:50,319
next step is to think what happens when

416
00:18:48,519 --> 00:18:53,519
the technology itself is getting better

417
00:18:50,319 --> 00:18:58,079
over time and that's what we call

418
00:18:53,519 --> 00:18:59,960
technological progress okay this is tfp

419
00:18:58,079 --> 00:19:03,158
let me not get into to specifics at the

420
00:18:59,960 --> 00:19:05,880
end I'll say a little more but P tfp

421
00:19:03,159 --> 00:19:08,440
stands for total Factor productivity and

422
00:19:05,880 --> 00:19:09,840
this index here captures the level of

423
00:19:08,440 --> 00:19:12,798
tfp in the

424
00:19:09,839 --> 00:19:14,798
US over time and it's clearly growing so

425
00:19:12,798 --> 00:19:17,720
technolog is getting better and better

426
00:19:14,798 --> 00:19:19,879
over time what that means well it I say

427
00:19:17,720 --> 00:19:21,079
a little more not a lot more but but

428
00:19:19,880 --> 00:19:25,559
it's getting

429
00:19:21,079 --> 00:19:27,879
better no h and so the question we have

430
00:19:25,558 --> 00:19:30,319
here is I'm going when to address next

431
00:19:27,880 --> 00:19:32,360
is how does this so now we're going to

432
00:19:30,319 --> 00:19:33,720
put together our entire economic growth

433
00:19:32,359 --> 00:19:35,678
model we're going to have population

434
00:19:33,720 --> 00:19:37,919
growth we're want to have also

435
00:19:35,679 --> 00:19:39,200
technology growing up to now the only

436
00:19:37,919 --> 00:19:42,559
reason you could

437
00:19:39,200 --> 00:19:44,519
grow a you could grow output per per

438
00:19:42,558 --> 00:19:46,359
worker was because you were accumulating

439
00:19:44,519 --> 00:19:47,918
lots of capital you were catching up

440
00:19:46,359 --> 00:19:49,879
with you're a steady state that's what

441
00:19:47,919 --> 00:19:53,120
would make you grow faster but then

442
00:19:49,880 --> 00:19:55,480
there was nothing else tfp is going to

443
00:19:53,119 --> 00:19:57,199
be the only growth in technology is

444
00:19:55,480 --> 00:19:59,159
going to be the only thing that will

445
00:19:57,200 --> 00:20:02,480
give you sustainable growth in the long

446
00:19:59,159 --> 00:20:07,159
run an output per person okay so this is

447
00:20:02,480 --> 00:20:09,319
a very important component of of H of

448
00:20:07,159 --> 00:20:11,720
growth again it's the only thing that

449
00:20:09,319 --> 00:20:15,720
will make you grow in a sustainable

450
00:20:11,720 --> 00:20:17,919
manner in in per person terms okay the

451
00:20:15,720 --> 00:20:20,480
previous model didn't have that in the

452
00:20:17,919 --> 00:20:24,240
previous model we had a steady

453
00:20:20,480 --> 00:20:26,360
state ER on on output per worker so in

454
00:20:24,240 --> 00:20:29,279
the previous model we didn't have growth

455
00:20:26,359 --> 00:20:31,479
in output per worker in the St state

456
00:20:29,279 --> 00:20:34,119
we could have transitional growth when

457
00:20:31,480 --> 00:20:35,558
we were catching up no if you if you

458
00:20:34,119 --> 00:20:38,959
started

459
00:20:35,558 --> 00:20:41,639
here then you were going to have growth

460
00:20:38,960 --> 00:20:45,798
fast growth but eventually will pet it

461
00:20:41,640 --> 00:20:48,360
out okay out work so so up to now we

462
00:20:45,798 --> 00:20:51,319
don't have a reason for why to to to

463
00:20:48,359 --> 00:20:54,798
explain why we see that output per

464
00:20:51,319 --> 00:20:57,480
worker grows in most economies in the

465
00:20:54,798 --> 00:20:59,038
world and the answer will be this this

466
00:20:57,480 --> 00:21:00,960
is the reason really how output per

467
00:20:59,038 --> 00:21:02,480
worker can grow in a sustained manner

468
00:21:00,960 --> 00:21:05,960
it's technolog is getting better and

469
00:21:02,480 --> 00:21:08,759
better over time so let's let's see so

470
00:21:05,960 --> 00:21:11,278
the question is let's now see what this

471
00:21:08,759 --> 00:21:15,240
does to the model we

472
00:21:11,278 --> 00:21:19,839
have now in practice technological

473
00:21:15,240 --> 00:21:24,120
progress takes many many forms er

474
00:21:19,839 --> 00:21:26,399
um it in at most basic level means that

475
00:21:24,119 --> 00:21:27,558
you can produce larger quantities output

476
00:21:26,400 --> 00:21:29,759
and that's really the meaning we're

477
00:21:27,558 --> 00:21:31,678
going to have here larger quantities of

478
00:21:29,759 --> 00:21:32,400
output for the same amount of capital

479
00:21:31,679 --> 00:21:35,240
and

480
00:21:32,400 --> 00:21:37,840
labor okay so you have 10 machines 10

481
00:21:35,240 --> 00:21:40,240
workers technological progress means

482
00:21:37,839 --> 00:21:43,240
well you used to produce 12 units now

483
00:21:40,240 --> 00:21:46,919
we're going to produce 12 14 15 and so

484
00:21:43,240 --> 00:21:49,038
on so forth that's that's a one way of

485
00:21:46,919 --> 00:21:51,679
techn that one of the main ways

486
00:21:49,038 --> 00:21:55,200
technological progress shows up we can

487
00:21:51,679 --> 00:21:57,679
do more with the same if you will second

488
00:21:55,200 --> 00:21:59,360
dimension is better product so it's not

489
00:21:57,679 --> 00:22:01,720
that you produce more cars but you

490
00:21:59,359 --> 00:22:04,038
produce better cars better computers and

491
00:22:01,720 --> 00:22:06,159
so on okay that's another dimension of

492
00:22:04,038 --> 00:22:09,158
technal prod you can produce new

493
00:22:06,159 --> 00:22:10,240
products things that didn't even exist

494
00:22:09,159 --> 00:22:13,080
but now you

495
00:22:10,240 --> 00:22:14,919
have that counts more than having one

496
00:22:13,079 --> 00:22:16,798
more unit of good it counts more because

497
00:22:14,919 --> 00:22:18,320
you have you know things that you

498
00:22:16,798 --> 00:22:20,359
couldn't even satisfy in the past you

499
00:22:18,319 --> 00:22:22,879
can satisfy now because you have the

500
00:22:20,359 --> 00:22:25,479
