1 00:00:00,000 --> 00:00:05,135 Hi, we just took in a very simple growth model and in that growth model we saw that 2 00:00:05,135 --> 00:00:09,962 well, growth stopped, right. Once we got to 144 machines and an output of 120, we 3 00:00:09,962 --> 00:00:14,643 no longer got any growth. So we use that very simple model to get at. A really 4 00:00:14,643 --> 00:00:18,697 important fact, that without innovation, if technology stays fixed, growth will 5 00:00:18,697 --> 00:00:22,803 stop. Now, sure the labor supply could get bigger, we could have more workers or 6 00:00:22,803 --> 00:00:26,751 something like that. But holding the amount of labor fixed and holding that 7 00:00:26,751 --> 00:00:30,488 technology fixed, if we've got a fixed savings rate, and a fixed rate of 8 00:00:30,488 --> 00:00:34,541 depreciation, there's no more growth at some point. We're gonna go up, up, up, up, 9 00:00:34,541 --> 00:00:38,356 up, and then stop. Well. That hasn't been human experience right. Economic well 10 00:00:38,356 --> 00:00:42,439 being continue to go way up right and GDP continues to go up, and so what's driving 11 00:00:42,439 --> 00:00:46,474 that. Well to get at that we're gonna look at a deeper model, richer model known as 12 00:00:46,474 --> 00:00:50,262 the solo growth model. And what's nice about this model and I love about this 13 00:00:50,262 --> 00:00:54,203 model, we're just gonna add one variable. We're just going to add one more variable 14 00:00:54,203 --> 00:00:57,633 to our other model, and that's suddenly going to give us a way to include 15 00:00:57,633 --> 00:01:02,145 innovation. Now, just to make this, you know. More interesting [laugh], maybe more 16 00:01:02,145 --> 00:01:05,884 real. These models are developed by real people. Right, and so, the speaker model's 17 00:01:05,884 --> 00:01:09,631 developed again by Bob Solo. And Bob Solo is an economist at MIT. And here's Bob 18 00:01:09,631 --> 00:01:13,045 right here. And this is Bob actually testifying before the House Science 19 00:01:13,045 --> 00:01:16,981 Technology committee on the need to have multiple models to understand the economy. 20 00:01:16,981 --> 00:01:20,584 Right, so this is a group of economists here and we're standing up and we're 21 00:01:20,584 --> 00:01:24,331 swearing to tell the truth, the whole truth, and nothing but the truth about why 22 00:01:24,331 --> 00:01:28,219 models are important to understand where growth comes from. And in this particular 23 00:01:28,219 --> 00:01:31,823 case, to prevent things like, you know, the home mortgage crisis, which cost us 24 00:01:31,823 --> 00:01:35,569 all a lot of money. Alright, so how does Solo's model work? What does Bob's model 25 00:01:35,569 --> 00:01:39,188 do? Well, what Bob does is this wonderful thing. He includes. Includes one more 26 00:01:39,188 --> 00:01:42,567 variable. So everything's the same as before, [inaudible] labor, capital, 27 00:01:42,567 --> 00:01:46,429 depreciation, savings. But we're gonna include this thing A of T which stands for 28 00:01:46,429 --> 00:01:51,287 technology. So when A is low technology is low when A is high technology is high it's 29 00:01:51,287 --> 00:01:55,672 better so A's just going to be the parameter we can tune to effect sort of 30 00:01:55,672 --> 00:02:00,643 how much or how good is the technology in the economy so for making cocoanut picking 31 00:02:00,643 --> 00:02:05,379 machines [laugh] right A is really small and if we're making incredibly cool you 32 00:02:05,379 --> 00:02:10,088 know laser pointers and IPhones and stuff like that, technology is great. Okay, so 33 00:02:10,088 --> 00:02:15,259 this is it. Very simple formula. Output is just equal to the technology at that time, 34 00:02:15,259 --> 00:02:19,835 times capital to some. Beta. And L to sum one minus. Now wait a minute. This also 35 00:02:19,835 --> 00:02:24,390 got a little more complicated. Now I got these betas here. Now before I had square 36 00:02:24,390 --> 00:02:28,440 roots. Well, if beta equals one half. Right, so beta is a half. Then this is 37 00:02:28,440 --> 00:02:32,770 just the square root of labor times the square root of capital. Right? Easy. If 38 00:02:32,770 --> 00:02:37,382 beta gets bigger than a half, that means that capital matters a little bit more. If 39 00:02:37,382 --> 00:02:41,712 beta gets less than a half, then that means that capital matters a little bit 40 00:02:41,712 --> 00:02:46,099 less. So depending on the technology, it could be that