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Hi, we just took in a very simple growth model and in that growth model we saw that

Â well, growth stopped, right. Once we got to 144 machines and an output of 120, we

Â no longer got any growth. So we use that very simple model to get at. A really

Â important fact, that without innovation, if technology stays fixed, growth will

Â stop. Now, sure the labor supply could get bigger, we could have more workers or

Â something like that. But holding the amount of labor fixed and holding that

Â technology fixed, if we've got a fixed savings rate, and a fixed rate of

Â depreciation, there's no more growth at some point. We're gonna go up, up, up, up,

Â up, and then stop. Well. That hasn't been human experience right. Economic well

Â being continue to go way up right and GDP continues to go up, and so what's driving

Â that. Well to get at that we're gonna look at a deeper model, richer model known as

Â the solo growth model. And what's nice about this model and I love about this

Â model, we're just gonna add one variable. We're just going to add one more variable

Â to our other model, and that's suddenly going to give us a way to include

Â innovation. Now, just to make this, you know. More interesting [laugh], maybe more

Â real. These models are developed by real people. Right, and so, the speaker model's

Â developed again by Bob Solo. And Bob Solo is an economist at MIT. And here's Bob

Â right here. And this is Bob actually testifying before the House Science

Â Technology committee on the need to have multiple models to understand the economy.

Â Right, so this is a group of economists here and we're standing up and we're

Â swearing to tell the truth, the whole truth, and nothing but the truth about why

Â models are important to understand where growth comes from. And in this particular

Â case, to prevent things like, you know, the home mortgage crisis, which cost us

Â all a lot of money. Alright, so how does Solo's model work? What does Bob's model

Â do? Well, what Bob does is this wonderful thing. He includes. Includes one more

Â variable. So everything's the same as before, [inaudible] labor, capital,

Â depreciation, savings. But we're gonna include this thing A of T which stands for

Â technology. So when A is low technology is low when A is high technology is high it's

Â better so A's just going to be the parameter we can tune to effect sort of

Â how much or how good is the technology in the economy so for making cocoanut picking

Â machines [laugh] right A is really small and if we're making incredibly cool you

Â know laser pointers and IPhones and stuff like that, technology is great. Okay, so

Â this is it. Very simple formula. Output is just equal to the technology at that time,

Â times capital to some. Beta. And L to sum one minus. Now wait a minute. This also

Â got a little more complicated. Now I got these betas here. Now before I had square

Â roots. Well, if beta equals one half. Right, so beta is a half. Then this is

Â just the square root of labor times the square root of capital. Right? Easy. If

Â beta gets bigger than a half, that means that capital matters a little bit more. If

Â beta gets less than a half, then that means that capital matters a little bit

Â less. So depending on the technology, it could be that it's a capital intensive

Â technology so that beta would be big. Doesn't use that much capital and beta

Â tends to be relatively small. So, you can estimate different [inaudible] betas for

Â different manufacturing processes or even for different countries, right? And a half

Â was just a convenience we assumed. So that's actually something that we take

Â models to beta, you go and estimate and figure out what is beta. And for us, if

Â we're just trying to get the ideas here, right? And we're going to take beta equals

Â a half. So let's go back, and just to remind ourselves of where we were before,

Â right? Remember our total output was ten because we [inaudible] a hundred workers,

Â so ten times the square root of N. We had a savings rate of 30%. And we added a

Â depreciation at a quarter. And we went through and we did all that stuff we saw

Â the equilibrium where the investment was exactly equal the depreciation. When we

Â got to that happened we put an output of 120 which required 144 machines, right? So

Â that meant that we were going to invest in 36 new machines but we'd lose 36 machines

Â to depreciation. So that was our equilibrium. Now we want to say well, what

Â would innovation do? Well, innovation would do, was, would we'd put an A in

Â front of this. Now have an A in front of this ten times the square root of m. So,

Â let's do that and let's see what happens. So now we're going to say the output it.

Â Two times ten times the square root of eleven. So what we're going to do is,

Â we're going to assume that somebody had a technological innovation and our coconut

Â machines are now, somehow like, everything's twice as good, or twice as

Â productive. Okay, well now let's, let's walk through the math. So, what's our

Â investment gonna be? Investment is gonna be 0.3. Times twenty the squared of M. So

Â that's gonna be six times the squared of M. And what's our depreciation? Well,

Â that's gonna be one-fourth M, right? So that's just M over four. And so we just

Â have to set these things equal again, right? So six squared of M equals M over

Â four. So that means 24. Square root of M, equals M. So that means 24, equals square

Â root of M. So that means M equals. Right? So our equilibrium is gonna be m is equal

Â 496. And output, right, is gonna be two times ten times the square root of 496,

Â which is 24, right? So that's 24 times ten which is 240, which is 480, right. So our

Â output 480. Before it was 120, and now it's 480. So, think about it. Productivity

Â doubled, right, [inaudible] our technology got twice as good. But long run GDP went

Â up by four. But why is that, well let's look back at our numbers here. Okay, we

Â became twice as productive so that means if we had kept the number of machines at a

Â 144, we now would have an output of 28, 240. Right, so we would have doubled where

Â we were at. But we didn't. Keep the number machines at 144 when the technology are

Â better we actually increase the number machines to 496. So when you have a

Â technological change two things happen. First you just get more productive you get

Â more stuff, second because you?re getting more stuff it makes sense to invest in

Â more machines. So there's this multiplier effect so that means productivity goes up

Â by two right. Output eventually the long run, long run [inaudible] goes up by four

Â right, and this is what you think of as sort of as a innovation multiplier because

Â it happens were there's these two effects, right. Labor and capital become more

Â productive. So that, boom, you just get more stuff. But second of all, because

Â they're more productive it makes sense to invest in more machines so then you get

Â even more stuff. So there's this multiplier. Well, let's think about it.

