1 00:00:00,000 --> 00:00:03,886 Hi. In this set of lectures we're talking about economic growth. And what we want to 2 00:00:03,886 --> 00:00:07,913 do is we want to understand why is it that some countries are rich and some countries 3 00:00:07,913 --> 00:00:11,519 are poor. So to get our bearings on how growth works, we've gotta start with a 4 00:00:11,519 --> 00:00:15,031 much simpler model. So economic growth models are gonna have a lot going on. 5 00:00:15,031 --> 00:00:18,637 Gonna have labor, they're gonna have physical capital, gonna have depreciation 6 00:00:18,637 --> 00:00:22,149 rates and saving rates and all sorts of stuff. So to just sort of get us to 7 00:00:22,149 --> 00:00:25,848 understand the basics of growth, we're gonna start out with a much simpler case. 8 00:00:25,848 --> 00:00:29,594 And we're gonna start by talking about just compounding. So you put money in the 9 00:00:29,594 --> 00:00:33,286 bank, and we talk about the rate at which that grows. From then we are gonna talk 10 00:00:33,286 --> 00:00:36,696 about then countries growth to make the GDP growing and we're gonna see why 11 00:00:36,696 --> 00:00:40,420 different growth rates are so important cuz we're gonna see that growth is sort of 12 00:00:40,420 --> 00:00:43,965 exponential, so we're gonna talk about a very simple sort of exponential growth 13 00:00:43,965 --> 00:00:47,656 rate. We just keep putting money in the bank from that we're going to learn a 14 00:00:47,656 --> 00:00:51,816 really cool trick called the Rule of 72. The Rule of 72 will tell us how quickly 15 00:00:51,816 --> 00:00:56,028 our money will double or how quickly GDP will double. So there if you think about 16 00:00:56,028 --> 00:00:59,408 it, what's the difference between an eight percent growth rate and a four percent 17 00:00:59,408 --> 00:01:03,516 growth rate and I think it's twice as much. We'll actually see from the Rule of 18 00:01:03,516 --> 00:01:07,104 72, that it's even more than that. Doubling the growth rate has really 19 00:01:07,104 --> 00:01:11,212 significant effects. Okay, so let's get started, so let's start with just sort of, 20 00:01:11,212 --> 00:01:15,157 like, you know. Basic accounting 101, you know, you put some money in the bank. So 21 00:01:15,157 --> 00:01:19,280 suppose you've got X dollars and you put it in the bank at R percent interest. How 22 00:01:19,280 --> 00:01:23,353 much do you get? Let's suppose you get 100 dollars and you put it in the bank. And 23 00:01:23,353 --> 00:01:27,073 let's suppose you get five percent interest. Well, what you're gonna get at 24 00:01:27,073 --> 00:01:30,995 the end of the next year is 105 dollars. Right? Because the general formula for 25 00:01:30,995 --> 00:01:34,967 this thing is, you just take X times one plus the interest rate. Right? So, that's 26 00:01:34,967 --> 00:01:38,788 the general formula. So you put 100 dollars in the bank at five percent, I'll 27 00:01:38,788 --> 00:01:43,005 get 105 back. Now if I put that 105 back in the bank I'll get 105 time times. One 28 00:01:43,005 --> 00:01:51,218 plus.05 and that's gonna be 105 plus 5.25, which is 110.25. So, in the two years I'll 29 00:01:51,218 --> 00:01:58,936 have 110.25. Now, if I kept this money in the bank for ten years, right, I'd just 30 00:01:58,936 --> 00:02:04,700 have 100 times one plus.05. [sound] Raised to the tenth power, right? Because they 31 00:02:04,700 --> 00:02:08,739 just keep multiplying this by 1.05, times 1.05, times 1.05, and that's what I get. 32 00:02:08,739 --> 00:02:12,982 So, that's - you what them to think about if I buy a certificate of deposit for some 33 00:02:12,982 --> 00:02:17,226 money, the bank say okay, I'm going to put this thousand dollars in for six years at 34 00:02:17,226 --> 00:02:21,111 five percent. They'll tell you, okay, well then you're going to get a thousand 35 00:02:21,111 --> 00:02:25,201 dollars times 1.05 raised to the sixth power. That's how much you'll get back at 36 00:02:25,201 --> 00:02:29,611 the end of the six years. You want to do that same thing -- the same very, very 37 00:02:29,611 --> 00:02:34,532 simple thing with GDP. Now with GDP, what we're going to do is that instead of setting X to be the 38 00:02:34,532 --> 00:02:39,772 amount of money we put in the bank, that's going to be per capita GDP. If there's a 39 00:02:39,772 --> 00:02:44,693 GDP right now of G, and we have R percent growth, then next year we'll get one Plus 40 00:02:44,693 --> 00:02:49,063 R. And in ten years, we'll have one plus R raised to the tenth power. Now, why does 41 00:02:49,063 --> 00:02:52,890 that matter so much? Why do we care so much about this R? Why do politicians 42 00:02:52,890 --> 00:02:56,718 always talk about it? Why do bankers always talk about it? Why do we care so 43 00:02:56,718 --> 00:03:00,801 much about growth rates? Well, to see why, let's look at two cases. Let's look at a 44 00:03:00,801 --> 00:03:04,577 sort of low growth case, the country that has a two percent growth rate. And a high 45 00:03:04,577 --> 00:03:08,048 growth case, a country that has a six percent growth rate. Let's start'em out 46 00:03:08,048 --> 00:03:11,875 both in year zero, with everybody making $1,000. So per capita income's $1,000. 