it's a capital intensive 41 00:02:46,099 --> 00:02:49,897 technology so that beta would be big. Doesn't use that much capital and beta 42 00:02:49,897 --> 00:02:53,465 tends to be relatively small. So, you can estimate different [inaudible] betas for 43 00:02:53,465 --> 00:02:57,121 different manufacturing processes or even for different countries, right? And a half 44 00:02:57,121 --> 00:03:00,469 was just a convenience we assumed. So that's actually something that we take 45 00:03:00,469 --> 00:03:03,860 models to beta, you go and estimate and figure out what is beta. And for us, if 46 00:03:03,860 --> 00:03:07,472 we're just trying to get the ideas here, right? And we're going to take beta equals 47 00:03:07,472 --> 00:03:10,864 a half. So let's go back, and just to remind ourselves of where we were before, 48 00:03:10,864 --> 00:03:14,432 right? Remember our total output was ten because we [inaudible] a hundred workers, 49 00:03:14,432 --> 00:03:18,076 so ten times the square root of N. We had a savings rate of 30%. And we added a 50 00:03:18,076 --> 00:03:22,019 depreciation at a quarter. And we went through and we did all that stuff we saw 51 00:03:22,019 --> 00:03:26,012 the equilibrium where the investment was exactly equal the depreciation. When we 52 00:03:26,012 --> 00:03:30,104 got to that happened we put an output of 120 which required 144 machines, right? So 53 00:03:30,104 --> 00:03:34,347 that meant that we were going to invest in 36 new machines but we'd lose 36 machines 54 00:03:34,347 --> 00:03:37,990 to depreciation. So that was our equilibrium. Now we want to say well, what 55 00:03:37,990 --> 00:03:41,584 would innovation do? Well, innovation would do, was, would we'd put an A in 56 00:03:41,584 --> 00:03:45,527 front of this. Now have an A in front of this ten times the square root of m. So, 57 00:03:45,527 --> 00:03:49,570 let's do that and let's see what happens. So now we're going to say the output it. 58 00:03:49,570 --> 00:03:52,858 Two times ten times the square root of eleven. So what we're going to do is, 59 00:03:52,858 --> 00:03:56,498 we're going to assume that somebody had a technological innovation and our coconut 60 00:03:56,498 --> 00:03:59,567 machines are now, somehow like, everything's twice as good, or twice as 61 00:03:59,567 --> 00:04:04,486 productive. Okay, well now let's, let's walk through the math. So, what's our 62 00:04:04,486 --> 00:04:10,557 investment gonna be? Investment is gonna be 0.3. Times twenty the squared of M. So 63 00:04:10,557 --> 00:04:16,791 that's gonna be six times the squared of M. And what's our depreciation? Well, 64 00:04:16,791 --> 00:04:23,108 that's gonna be one-fourth M, right? So that's just M over four. And so we just 65 00:04:23,108 --> 00:04:29,425 have to set these things equal again, right? So six squared of M equals M over 66 00:04:29,425 --> 00:04:37,968 four. So that means 24. Square root of M, equals M. So that means 24, equals square 67 00:04:37,968 --> 00:04:45,812 root of M. So that means M equals. Right? So our equilibrium is gonna be m is equal 68 00:04:45,812 --> 00:04:52,055 496. And output, right, is gonna be two times ten times the square root of 496, 69 00:04:52,055 --> 00:04:58,627 which is 24, right? So that's 24 times ten which is 240, which is 480, right. So our 70 00:04:58,627 --> 00:05:04,952 output 480. Before it was 120, and now it's 480. So, think about it. Productivity 71 00:05:04,952 --> 00:05:11,606 doubled, right, [inaudible] our technology got twice as good. But long run GDP went 72 00:05:11,606 --> 00:05:16,155 up by four. But why is that, well let's look back at our numbers here. Okay, we 73 00:05:16,155 --> 00:05:20,866 became twice as productive so that means if we had kept the number of machines at a 74 00:05:20,866 --> 00:05:25,297 144, we now would have an output of 28, 240. Right, so we would have doubled where 75 00:05:25,297 --> 00:05:29,798 we were at. But we didn't. Keep the number machines at 144 when the technology are 76 00:05:29,798 --> 00:05:33,893 better we actually increase the number machines to 496. So when you have a 77 00:05:33,893 --> 00:05:38,375 technological change two things happen. First you just get more productive you get 78 00:05:38,375 --> 00:05:42,691 more stuff, second because you?re getting more stuff it makes sense to invest in 79 00:05:42,691 --> 00:05:47,284 more machines. So there's this multiplier effect so that means productivity goes up 80 00:05:47,284 --> 00:05:51,766 by two