certain kind of goods that DNX is before

501
00:22:22,880 --> 00:22:28,640
that's a very important dimension of

502
00:22:25,480 --> 00:22:30,558
technological progress is just create no

503
00:22:28,640 --> 00:22:34,000
new sort of forms of inputs of

504
00:22:30,558 --> 00:22:36,599
production and Technologies think of AI

505
00:22:34,000 --> 00:22:38,960
what that will do to to technology in

506
00:22:36,599 --> 00:22:43,079
general and to consumption very

507
00:22:38,960 --> 00:22:45,079
directly ER and that's what I mean even

508
00:22:43,079 --> 00:22:46,960
within a product you you can get more

509
00:22:45,079 --> 00:22:48,839
variety and more variety you know

510
00:22:46,960 --> 00:22:53,120
improves welfare because you can align

511
00:22:48,839 --> 00:22:54,720
better the needs H with with the product

512
00:22:53,119 --> 00:22:57,639
and so on but we're going to make it

513
00:22:54,720 --> 00:22:59,120
very simple in this in this in this

514
00:22:57,640 --> 00:23:02,400
course we're going to we're going to

515
00:22:59,119 --> 00:23:03,278
model technological progress as if it

516
00:23:02,400 --> 00:23:06,759
was

517
00:23:03,278 --> 00:23:10,558
workers okay so

518
00:23:06,759 --> 00:23:13,879
uh we're going to capture technology

519
00:23:10,558 --> 00:23:15,839
with this Con with this variable a which

520
00:23:13,880 --> 00:23:20,559
is going to be we're going to model it

521
00:23:15,839 --> 00:23:23,199
as labor equivalent that is if a grows

522
00:23:20,558 --> 00:23:24,440
it's going to count for us as if we had

523
00:23:23,200 --> 00:23:26,558
more

524
00:23:24,440 --> 00:23:28,278
workers okay that's just one way of

525
00:23:26,558 --> 00:23:30,440
model it I mean I can I can do it in

526
00:23:28,278 --> 00:23:32,720
many different ways andan some many of

527
00:23:30,440 --> 00:23:34,798
these are equivalent but that's a very

528
00:23:32,720 --> 00:23:37,400
very nice way of modeling so we can use

529
00:23:34,798 --> 00:23:39,000
exactly the same diagrams we have and so

530
00:23:37,400 --> 00:23:40,559
okay so you can think of technological

531
00:23:39,000 --> 00:23:42,839
progress the way I'm going to model this

532
00:23:40,558 --> 00:23:45,158
here is you can think of technological

533
00:23:42,839 --> 00:23:46,759
progress as if this economy was

534
00:23:45,159 --> 00:23:50,799
receiving more

535
00:23:46,759 --> 00:23:53,400
workers okay or a more accurate

536
00:23:50,798 --> 00:23:56,839
description is with the same workers it

537
00:23:53,400 --> 00:23:58,960
can produce is as if he had more labor

538
00:23:56,839 --> 00:24:01,639
input okay that's that's one way of

539
00:23:58,960 --> 00:24:04,200
capturing technology technological

540
00:24:01,640 --> 00:24:07,679
progress so now that means that I'm

541
00:24:04,200 --> 00:24:11,440
going to refer to this term a n as

542
00:24:07,679 --> 00:24:13,919
effective labor you know so with the

543
00:24:11,440 --> 00:24:15,759
same number of n bodies I may get more

544
00:24:13,919 --> 00:24:18,159
effective label because each worker can

545
00:24:15,759 --> 00:24:21,839
produce more things it's a better input

546
00:24:18,159 --> 00:24:25,039
of production factor of production

547
00:24:21,839 --> 00:24:26,599
okay so it and I like to mod it this way

548
00:24:25,038 --> 00:24:29,079
because now I can use exactly the same

549
00:24:26,599 --> 00:24:32,079
diagrams we had before but rather than

550
00:24:29,079 --> 00:24:37,398
normalizing by population I'm going to

551
00:24:32,079 --> 00:24:38,918
normalize by effective labor by a n

552
00:24:37,398 --> 00:24:41,879
okay

553
00:24:38,919 --> 00:24:43,520
so let me do that so recall that we had

554
00:24:41,880 --> 00:24:46,278
our production function with constant

555
00:24:43,519 --> 00:24:50,240
return so this hold I'm going to set

556
00:24:46,278 --> 00:24:53,480
this x now as 1/ a n we used to have 1/

557
00:24:50,240 --> 00:24:56,640
n I'm going to have 1/ a n and so I'm

558
00:24:53,480 --> 00:24:59,038
going to now have output per effective

559
00:24:56,640 --> 00:25:02,120
worker is going to be also the same

560
00:24:59,038 --> 00:25:03,240
little function f of capital per

561
00:25:02,119 --> 00:25:06,719
effective

562
00:25:03,240 --> 00:25:08,480
worker okay and what is nice of this is

563
00:25:06,720 --> 00:25:12,200
that now here rather than plotting y

564
00:25:08,480 --> 00:25:13,960
Over N I'm going to PL plot y over a n

565
00:25:12,200 --> 00:25:16,840
rather than plotting K Over N here I'm

566
00:25:13,960 --> 00:25:19,038
going to plot K over a n and I have the

567
00:25:16,839 --> 00:25:21,959
blue line looks exactly like it used to

568
00:25:19,038 --> 00:25:24,200
look it's just I'm dividing by a Over N

569
00:25:21,960 --> 00:25:26,079
remember the trick in all these models

570
00:25:24,200 --> 00:25:28,319
is to find the right normalization that

571
00:25:26,079 --> 00:25:30,678
is to find the right X so I can find

572
00:25:28,319 --> 00:25:32,038
find a steady state in my diagram I

573
00:25:30,679 --> 00:25:34,720
don't want these curves to be moving

574
00:25:32,038 --> 00:25:36,359
around I want this to have a a steady

575
00:25:34,720 --> 00:25:38,839
state something a point that that we're

576
00:25:36,359 --> 00:25:42,079
going to converge to after enough time

577
00:25:38,839 --> 00:25:43,480
has passed okay and I know that that the

578
00:25:42,079 --> 00:25:45,439
thing that will do it in a model in

579
00:25:43,480 --> 00:25:47,480
which I have popul effective workers

580
00:25:45,440 --> 00:25:50,240
growing is one in which I divide

581
00:25:47,480 --> 00:25:52,720
everything by effective

582
00:25:50,240 --> 00:25:54,278
workers okay so that's what I'm doing

583
00:25:52,720 --> 00:25:55,720
here I'm going to build a diagram that

584
00:25:54,278 --> 00:25:58,440
looks like the other one that has a nice

585
00:25:55,720 --> 00:26:00,720
steady state as the previous one had

