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Hi, during this set of lectures. I talked about how, in the past, Japan had, had

Â extremely high levels of growth. Remember in the 1950's to 1970's, early 1970's, you

Â see that Japan has growth rates that hang out in the seven to eight percent range. I

Â also talked about how China is currently experiencing levels of growth that are

Â equally high. In the same sort of range eight to nine percent. And there's a

Â question, can China continue to sustain those levels of growth? But what we want

Â to see, is we want to use our very simple growth model to see why countries like

Â Japan and the post [inaudible] can have incredibly high growth. Why China during

Â this era of industrialization can have incredibly high growth. But why would we,

Â we should be somewhat dubious about the prospects of China being able to maintain

Â these levels of growth, unless, they're able to somehow have massive increases in

Â technological improvement. So we'll see that if you're catching up. To other

Â countries. And it's highly likely that you can have, experience super high growth

Â levels just like the ones we see here. But once you've caught up to other countries

Â it's gonna be hard to maintain those growth levels unless you somehow can

Â support massive amounts of innovation. So let?s see how this works we're going to do

Â it just by doing some math so we use slightly different numbers than we used

Â before with the exact same argument so here what we're going to do is we're going

Â to assume that the savings rate is twenty%. The depreciation is ten percent

Â and we're also going to assume a much larger economy, so we get bigger numbers.

Â So instead of assuming that there's a 100 people, so the square root of that is ten,

Â we're going to assume that there's 10,000 people so that the square root is 100.

Â We're also going to start with a lot more machines, we're going to start with 3.600

Â machines, as opposed to just six, so this is a bigger economy and it that will allow

Â us to get slightly more reasonable. Numbers when we work through the math. So

Â remember how this works right, what we do is, we compute total output. We see how

Â many new machines then get invested in. We see how many machines get depreciated. We

Â solve for the new number of machines, and after we solve for the new number of

Â machines, then we can solve for the output, next period. So let?s get started

Â here we go 3,600 machines so output is 100 times the square root of 3,600 so that's

Â 100 times 60 so that means output is 6,000 so let's think of that as per-capita.

Â Income of $6,000 dollars. So how much do they need to invest? Well investment is

Â going to be.2 times 6,000 so that's 1200, they're going to invest in 1200 new

Â machines. The depreciation is ten percent of the existing machines of 3600 which is

Â 36, 360 so if we net those out we get 840 new machines. And with those 840 new

Â machines that means the new machines the next period is going to be 4,440 so that's

Â we got the first period. Output is 6,000 and now they've got 4,440 new machines, so

Â let's go to the next period, the next period we're going to start out with 4,440

Â machines and what we're going to do is then we're going to compute the output in

Â this set there we go the square root of 4,440 is approximately. 67. So we're gonna

Â get 100 X the square root of 4,440, which is 100 X 67, which is 6,700. So investment

Â in new machines is gonna be twenty percent of that, which is gonna be 1,000. 340. And

Â our depreciation is gonna be ten percent of this which is roughly 440. So we're

Â gonna invest in about 900 new machines. So, the new machines next time is going to

Â be 5,340. What we can also do is we can look at, what is our growth rate. So,

Â currently we've got $6,700 per person. Before we had a GDP of 6,000. So that's

Â roughly eleven percent growth. So this is a growth rate not unlike, a little bit

Â higher, but not unlike what we currently see in China. We went from 6,000 to 6,700

Â and now we've got 5,340 machines. Let?s go ahead in one more period we've now had

Â [laugh] 5,340 machines we want to ask what's output going to be and what's

Â growth going to be this is just some very basic math. So if we take the output as

Â 100 times the square root of 5,340 [inaudible] again that's going to be 100

Â times turns out again do this your [inaudible] about 73 so that's 7,300

Â that's going to be GDP per capita. Investment in new machines, is twenty

Â percent of that which is 14-. 160. That's twenty percent of 7300. And depreciation

Â is ten percent which is 530. So we are gonna add 930 new machines. Which is gonna

Â gave us 60 to 70 new machines. What's our growth rate. Our growth rate we had 6700

Â before now 7300 went up 600 which is about. Eight to nine percent. So what we

Â look at, is, in the previous period, we had eleven percent growth, now we've got

Â nine percent growth. So what we're seeing is consistently high levels of growth,

Â because of the fact that, relative to how much labor you've got, the amount of

Â capital is pretty low. So just by investing and saving, you can maintain

Â fairly high levels of growth. Now let's jump ahead. Let's suppose that we've been

Â accumulating capital. We've gone from 3,600 to 4,400 machines to 5,300 machines

Â to 6,200 machines. And now, we're all the way up to 10,000 machines. We can ask,

Â what's gonna happen to output. And we can ask even what's gonna happen to growth.