right. Output eventually the long run, long run [inaudible] goes up by four 81 00:05:51,766 --> 00:05:56,303 right, and this is what you think of as sort of as a innovation multiplier because 82 00:05:56,303 --> 00:06:00,450 it happens were there's these two effects, right. Labor and capital become more 83 00:06:00,450 --> 00:06:04,128 productive. So that, boom, you just get more stuff. But second of all, because 84 00:06:04,128 --> 00:06:08,203 they're more productive it makes sense to invest in more machines so then you get 85 00:06:08,203 --> 00:06:11,632 even more stuff. So there's this multiplier. Well, let's think about it. 86 00:06:11,632 --> 00:06:15,111 Productivity are up by two. Total it up. Eventually in the long run, not 87 00:06:15,111 --> 00:06:18,988 immediately. Gotta build up all of those machines. It goes up by four. Well that 88 00:06:18,988 --> 00:06:23,358 leads to a puzzle and here's where models are really useful. Is it additive, or is 89 00:06:23,358 --> 00:06:28,780 it multiplicative? Here's the issue with two. It could be that productivity went up 90 00:06:28,780 --> 00:06:33,408 by two. And so we get two plus two, and, so [inaudible] by four. Or it could be we 91 00:06:33,408 --> 00:06:38,367 get 2X2, two squared is the reason productivity went up by four. So we wanna 92 00:06:38,367 --> 00:06:42,599 figure out, is this additive effect, right? The machine effect plus the 93 00:06:42,599 --> 00:06:47,094 productivity effect. Or is it multiplicative, is it 2X2? Well, to make 94 00:06:47,094 --> 00:06:52,787 sense of that, what we can do is, we can increase the multiplier to three. Because 95 00:06:52,787 --> 00:06:58,399 if it's additive then we get six, and if it's multiplicative, we get nine. Right so 96 00:06:58,399 --> 00:07:02,914 if we make this three times as productive we're going to ask in the long run do we 97 00:07:02,914 --> 00:07:07,375 end up with six times as much stuff or do we end up with nine times as much stuff 98 00:07:07,375 --> 00:07:11,890 and again this is [inaudible] why do we model we model to get the logic right okay 99 00:07:11,890 --> 00:07:15,490 without the model. It'd be very hard to figure out, is this gonna go by six, or is 100 00:07:15,490 --> 00:07:18,872 this gonna go by nine. Heck, we might not have even have got the second effect of 101 00:07:18,872 --> 00:07:22,085 more machines. Right, so the model was only useful just to giving us that. Now 102 00:07:22,085 --> 00:07:25,340 it's gonna tell us the magnitude of the effect. 'Kay, just to get our bearings 103 00:07:25,340 --> 00:07:28,721 again, let's remember where we started from. We start from an existing technology 104 00:07:28,721 --> 00:07:32,188 where it's just the square root of labor times the square root of machines. We see 105 00:07:32,188 --> 00:07:35,489 100 units of labor. So it's ten times the square root of M. We save 30 percent and 106 00:07:35,489 --> 00:07:39,794 invest that in new machines. Right, so that's gonna be three times the square 107 00:07:39,794 --> 00:07:44,155 root of M. We lose a quarter of our machines to depreciation, so that's just M 108 00:07:44,155 --> 00:07:48,517 over four. We set those things equal. We get m equals 144, we get output of 120. 109 00:07:48,517 --> 00:07:52,920 That's our equilibrium. Now we wanna say lets triple it okay so let?s suddenly 110 00:07:52,920 --> 00:07:57,571 assume there's an A that comes in that's got a value of three, so now we're going 111 00:07:57,571 --> 00:08:02,395 to get three times ten times the squared of M [inaudible] 30 times the squared of M 112 00:08:02,395 --> 00:08:06,931 and let?s see what happens okay so what's our total investment going to be? Well 113 00:08:06,931 --> 00:08:11,640 that's going to be 0.3 times 30 times the squared of M so that's going to be nine. 114 00:08:11,640 --> 00:08:16,261 Times the square root of M. What's our depreciation? Well, that's still just M 115 00:08:16,261 --> 00:08:22,839 over four. So let's set these equal. Nine times the square root of M equals M over 116 00:08:22,839 --> 00:08:30,965 four, so that means 36 squared of M equals M. So that means 36 equals the square root 117 00:08:30,965 --> 00:08:38,371 of M. So is equal to 36 squared, right? So M, we just keep it as 36 squared. Right? 