586
00:25:58,440 --> 00:26:02,558
okay so I have my blue line you I have

587
00:26:00,720 --> 00:26:03,919
my blue line I know I have my green line

588
00:26:02,558 --> 00:26:06,480
no because the green line was just

589
00:26:03,919 --> 00:26:09,679
little s times the blue line so I have

590
00:26:06,480 --> 00:26:11,440
that the last thing I need and I already

591
00:26:09,679 --> 00:26:14,919
show you that but I'm going to show it

592
00:26:11,440 --> 00:26:17,038
again is is the is the red line okay but

593
00:26:14,919 --> 00:26:19,440
for the red line I need to find this

594
00:26:17,038 --> 00:26:21,919
term the term remember the red line

595
00:26:19,440 --> 00:26:24,080
represents the capital we need to

596
00:26:21,919 --> 00:26:26,799
maintain the current stock of capital

597
00:26:24,079 --> 00:26:29,480
per effective worker constant that's

598
00:26:26,798 --> 00:26:31,038
what I need my red line for so let's get

599
00:26:29,480 --> 00:26:32,720
there and it always start from this

600
00:26:31,038 --> 00:26:34,158
equation so this equation is still the

601
00:26:32,720 --> 00:26:36,600
same as it used to be that doesn't

602
00:26:34,159 --> 00:26:39,000
change but what I'm going to do now is

603
00:26:36,599 --> 00:26:43,319
rather than dividing by n I'm going to

604
00:26:39,000 --> 00:26:45,480
divide by a * n so the same as I did

605
00:26:43,319 --> 00:26:48,960
earlier in this lecture I now want to

606
00:26:45,480 --> 00:26:51,319
divide by a Over N so I get Capital per

607
00:26:48,960 --> 00:26:53,200
effective work on the left hand side I

608
00:26:51,319 --> 00:26:57,000
don't like what I get here but you know

609
00:26:53,200 --> 00:27:00,200
that I can divide and multiply by a n n

610
00:26:57,000 --> 00:27:03,200
over a n so I can write the right hand

611
00:27:00,200 --> 00:27:04,840
side after do all my substitutions as

612
00:27:03,200 --> 00:27:08,720
this

613
00:27:04,839 --> 00:27:13,000
okay you know so I first step one I

614
00:27:08,720 --> 00:27:16,159
divided everything by a t + 1 * NT + 1

615
00:27:13,000 --> 00:27:19,839
step two I multiply each of these terms

616
00:27:16,159 --> 00:27:22,919
by a and t i multiply by AT and T divide

617
00:27:19,839 --> 00:27:25,918
by AT and T and T okay and then I

618
00:27:22,919 --> 00:27:27,799
regroup things so I end up with that

619
00:27:25,919 --> 00:27:31,480
well this using the approximation we

620
00:27:27,798 --> 00:27:33,679
have here here is equal to approximately

621
00:27:31,480 --> 00:27:37,240
equal to 1 minus g

622
00:27:33,679 --> 00:27:37,240
n and g

623
00:27:41,798 --> 00:27:48,519
n is equal to

624
00:27:45,278 --> 00:27:48,519
GA plus

625
00:27:48,599 --> 00:27:53,918
GN okay so I already show you that that

626
00:27:51,839 --> 00:27:57,839
case for the case in which GA was equal

627
00:27:53,919 --> 00:27:59,840
to zero I'm doing now the same thing but

628
00:27:57,839 --> 00:28:03,158
but you know since I renormalize things

629
00:27:59,839 --> 00:28:06,639
by effective workers effective labor

630
00:28:03,159 --> 00:28:08,480
rather than actual label I need to use a

631
00:28:06,640 --> 00:28:10,720
n rather than

632
00:28:08,480 --> 00:28:12,679
n okay and then by the same

633
00:28:10,720 --> 00:28:15,240
approximation I had before which is that

634
00:28:12,679 --> 00:28:18,240
you know these products are close to

635
00:28:15,240 --> 00:28:20,720
zero then I get to the equation I want

636
00:28:18,240 --> 00:28:22,679
and if I write it in first difference

637
00:28:20,720 --> 00:28:24,480
then I get my Red Line This is my red

638
00:28:22,679 --> 00:28:28,278
line

639
00:28:24,480 --> 00:28:29,720
here okay

640
00:28:28,278 --> 00:28:35,679
good

641
00:28:29,720 --> 00:28:38,600
so H in um this tells me that when the

642
00:28:35,679 --> 00:28:42,240
ER the green line green line is equal to

643
00:28:38,599 --> 00:28:44,158
the red line then I have a steady state

644
00:28:42,240 --> 00:28:45,839
capital perfective worker is constant

645
00:28:44,159 --> 00:28:47,960
that this this is equal to zero that's

646
00:28:45,839 --> 00:28:49,839
the way I find my steady state if I ask

647
00:28:47,960 --> 00:28:51,720
you a question find the steady state of

648
00:28:49,839 --> 00:28:54,158
this economy what you'll do is you'll

649
00:28:51,720 --> 00:28:56,480
set this equal to zero and find the

650
00:28:54,159 --> 00:29:00,640
Capital stock that gives you this equal

651
00:28:56,480 --> 00:29:04,079
to zero that's the way you do it okay

652
00:29:00,640 --> 00:29:06,880
so so that's that's that and then we get

653
00:29:04,079 --> 00:29:09,398
back to

654
00:29:06,880 --> 00:29:10,760
um well this is this is the same as we

655
00:29:09,398 --> 00:29:13,038
had

656
00:29:10,759 --> 00:29:16,839
before that's what I just said that's

657
00:29:13,038 --> 00:29:18,640
the way you find the stud State okay and

658
00:29:16,839 --> 00:29:21,240
then we get back to the diagram I

659
00:29:18,640 --> 00:29:25,440
started with in this lecture okay but

660
00:29:21,240 --> 00:29:28,200
now we have here a a n and now in in in

661
00:29:25,440 --> 00:29:32,240
the first part I said assume this G ga

662
00:29:28,200 --> 00:29:36,240
GA is equal to zero now the main actor

663
00:29:32,240 --> 00:29:38,120
is GA positive okay and and we get this

664
00:29:36,240 --> 00:29:39,960
diagram so now I can ask you the

665
00:29:38,119 --> 00:29:42,479
question that that that I asked you

666
00:29:39,960 --> 00:29:45,600
before with population growth and see

667
00:29:42,480 --> 00:29:48,079
how much I can confuse you suppose that

668
00:29:45,599 --> 00:29:50,839
GA goes up that sounds like a good thing

669
00:29:48,079 --> 00:29:54,278
no I mean ER suppose that we're at the

670
00:29:50,839 --> 00:29:59,000
steady state here and I mean this

671
00:29:54,278 --> 00:29:59,000
diagram has too much stuff let me

672
00:29:59,329 --> 00:30:02,529
[Music]