47 00:03:11,875 --> 00:03:15,958 Well, what happens after [inaudible] the first year, the first country goes up by 48 00:03:15,958 --> 00:03:19,734 twenty%, so it's 1020, and the other countries at 1060. Now, you could say, big 49 00:03:19,734 --> 00:03:24,073 deal. $40 more per person. That's not a huge difference. Well let's go ahead ten 50 00:03:24,073 --> 00:03:28,213 years. In ten years, if I use that formula, the people in the first country 51 00:03:28,213 --> 00:03:33,080 are making $1200 apiece. The people in the second country are making $1800 apiece. 52 00:03:33,080 --> 00:03:38,371 So now, they're 50 percent better off and if I go ahead 35 years, right, so really 53 00:03:38,371 --> 00:03:44,078 maybe one generation, maybe a generation and a half, the first country has now doubled. So 54 00:03:44,078 --> 00:03:50,057 they're now at 2,000. The second country's at 7600. They've gone up 3.8 times. So now, they're 55 00:03:50,057 --> 00:03:54,459 almost -- or 7.6 times, I'm sorry -- so they're almost four times better off. 56 00:03:54,459 --> 00:03:59,489 Let's suppose I go ahead 100 years, move ahead a century. One country plugs along 57 00:03:59,489 --> 00:04:03,513 at two percent growth. The other country plugs along at six percent growth, right? 58 00:04:03,513 --> 00:04:08,543 The first country's now making $7,000 per person. The second country, right? People 59 00:04:08,543 --> 00:04:13,318 are making $339,000 per person. Right? So that's like forty five times as much. So 60 00:04:13,318 --> 00:04:18,327 in a hundred year period, this two percent versus six percent difference just becomes 61 00:04:18,327 --> 00:04:23,219 enormous, and that's because this growth is exponential, right? Cuz that's one plus 62 00:04:23,219 --> 00:04:27,758 our raise to the power of T, and so if R is bigger, you get a huge increase. So 63 00:04:27,758 --> 00:04:32,767 here's the Rule of 72. And this explains sort of why what was going on was 64 00:04:32,767 --> 00:04:39,004 going on like that. The Rule of 72 says divide the growth rate into 72. And the 65 00:04:39,004 --> 00:04:44,049 answer you get, will give you the number of years it takes to double, right? So 66 00:04:44,049 --> 00:04:49,422 let's suppose that our growth rate is two percent, right? If our growth rate is two 67 00:04:49,422 --> 00:04:54,599 percent I take seventy two, divide it by two and I get thirty six, that means it 68 00:04:54,599 --> 00:04:59,382 will take about thirty six years to double. Let's go back to our graph, go 69 00:04:59,382 --> 00:05:04,493 back to our graph you see it took thirty five years to double, so pretty close 70 00:05:04,493 --> 00:05:10,358 right? What if I had six percent. Well 72 divide by twelve I'm sorry, divided by six 71 00:05:10,358 --> 00:05:17,036 means it's gonna be twelve years to double. So what that means is, in this 72 00:05:17,036 --> 00:05:22,760 first period there's two%. It's gonna take me 36 years to double. At six percent, no 73 00:05:22,760 --> 00:05:26,999 it takes me twelve years to double. Which means that this country will double three 74 00:05:26,999 --> 00:05:31,085 times. Which is two times two times two. Which is eight. So its GDP will be eight 75 00:05:31,085 --> 00:05:35,171 times its original GDP, in the time it takes the first country to double. And if 76 00:05:35,171 --> 00:05:39,053 we go back and look at our data, sure enough after 35 years it's effectively 77 00:05:39,053 --> 00:05:43,292 eight times as big. So you see the rule of 72 isn't exactly right. Like, it took only 78 00:05:43,292 --> 00:05:47,072 35 years to double. And this isn't quite at eight thousand. But it's really 79 00:05:47,072 --> 00:05:50,606 accurate. So for low interest rates, it tends to, you know underestimate -- 80 00:05:50,606 --> 00:05:54,250 overestimate the number of years and for high interest rates it tends to 81 00:05:54,250 --> 00:05:58,293 overestimate the number of years. But at eight percent, nine percent it works