118 00:08:38,371 --> 00:08:43,522 So N equals 36 squared. What's total output gonna be? So if we've got 36 119 00:08:43,522 --> 00:08:49,188 squared machines, which is a big number, what's output gonna be? Well, output is 120 00:08:49,188 --> 00:08:54,928 three times ten times the square root of 36 squared. So that's three times ten 121 00:08:54,928 --> 00:09:00,594 times 36. Well, three times 36 is 108, so that's 1,080. So what happened when we 122 00:09:00,594 --> 00:09:05,734 made ourselves three times as productive? Well. Total output went up nine times. So 123 00:09:05,734 --> 00:09:09,042 what we see, remember what was our question? Our question was, is it 124 00:09:09,042 --> 00:09:12,802 additive? Are we gonna get three plus three are six. Or multiplicative, three 125 00:09:12,802 --> 00:09:16,912 times three are nine? The answer is, it's gonna be multiplicative. We're gonna three 126 00:09:16,912 --> 00:09:20,472 times three is nine. Two effects multiplied on top of one another. Right, 127 00:09:20,472 --> 00:09:24,281 the first one is we just get more stuff. The second one is we invest in more 128 00:09:24,281 --> 00:09:27,941 machines. And those two effects get multiplied together. So becoming three 129 00:09:27,941 --> 00:09:31,951 times more effective means we get nine times in the long run equilibrium. So let 130 00:09:31,951 --> 00:09:35,842 me summarize for a second. In the simple growth model, growth stopped. Right? At 131 00:09:35,842 --> 00:09:40,397 some point we got to 144 machines and then we no longer had any growth. When we go to 132 00:09:40,397 --> 00:09:44,524 the Solow growth model, what happens is, if we can continue to increase that A, 133 00:09:44,524 --> 00:09:48,436 right? So, if we can continue to increase our productivity, then growth can 134 00:09:48,436 --> 00:09:52,693 continue. That sort of begs the question. Where do increases in A come from? And 135 00:09:52,693 --> 00:09:56,865 this has led to what people call endogenous growth models. So an endogenous 136 00:09:56,865 --> 00:10:01,260 growth model, labor can go to things like picking coconuts. Labor can also go to 137 00:10:01,260 --> 00:10:04,932 things like, investing in new technologies, research and design, and 138 00:10:04,932 --> 00:10:09,549 those sorts of things, to try and increase that A parameter. So what we can think of 139 00:10:09,549 --> 00:10:13,610 is before all of our labor went to increasing cap, picking coconuts, right? 140 00:10:13,610 --> 00:10:18,315 Now, that labor could also go to doing research on new coconut picking machines. 141 00:10:18,315 --> 00:10:23,317 What you get in indigenous growth model is how much labor goes into actually making 142 00:10:23,317 --> 00:10:28,201 stuff, and how much goes into research and design and thinking, right. It's a choice 143 00:10:28,201 --> 00:10:32,856 variable. In the model, right, and you solve for how much of that you get. Quick 144 00:10:32,856 --> 00:10:37,876 summary, right. Growth ceases without innovation, if that's true. Everybody 145 00:10:37,876 --> 00:10:42,375 should be pro innovation. And in fact, most people are. Right, so here's two 146 00:10:42,375 --> 00:10:47,305 quotes. Here's a fun little quiz. One of these quotes is from President Obama, who 147 00:10:47,305 --> 00:10:52,050 is a democrat. The other quote is from President Reagan. I want you to try and 148 00:10:52,050 --> 00:10:58,145 guess which quote came from Obama, and which quote came from Reagan. All right? 149 00:10:58,145 --> 00:11:02,534 So both Reagan are pro innovation, right? They, they are, because they are pro GDP 150 00:11:02,534 --> 00:11:06,700 growth, because [inaudible] gonna lift those people out of poverty. Right? We 151 00:11:06,700 --> 00:11:11,366 wanna make everyone better off. Because if we can lift people out of poverty, we make 152 00:11:11,366 --> 00:11:15,620 people happier. And what we've learned is the way to do that, right, is. First, by 153 00:11:15,620 --> 00:11:19,308 investing in capital. Right? Because that makes us, you know, all do better. We get 154 00:11:19,308 --> 00:11:22,762 to the 144 machines. But at some point then growth stops and then you need 155 00:11:22,762 --> 00:11:26,544 investment in technology. Then investment in technology leads to innovation which 156 00:11:26,544 --> 00:11:30,138 raises the whole thing up and we get this multiplier effect. Right? We get the 157 00:11:30,138 --> 00:11:33,639 increased productivity and then we also get the incentives to produce more 158 00:11:33,639 --> 00:11:38,062 machines. Right? Which raises our statement [inaudible] even more. So that's 159 00:11:38,062 --> 00:11:41,936 the E, in essence what growth theory is. Thanks.