673
00:30:19,640 --> 00:30:22,720
okay so we're

674
00:30:22,919 --> 00:30:29,960
here that's our initial

675
00:30:26,519 --> 00:30:29,960
State um

676
00:30:37,798 --> 00:30:44,679
zero and and this line here is Delta

677
00:30:42,240 --> 00:30:48,000
plus

678
00:30:44,679 --> 00:30:48,000
GA plus

679
00:30:49,079 --> 00:30:59,480
GN * K over a n okay

680
00:30:55,599 --> 00:31:03,359
so the question well first let's let's

681
00:30:59,480 --> 00:31:03,360
so suppose we're at the say

682
00:31:03,720 --> 00:31:11,600
state is output constant there I mean

683
00:31:08,480 --> 00:31:14,480
that's it's a state state it's output

684
00:31:11,599 --> 00:31:16,839
output constant there so suppose we are

685
00:31:14,480 --> 00:31:16,839
at that

686
00:31:17,638 --> 00:31:24,599
point here here we know that investment

687
00:31:21,359 --> 00:31:26,558
exactly how much we need to maintain the

688
00:31:24,599 --> 00:31:28,359
stock of capital per effective worker

689
00:31:26,558 --> 00:31:29,158
constant that's what what the state

690
00:31:28,359 --> 00:31:33,719
state

691
00:31:29,159 --> 00:31:37,120
means question is output constant

692
00:31:33,720 --> 00:31:37,120
there state

693
00:31:48,798 --> 00:31:54,879
state

694
00:31:51,359 --> 00:31:58,638
no this only says

695
00:31:54,880 --> 00:32:01,919
that Capital per effective work

696
00:31:58,638 --> 00:32:05,398
is constant that means that if effective

697
00:32:01,919 --> 00:32:07,679
workers or labor is growing then capital

698
00:32:05,398 --> 00:32:10,119
is growing at the same rate and

699
00:32:07,679 --> 00:32:15,278
therefore output is growing at the same

700
00:32:10,119 --> 00:32:17,278
rate as effective workers okay that's

701
00:32:15,278 --> 00:32:19,000
the reason remember the whole trick so

702
00:32:17,278 --> 00:32:21,079
the curves would not be moving around is

703
00:32:19,000 --> 00:32:23,000
I find the right normalization so

704
00:32:21,079 --> 00:32:24,319
everything is growing at the same rate

705
00:32:23,000 --> 00:32:28,319
in that St

706
00:32:24,319 --> 00:32:28,319
State okay

707
00:32:29,119 --> 00:32:33,479
so let me actually show you that and

708
00:32:30,839 --> 00:32:35,558
then I'm going to go over the experiment

709
00:32:33,480 --> 00:32:37,480
I want to have so this is what is

710
00:32:35,558 --> 00:32:42,079
happening in that steady

711
00:32:37,480 --> 00:32:45,519
state so Capital per effective worker at

712
00:32:42,079 --> 00:32:49,199
the steady state so at that point

713
00:32:45,519 --> 00:32:52,319
there is zero no that's a stady that's

714
00:32:49,200 --> 00:32:55,519
my definition of a steady state okay

715
00:32:52,319 --> 00:32:58,079
output effective worker is also growing

716
00:32:55,519 --> 00:33:01,480
at at at the rate zero that's that one

717
00:32:58,079 --> 00:33:05,480
over there

718
00:33:01,480 --> 00:33:09,240
sorry that's my state level of output

719
00:33:05,480 --> 00:33:09,240
per effective worker

720
00:33:11,798 --> 00:33:18,319
okay so these are constant that's a say

721
00:33:14,759 --> 00:33:21,119
State those are constant this ratio is

722
00:33:18,319 --> 00:33:22,960
constant each of those components is

723
00:33:21,119 --> 00:33:25,558
not

724
00:33:22,960 --> 00:33:30,480
so that's what I'm plotting there so

725
00:33:25,558 --> 00:33:33,759
that's those are not growing Capital per

726
00:33:30,480 --> 00:33:37,720
worker what about that well you you see

727
00:33:33,759 --> 00:33:41,359
there explain why why so claim Capital

728
00:33:37,720 --> 00:33:44,880
per worker is growing at the rate GA how

729
00:33:41,359 --> 00:33:44,879
do I know that

730
00:33:54,250 --> 00:33:57,608
[Music]