Â So, let's again, do the math. The output is gonna be 100 times the square root of

Â 10,000, which is 100. That means, now, per capita GDP, let's just say is 10,000. What

Â is investment gonna be? Investment is gonna be. Twenty percent of that which is

Â two thousand, but what is depreciation going to be. Depreciation is ten percent

Â of ten thousand machines, which is a thousand, so that now we're going to have

Â eleven thousand machines next period. Well if we have eleven thousand machines next

Â period, we can ask what?s growth going to be well that's going to be a hundred times

Â the square root of eleven thousand is what g d p is going to be so that's going to be

Â a hundred times approximately a hundred and five. Which is 10,500. So GDP is going

Â to go from 10,000 to 10,500. But what sort of growth rate is that? Well that's only

Â five percent growth. So what you can see is when we went from 3,000 to 4,000, to

Â 5,000 to 6,000, during that period, the economy is sustaining, you know, ten,

Â eleven, eight, nine percent growth. Really high growth rates. Just like those growth

Â rates we're seeing in China. Once the machine number gets to 10,000, now

Â suddenly the growth rate drops to five percent. But we're still adding net, 1000

Â machines. Well, let's keep going. Let's go ahead, you know, another 10-20 years. And

Â let's suppose now, the economy's got 22, 500 machines. And let's ask what happens

Â here. What's, what's total output gonna be? Well, that's gonna be 100 times the

Â square root of 22-5. Which is 100 times 150 so now, we've got 15,000 per capita

Â GDP. That's really good. How much are we gonna invest when investment is gonna be

Â twenty percent of that which is 3,000. That's a lot of new machines. But what's

Â depreciation gonna be? It's gonna be ten percent of that which is. Of the 22,000

Â machines we have. Which is 225. I'm sorry. 2,250 machines. So that means net we add

Â 750 machines. So that gives us 23,250 machines. Well now we can ask how many,

Â what's our output gonna be next period. Well next period our output is gonna be a

Â 100 times the square root of 23,250. Well how much is that? Well, that's 15,000. And

Â 250, ballpark. So now GDP's only gone up 250, and that's really like, just a one to

Â two percent increase. So growth is now in the one per, one to two percent range. So

Â we've seen this economy, let's step all the way back a second. When we started out

Â with 3,600 machines, output was 6,000. Then we had eleven percent growth. Then we

Â had eight to nine percent growth. So this economy's growing at a fairly fast clip.

Â Once it gets to 10,000 machines, though, now GDP only grows at five%. And once it

Â gets to 22,000 machines, now GDP only grows at one to two percent. What's going

Â on? Well number our curve output if you have a fixed technology is going to be

Â concave, so there's this fixed region here where you see ten percent growth. Early on

Â when you don't have enough capital given your amount of labor you can get massive

Â amounts of growth but once you get in this region here growth is going to fall to one

Â to two percent it's going to fall off unless, right remember from our mono-

Â unless you get lots of investment in new technology, so if you look at a country

Â like China. With really high growth rates and ask what's causing that. And you can

Â think, well maybe what's causing it is they don't have enough capital, given how

Â much labor they've got. In the case of China that's true. So they're at this part

Â of the curve. So they're experiencing incredibly high growth. When they get to

Â this part of the curve, then, most likely, you not going to see the same, sort of,

Â high growth rate. It's going to look a lot like, more like the picture in Japan. So

Â for them to sustain high growth, they can't just continue to pour money into

Â capital. What they're going to need to do is they're going to need to change

Â technology they're going to need A to increase, now increases in A necessary to

Â give up eight to nine percent growth just have never been seen before so it would be

Â remarkable if technological advances occurred at such a rate that they can

Â maintain this level of growth once their capital levels get to the same level of

Â other countries. What the model tells us, is we're much more likely to see China

Â follow a path similar to Japan. Where we see high growth rates for a period but as

Â capital accumulates. Those growth rates fall over time. So what have we done? What

Â we've done is kind of fun: taken a very simple growth model, Solo growth model.

Â We've looked at data from China and Japan and seen how China has these incredibly

Â high growth rates now. Japan used to have incredibly high growth rates. And we've

Â seen from our model, that if a country's undercapitalized, that's their levels of

Â capital are low level to the amount of labor they've got, then you can sustain

Â super high growth rates for quite a while as you accumulate capital. But once your

Â capital levels become sort of appropriate for the technology your growth rate is

Â going to fall off and the only way you can sustain that growth rate is through

Â technological innovation. By driving up in solos models that parameter A. This

Â doesn't mean that China's not going to continue to have growth, or that Japan is

Â all growth will end. Or that the United States, or Europe all growth is going to

Â end. What it says is there's two different ways to think about growth. One type of

Â growth, what we're seeing in China now and what we saw in Japan post war. And what we

Â saw in Europe and the United States post war, is growth that occurs through capital

Â accumulation. Another type of growth, is what we're, which is what we see in the

Â United States and Japan and Europe now, but not in China, occurs from

Â technological advances, not from buildup of capital. And as you advance technology

Â and you increase that A term, then it makes sense to. Buy more capital, but

Â different types of capital and that's what drives growth. Okay [laugh] lot going on

Â here lot of fun though right? What we're going to talk about next, final lecture,

Â is why then are some countries poor? This, this seems to make a lot of sense just

Â invest in capital if you invest in capital you get lots of growth you catch up with

Â everybody else why is it still the case that some countries are poor if we

Â understand where growth comes from? Thanks.

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