Â Productivity are up by two. Total it up. Eventually in the long run, not

Â immediately. Gotta build up all of those machines. It goes up by four. Well that

Â leads to a puzzle and here's where models are really useful. Is it additive, or is

Â it multiplicative? Here's the issue with two. It could be that productivity went up

Â by two. And so we get two plus two, and, so [inaudible] by four. Or it could be we

Â get 2X2, two squared is the reason productivity went up by four. So we wanna

Â figure out, is this additive effect, right? The machine effect plus the

Â productivity effect. Or is it multiplicative, is it 2X2? Well, to make

Â sense of that, what we can do is, we can increase the multiplier to three. Because

Â if it's additive then we get six, and if it's multiplicative, we get nine. Right so

Â if we make this three times as productive we're going to ask in the long run do we

Â end up with six times as much stuff or do we end up with nine times as much stuff

Â and again this is [inaudible] why do we model we model to get the logic right okay

Â without the model. It'd be very hard to figure out, is this gonna go by six, or is

Â this gonna go by nine. Heck, we might not have even have got the second effect of

Â more machines. Right, so the model was only useful just to giving us that. Now

Â it's gonna tell us the magnitude of the effect. 'Kay, just to get our bearings

Â again, let's remember where we started from. We start from an existing technology

Â where it's just the square root of labor times the square root of machines. We see

Â 100 units of labor. So it's ten times the square root of M. We save 30 percent and

Â invest that in new machines. Right, so that's gonna be three times the square

Â root of M. We lose a quarter of our machines to depreciation, so that's just M

Â over four. We set those things equal. We get m equals 144, we get output of 120.

Â That's our equilibrium. Now we wanna say lets triple it okay so let?s suddenly

Â assume there's an A that comes in that's got a value of three, so now we're going

Â to get three times ten times the squared of M [inaudible] 30 times the squared of M

Â and let?s see what happens okay so what's our total investment going to be? Well

Â that's going to be 0.3 times 30 times the squared of M so that's going to be nine.

Â Times the square root of M. What's our depreciation? Well, that's still just M

Â over four. So let's set these equal. Nine times the square root of M equals M over

Â four, so that means 36 squared of M equals M. So that means 36 equals the square root

Â of M. So is equal to 36 squared, right? So M, we just keep it as 36 squared. Right?

Â So N equals 36 squared. What's total output gonna be? So if we've got 36

Â squared machines, which is a big number, what's output gonna be? Well, output is

Â three times ten times the square root of 36 squared. So that's three times ten

Â times 36. Well, three times 36 is 108, so that's 1,080. So what happened when we

Â made ourselves three times as productive? Well. Total output went up nine times. So

Â what we see, remember what was our question? Our question was, is it

Â additive? Are we gonna get three plus three are six. Or multiplicative, three

Â times three are nine? The answer is, it's gonna be multiplicative. We're gonna three

Â times three is nine. Two effects multiplied on top of one another. Right,

Â the first one is we just get more stuff. The second one is we invest in more

Â machines. And those two effects get multiplied together. So becoming three

Â times more effective means we get nine times in the long run equilibrium. So let

Â me summarize for a second. In the simple growth model, growth stopped. Right? At

Â some point we got to 144 machines and then we no longer had any growth. When we go to

Â the Solow growth model, what happens is, if we can continue to increase that A,

Â right? So, if we can continue to increase our productivity, then growth can

Â continue. That sort of begs the question. Where do increases in A come from? And

Â this has led to what people call endogenous growth models. So an endogenous

Â growth model, labor can go to things like picking coconuts. Labor can also go to

Â things like, investing in new technologies, research and design, and

Â those sorts of things, to try and increase that A parameter. So what we can think of

Â is before all of our labor went to increasing cap, picking coconuts, right?

Â Now, that labor could also go to doing research on new coconut picking machines.

Â What you get in indigenous growth model is how much labor goes into actually making

Â stuff, and how much goes into research and design and thinking, right. It's a choice

Â variable. In the model, right, and you solve for how much of that you get. Quick

Â summary, right. Growth ceases without innovation, if that's true. Everybody

Â should be pro innovation. And in fact, most people are. Right, so here's two

Â quotes. Here's a fun little quiz. One of these quotes is from President Obama, who

Â is a democrat. The other quote is from President Reagan. I want you to try and

Â guess which quote came from Obama, and which quote came from Reagan. All right?

Â So both Reagan are pro innovation, right? They, they are, because they are pro GDP

Â growth, because [inaudible] gonna lift those people out of poverty. Right? We

Â wanna make everyone better off. Because if we can lift people out of poverty, we make

Â people happier. And what we've learned is the way to do that, right, is. First, by

Â investing in capital. Right? Because that makes us, you know, all do better. We get

Â to the 144 machines. But at some point then growth stops and then you need

Â investment in technology. Then investment in technology leads to innovation which

Â raises the whole thing up and we get this multiplier effect. Right? We get the

Â increased productivity and then we also get the incentives to produce more

Â machines. Right? Which raises our statement [inaudible] even more. So that's

Â the E, in essence what growth theory is. Thanks.

Â