731
00:33:58,960 --> 00:34:05,038
so the question I'm asking

732
00:34:01,278 --> 00:34:10,239
there is what is the rate of

733
00:34:05,038 --> 00:34:10,239
growth of k/

734
00:34:14,039 --> 00:34:24,358
n Pro given that I already know that the

735
00:34:18,760 --> 00:34:24,359
rate of growth of K over a

736
00:34:24,760 --> 00:34:29,440
n is equal to zero

737
00:34:34,239 --> 00:34:45,439
well this the rate of growth of K Over N

738
00:34:38,119 --> 00:34:47,599
is the rate of growth of K over a n plus

739
00:34:45,440 --> 00:34:49,240
the rate of growth of

740
00:34:47,599 --> 00:34:53,679
a

741
00:34:49,239 --> 00:34:54,479
no I mean if a is growing and this ratio

742
00:34:53,679 --> 00:34:57,358
is

743
00:34:54,480 --> 00:34:59,199
constant that means that k/ n must be

744
00:34:57,358 --> 00:35:00,960
growing

745
00:34:59,199 --> 00:35:04,679
and it has to be growing at exactly the

746
00:35:00,960 --> 00:35:05,800
same rate as this a is growing otherwise

747
00:35:04,679 --> 00:35:07,000
I wouldn't be able to maintain that

748
00:35:05,800 --> 00:35:09,440
ratio

749
00:35:07,000 --> 00:35:12,679
constant

750
00:35:09,440 --> 00:35:15,400
okay and the same logic applies

751
00:35:12,679 --> 00:35:18,358
to Output per worker because in that

752
00:35:15,400 --> 00:35:19,320
steady state output per effective worker

753
00:35:18,358 --> 00:35:23,239
is

754
00:35:19,320 --> 00:35:26,160
constant but a is growing so output per

755
00:35:23,239 --> 00:35:28,479
worker must be growing at the same rate

756
00:35:26,159 --> 00:35:31,598
as a is growing and that's

757
00:35:28,480 --> 00:35:34,358
G okay

758
00:35:31,599 --> 00:35:36,880
good labor well labor is exogenous which

759
00:35:34,358 --> 00:35:40,119
say population is growing at the rate n

760
00:35:36,880 --> 00:35:44,599
that's given what about

761
00:35:40,119 --> 00:35:49,160
Capital an output well claim capital and

762
00:35:44,599 --> 00:35:49,160
output are growing at the rate GA plus

763
00:35:49,800 --> 00:35:56,079
GN and I can do the same as I was in

764
00:35:52,400 --> 00:35:58,680
here I'm asking you the question GK what

765
00:35:56,079 --> 00:36:01,760
is the rate of growth of GK

766
00:35:58,679 --> 00:36:03,838
well is going to be equal to the rate of

767
00:36:01,760 --> 00:36:09,040
growth of k/

768
00:36:03,838 --> 00:36:09,039
n plus the rate of growth of

769
00:36:09,159 --> 00:36:13,879
n okay this is equal to

770
00:36:14,239 --> 00:36:22,039
GA so it's G Plus

771
00:36:16,960 --> 00:36:24,318
GN and the same happens for uh

772
00:36:22,039 --> 00:36:25,838
um for

773
00:36:24,318 --> 00:36:28,159
output

774
00:36:25,838 --> 00:36:30,039
okay so that's what is remember I said

775
00:36:28,159 --> 00:36:32,440
earlier on that

776
00:36:30,039 --> 00:36:34,960
that if an economy has more population

777
00:36:32,440 --> 00:36:38,599
growth it will grow

778
00:36:34,960 --> 00:36:40,440
more okay there's no doubt of that

779
00:36:38,599 --> 00:36:42,599
obviously output per worker will not

780
00:36:40,440 --> 00:36:44,920
grow more because population growth

781
00:36:42,599 --> 00:36:46,160
grows more in the new state G doesn't

782
00:36:44,920 --> 00:36:48,920
show up

783
00:36:46,159 --> 00:36:51,159
there okay but the only thing that will

784
00:36:48,920 --> 00:36:54,639
make output per

785
00:36:51,159 --> 00:36:55,598
worker grow is technological progress so

786
00:36:54,639 --> 00:37:00,400
it's

787
00:36:55,599 --> 00:37:00,400
G that was my claim

788
00:37:01,639 --> 00:37:07,879
earlier there's another we're going to

789
00:37:04,440 --> 00:37:07,880
use this later

790
00:37:09,838 --> 00:37:12,838
but

791
00:37:13,000 --> 00:37:19,119
um

792
00:37:15,920 --> 00:37:21,318
um no I'm not going to do this myself

793
00:37:19,119 --> 00:37:23,480
now we're I'm going to get back to what

794
00:37:21,318 --> 00:37:24,519
I wanted to do now because I need to

795
00:37:23,480 --> 00:37:26,480
tell you a little bit more about the

796
00:37:24,519 --> 00:37:29,838
production function to do growth

797
00:37:26,480 --> 00:37:34,119
accounting um which is what I wanted to

798
00:37:29,838 --> 00:37:36,239
do so but this is clear I mean this is

799
00:37:34,119 --> 00:37:38,079
important

800
00:37:36,239 --> 00:37:40,919
okay

801
00:37:38,079 --> 00:37:43,720
good so this is the reason GA is such an

802
00:37:40,920 --> 00:37:46,200
important variable what you guys do here

803
00:37:43,719 --> 00:37:48,000
at MIT is very important afterwards very

804
00:37:46,199 --> 00:37:49,919
important

805
00:37:48,000 --> 00:37:52,440
okay that's the only thing that can

806
00:37:49,920 --> 00:37:54,639
drive really growth in the long run in

807
00:37:52,440 --> 00:37:54,639
per

808
00:37:54,880 --> 00:38:00,800
capita this GM plays also role I mean

809
00:37:58,318 --> 00:38:02,800
you look at countries not only the

810
00:38:00,800 --> 00:38:05,880
growth in per capita output you'll tend

811
00:38:02,800 --> 00:38:07,920
to look at growth a total growth one of

812
00:38:05,880 --> 00:38:10,880
the big concerns in big parts of Asia

813
00:38:07,920 --> 00:38:13,519
now in Europe as well as I said earlier

814
00:38:10,880 --> 00:38:15,640
in the course is that g is turning

815
00:38:13,519 --> 00:38:18,358
negative that's not going to affect

816
00:38:15,639 --> 00:38:23,199
output per worker growth but it does

817
00:38:18,358 --> 00:38:26,400
affect output growth in general okay and

818
00:38:23,199 --> 00:38:29,159
you can see it here so if G goes down

819
00:38:26,400 --> 00:38:31,639
that will reduce the rate of growth of

820
00:38:29,159 --> 00:38:33,118
output doesn't reduce the rate of growth

821
00:38:31,639 --> 00:38:34,598
output of worker but it does reduce the

822
00:38:33,119 --> 00:38:37,599
rate of growth of

823
00:38:34,599 --> 00:38:37,599
output

824
00:38:37,920 --> 00:38:42,800
good so what happens remember we did in

825
00:38:40,639 --> 00:38:44,960
the in the in the in the basic model we

826
00:38:42,800 --> 00:38:48,079
did an experiment in which we increase

827
00:38:44,960 --> 00:38:49,880
the saving rate so we can do the same

828
00:38:48,079 --> 00:38:53,359
here what happens if we get an increase

829
00:38:49,880 --> 00:38:55,480
in the saving rate do we get more growth

830
00:38:53,358 --> 00:38:58,000
in the long run and the answer is for

831
00:38:55,480 --> 00:38:59,679
the same reasons we had before no

832
00:38:58,000 --> 00:39:02,599
if we increase the saving rate in this

833
00:38:59,679 --> 00:39:04,960
now this full model all that happens is

834
00:39:02,599 --> 00:39:06,960
that this green line moves up it means

835
00:39:04,960 --> 00:39:08,240
that at initial St State now we have

836
00:39:06,960 --> 00:39:09,720
more saving and therefore more

837
00:39:08,239 --> 00:39:11,679
investment than we need to maintain the

838
00:39:09,719 --> 00:39:13,598
stock of capital per effective worker

839
00:39:11,679 --> 00:39:16,559
constant which means that we're going to

840
00:39:13,599 --> 00:39:18,680
get transitional growth Capital per

841
00:39:16,559 --> 00:39:21,759
effective worker will start growing for

842
00:39:18,679 --> 00:39:24,118
a while and as that happens output per

843
00:39:21,760 --> 00:39:27,359
effective worker will also start

844
00:39:24,119 --> 00:39:29,400
growing okay but eventually the

845
00:39:27,358 --> 00:39:31,440
increasing returns will kick in here as

846
00:39:29,400 --> 00:39:35,160
well and we are going to that

847
00:39:31,440 --> 00:39:38,200
transitional growth will stop and H will

848
00:39:35,159 --> 00:39:40,000
end up at a higher level of output per

849
00:39:38,199 --> 00:39:41,879
effective worker and a higher level of

850
00:39:40,000 --> 00:39:44,880
capital per effective worker but the

851
00:39:41,880 --> 00:39:46,838
rate of growth in the long run will not

852
00:39:44,880 --> 00:39:50,000
be affected by the saving rate we'll get

853
00:39:46,838 --> 00:39:54,599
more transitional growth but we will not

854
00:39:50,000 --> 00:39:58,000
get a faster long-term

855
00:39:54,599 --> 00:39:59,599
growth a lot of the Asian Miracle that's

856
00:39:58,000 --> 00:40:02,079
that the Southeast Asian milon in

857
00:39:59,599 --> 00:40:05,000
particular we saw very fast rates of

858
00:40:02,079 --> 00:40:08,920
growth in many economies of

859
00:40:05,000 --> 00:40:11,039
Asia was a lot of that kind meaning was

860
00:40:08,920 --> 00:40:13,800
a combination of what we had before

861
00:40:11,039 --> 00:40:16,559
economies that were relatively poor had

862
00:40:13,800 --> 00:40:18,519
low Capital per work early on in which a

863
00:40:16,559 --> 00:40:20,480
saving rate increased enormously and

864
00:40:18,519 --> 00:40:23,358
that combination gave them

865
00:40:20,480 --> 00:40:26,240
enormous a transitional growth so rate

866
00:40:23,358 --> 00:40:29,000
of growth of 10 12% that was Japan and

867
00:40:26,239 --> 00:40:30,959
then it was Korea Taiwan and so on all

868
00:40:29,000 --> 00:40:33,599
those economies had very fast rates of

869
00:40:30,960 --> 00:40:35,318
growth as a result of that China later

870
00:40:33,599 --> 00:40:37,119
on and China was a big thing for the

871
00:40:35,318 --> 00:40:39,519
world because it was much bigger at the

872
00:40:37,119 --> 00:40:41,800
same time but it was mostly a

873
00:40:39,519 --> 00:40:43,440
combination of those two things it was

874
00:40:41,800 --> 00:40:47,359
being having a low stock of capital

875
00:40:43,440 --> 00:40:49,720
early on combined with for a variety of

876
00:40:47,358 --> 00:40:51,759
reasons and increasing the saving rate

877
00:40:49,719 --> 00:40:54,199
and that combination so gave them very

878
00:40:51,760 --> 00:40:56,160
fast transitional growth but they're all

879
00:40:54,199 --> 00:40:58,358
getting a little stuck now and they're

880
00:40:56,159 --> 00:41:01,118
very concerned with that well they're

881
00:40:58,358 --> 00:41:02,719
fighting against this model there's lots

882
00:41:01,119 --> 00:41:05,280
of concerns of what is happening to

883
00:41:02,719 --> 00:41:07,199
China are we going to follow the Japan

884
00:41:05,280 --> 00:41:09,680
path and so on well they're following

885
00:41:07,199 --> 00:41:12,039
this model that's what's happening to

886
00:41:09,679 --> 00:41:12,039
aair

887
00:41:12,599 --> 00:41:18,480
order I I'll say a little bit more later

888
00:41:15,880 --> 00:41:21,838
on about that so in this particular case

889
00:41:18,480 --> 00:41:23,838
no what what what I have done is in log

890
00:41:21,838 --> 00:41:27,000
space so I can have linear things when

891
00:41:23,838 --> 00:41:29,480
it's growing in log space this economy

892
00:41:27,000 --> 00:41:33,239
with the the low saving rate was

893
00:41:29,480 --> 00:41:35,960
growing here the slope of this was this

894
00:41:33,239 --> 00:41:38,559
is output so the slope of this was GA

895
00:41:35,960 --> 00:41:41,800
plus GN remember in a stady state output

896
00:41:38,559 --> 00:41:44,039
is growing at GA plus GN if the saving

897
00:41:41,800 --> 00:41:46,200
rate now increases then output starts

898
00:41:44,039 --> 00:41:49,119
growing transitionally faster than GA

899
00:41:46,199 --> 00:41:51,480
plus GN that's the reason sort of output

900
00:41:49,119 --> 00:41:54,760
grows faster than G here is all is

901
00:41:51,480 --> 00:41:56,440
growing faster than G here is very fast

902
00:41:54,760 --> 00:41:58,440
okay this is when we saw in Asia the

903
00:41:56,440 --> 00:42:02,480
rate of growth of 12% and stuff like

904
00:41:58,440 --> 00:42:04,599
that we were there moving there and and

905
00:42:02,480 --> 00:42:06,400
and but eventually it sort of PS out you

906
00:42:04,599 --> 00:42:08,400
end up with a higher level of output per

907
00:42:06,400 --> 00:42:12,440
capita per

908
00:42:08,400 --> 00:42:15,200
worker a higher sort of path no it's an

909
00:42:12,440 --> 00:42:16,720
entire path the rate of growth goes back

910
00:42:15,199 --> 00:42:19,960
to GA plus

911
00:42:16,719 --> 00:42:22,279
GN er uh but but you get this

912
00:42:19,960 --> 00:42:25,440
transitional growth which is very

913
00:42:22,280 --> 00:42:27,400
strong and once you're here once you all

914
00:42:25,440 --> 00:42:29,720
you run out of sort of the high saving

915
00:42:27,400 --> 00:42:31,440
and the catching up growth and so on

916
00:42:29,719 --> 00:42:33,159
there is little the only way you're

917
00:42:31,440 --> 00:42:37,000
going to really change your rate of

918
00:42:33,159 --> 00:42:37,000
growth in a sustained manner is doing

919
00:42:39,039 --> 00:42:45,920
what once you have used the tool of you

920
00:42:42,358 --> 00:42:48,358
know of catching up with the world of

921
00:42:45,920 --> 00:42:51,880
increasing your saving rate sometimes to

922
00:42:48,358 --> 00:42:54,239
levels incredibly High you still want to

923
00:42:51,880 --> 00:42:59,039
keep growing very fast what is the only

924
00:42:54,239 --> 00:42:59,039
option you have according to this model

925
00:43:06,639 --> 00:43:13,558
particularly let me bring even more ER

926
00:43:11,199 --> 00:43:15,519
realism to the story particular if GN is

927
00:43:13,559 --> 00:43:18,720
dropping and you still want to keep your

928
00:43:15,519 --> 00:43:21,199
growth high and your GN now you sort of

929
00:43:18,719 --> 00:43:22,959
use the catching up growth you use the

930
00:43:21,199 --> 00:43:24,439
higher saving rate which gives you

931
00:43:22,960 --> 00:43:26,400
transitional growth but it doesn't give

932
00:43:24,440 --> 00:43:27,920
you permanently higher rate of growth

933
00:43:26,400 --> 00:43:29,760
and on top of that for reasons you don't

934
00:43:27,920 --> 00:43:32,559
control population growth is declining

935
00:43:29,760 --> 00:43:34,920
even turning negative in some

936
00:43:32,559 --> 00:43:36,559
cases but suppose you still want to keep

937
00:43:34,920 --> 00:43:39,280
the rate of growth very high what is the

938
00:43:36,559 --> 00:43:39,280
only option you

939
00:43:41,159 --> 00:43:46,480
have increase G exactly technological

940
00:43:44,480 --> 00:43:48,159
progress that's the only option you have

941
00:43:46,480 --> 00:43:49,599
so it makes sense you see that you know

942
00:43:48,159 --> 00:43:51,838
in the case of china they're obsessed

943
00:43:49,599 --> 00:43:54,160
about technology and so on they

944
00:43:51,838 --> 00:43:56,880
understand the solo model okay if you

945
00:43:54,159 --> 00:43:58,799
want to maintain growth at a high Pace

946
00:43:56,880 --> 00:44:01,680
you you're going to need to work on that

947
00:43:58,800 --> 00:44:03,240
side a lot now it doesn't have to be you

948
00:44:01,679 --> 00:44:05,440
necessarily it's the world as a whole

949
00:44:03,239 --> 00:44:08,439
because technology you know moves around

950
00:44:05,440 --> 00:44:12,519
the world but but GA is at the end what

951
00:44:08,440 --> 00:44:12,519
puts the limits of what we can

952
00:44:12,639 --> 00:44:17,279
do ah what I what I was going to do is

953
00:44:15,760 --> 00:44:20,119
that's what I was drawing this diagram

954
00:44:17,280 --> 00:44:22,480
for is say well suppose that in this D

955
00:44:20,119 --> 00:44:24,920
this situation we are in a state state

956
00:44:22,480 --> 00:44:27,838
and we do increase

957
00:44:24,920 --> 00:44:29,358
GA what happens if we increase ga a well

958
00:44:27,838 --> 00:44:34,318
this

959
00:44:29,358 --> 00:44:37,199
curve rotates up no and at that point

960
00:44:34,318 --> 00:44:38,199
it's clear that that if if GA grows

961
00:44:37,199 --> 00:44:41,199
you're going to start growing at a

962
00:44:38,199 --> 00:44:43,078
faster rate but transitionally actually

963
00:44:41,199 --> 00:44:46,960
you're going to grow less than in your

964
00:44:43,079 --> 00:44:46,960
long-term rate of growth why is that the

965
00:44:47,519 --> 00:44:55,960
case so my claim is suppose we manage to

966
00:44:51,400 --> 00:45:00,559
increase GA so now we know that this

967
00:44:55,960 --> 00:45:03,358
line here now going to a um be steeper

968
00:45:00,559 --> 00:45:05,480
or say this we were in this line

969
00:45:03,358 --> 00:45:06,960
whatever we were in this line and now we

970
00:45:05,480 --> 00:45:09,159
make it a steeper so we're want to start

971
00:45:06,960 --> 00:45:11,400
growing faster eventually in the new

972
00:45:09,159 --> 00:45:12,318
state state and my claim now is that in

973
00:45:11,400 --> 00:45:15,039
the

974
00:45:12,318 --> 00:45:16,920
transition growth is less than the new

975
00:45:15,039 --> 00:45:18,440
rate of growth in the new in the new

976
00:45:16,920 --> 00:45:21,800
state state rate of

977
00:45:18,440 --> 00:45:24,358
growth is higher than the rate of growth

978
00:45:21,800 --> 00:45:27,599
of the previous St state but it's lower

979
00:45:24,358 --> 00:45:30,759
than the long run how do I see that I

980
00:45:27,599 --> 00:45:30,760
need another diagram you

981
00:45:36,639 --> 00:45:44,799
think so let me

982
00:45:39,599 --> 00:45:44,800
just put the the s y curve

983
00:45:45,159 --> 00:45:54,199
here so we were

984
00:45:48,800 --> 00:45:55,480
here at this state if I increase GA the

985
00:45:54,199 --> 00:45:57,239
only thing that will move here and

986
00:45:55,480 --> 00:45:58,800
remember the output equation is there

987
00:45:57,239 --> 00:46:02,719
but I don't want to put it the only

988
00:45:58,800 --> 00:46:07,039
thing I do is I rotate this curve

989
00:46:02,719 --> 00:46:07,039
up okay so this moves

990
00:46:07,199 --> 00:46:12,519
up do you see yes so this curves moves

991
00:46:11,519 --> 00:46:16,838
up when

992
00:46:12,519 --> 00:46:19,239
GA goes up so at the oldest steady state

993
00:46:16,838 --> 00:46:21,679
what I have now is a gap between the

994
00:46:19,239 --> 00:46:24,719
saving this economy investment and how

995
00:46:21,679 --> 00:46:27,558
much I need in order to maintain Capital

996
00:46:24,719 --> 00:46:29,879
per effective worker constant

997
00:46:27,559 --> 00:46:33,079
which means that I'm going to start

998
00:46:29,880 --> 00:46:34,640
moving in this direction until I reach

999
00:46:33,079 --> 00:46:37,800
the new stady

1000
00:46:34,639 --> 00:46:40,679
state okay during this transition I'm

1001
00:46:37,800 --> 00:46:43,318
growing at a lower Pace than in the new

1002
00:46:40,679 --> 00:46:45,440
steady state in this new steady state I

1003
00:46:43,318 --> 00:46:45,440
be

1004
00:46:46,079 --> 00:46:51,960
growing much faster than in this state

1005
00:46:48,559 --> 00:46:53,760
how much faster well equal to Delta GA

1006
00:46:51,960 --> 00:46:55,960
but in the transition I will grow faster

1007
00:46:53,760 --> 00:46:59,400
than that but not as fast as in the new

1008
00:46:55,960 --> 00:46:59,400
today St that's the name was

1009
00:47:06,480 --> 00:47:11,440
making H okay

1010
00:47:15,119 --> 00:47:20,440
good do I you know i' rather discuss

1011
00:47:18,760 --> 00:47:24,240
this with more time so questions about

1012
00:47:20,440 --> 00:47:24,240
what we have done up to now

1013
00:47:31,199 --> 00:47:37,078
is it clear or is it very unclear and

1014
00:47:34,599 --> 00:47:37,079
probably

1015
00:47:38,239 --> 00:47:43,679
both so let me I I I want to let me keep

1016
00:47:42,239 --> 00:47:45,519
this for the next the next lecture

1017
00:47:43,679 --> 00:47:49,519
because going to take a little time just

1018
00:47:45,519 --> 00:47:49,519
play okay