just 82 00:05:58,293 --> 00:06:02,186 about perfectly. So the rule of 72, right, again, which is really cool -- so it's just, 83 00:06:02,186 --> 00:06:06,129 take your growth rate and divide it into 72, that tells you how long it's gonna 84 00:06:06,129 --> 00:06:09,973 take to double. So the move from two percent to six percent isn't just a four 85 00:06:09,973 --> 00:06:14,400 percent increase in the growth rate. Right? It's a dividing by three of the 86 00:06:14,400 --> 00:06:19,870 time to double. So it means that every twelve years your country's gonna double 87 00:06:19,870 --> 00:06:25,409 its well being, its GDP. Whereas in the first case at two percent it's gonna take 88 00:06:25,409 --> 00:06:29,970 36 years. That's why this... people focus so much on growth rates and that's why we 89 00:06:29,970 --> 00:06:34,087 wanna look at models that explain where growth comes from. Let's go back and look 90 00:06:34,087 --> 00:06:38,152 at the United States. Remember we're hanging out at about three, four percent. Well, to think, 91 00:06:38,152 --> 00:06:42,321 what's the difference between three, four percent. Well four percent is 72 divided 92 00:06:42,321 --> 00:06:46,369 by four, which means every eighteen years we'll double. And three percent is 72 93 00:06:46,369 --> 00:06:50,443 divided by three. Which means every 24 years we'll double. Well, what would you 94 00:06:50,443 --> 00:06:54,517 rather do? Double every eighteen years, or double every [laughs] 24 years? Clearly you'd 95 00:06:54,517 --> 00:06:58,644 rather double every eighteen years. So that's why we care a lot about boosting 96 00:06:58,644 --> 00:07:02,718 that growth rate. Even from something like three percent to four percent. 97 00:07:02,718 --> 00:07:06,740 Because that means we are going to increase our well being much, much faster. 98 00:07:06,740 --> 00:07:11,617 Okay, whew, exit. There's a lot going on here, right? We've talked about this sort 99 00:07:11,617 --> 00:07:16,682 of you know, simple interest rate thing where we've got X right, [sound] times one 100 00:07:16,682 --> 00:07:21,149 plus R, raised to the t power. Well this is sort of a cheat here because what 101 00:07:21,149 --> 00:07:25,465 we've done is I've just assumed for the interest of simplification that the growth 102 00:07:25,465 --> 00:07:30,128 is happening just once a year. So it's like once a year we do growth rates. When I was a kid 103 00:07:30,128 --> 00:07:35,020 there was a commercial on television for a bank and they talked about how some banks 104 00:07:35,020 --> 00:07:39,750 only gave interest once a year and it said, this new bank, we give interest every 105 00:07:39,750 --> 00:07:44,236 second of the day. So what we do is, instead of saying, okay we're going to 106 00:07:44,236 --> 00:07:48,040 give you at the end of one year, X times one plus R, we're going to give you 107 00:07:48,040 --> 00:07:52,347 interest, let's just say, suppose first we're going to give you interest every 108 00:07:52,347 --> 00:07:56,431 say, so we're going to give you one plus R over 365. So we're going to reduce the 109 00:07:56,431 --> 00:08:00,738 rate, divide it by 365. We're going to give it to you 365 times. So we're going 110 00:08:00,738 --> 00:08:05,269 to compute your interest daily and then they said, we'll do even better than that, 111 00:08:05,269 --> 00:08:09,632 we're going to do it, we can even do it hourly, so we'll do it over, we're going 112 00:08:09,632 --> 00:08:13,940 to divide the interest rate by the number of hours in the day and then we'll 113 00:08:13,940 --> 00:08:18,154 compute this interest every hour. And then we can even do it every second and so on 114 00:08:18,154 --> 00:08:21,810 and so on. And they show this guy at a calculator that's pluging away, right, 115 00:08:21,810 --> 00:08:25,963 [laugh], computing these interest rates and I thought how are they doing that? Well 116 00:08:25,963 --> 00:08:30,545 the way they did it, is that they just used math. It turns out if you have this 117 00:08:30,545 --> 00:08:35,303 formula, and this should be an infinity here. If you have the number of periods go 118 00:08:35,303 --> 00:08:39,827 to infinity, right so if you're doing it infinitely fast. Then what happens is, 119 00:08:39,827 --> 00:08:44,526 this formula, this one plus the interest rate over N, raised to the power NT, just 120 00:08:44,526 --> 00:08:49,284 becomes E to the RT. And remember E was that number Euler's constant, which is 2.71828. 121 00:08:49,284 --> 00:08:53,808 So why do we do this? Why do we do all this math? Reason we are doing all this 122 00:08:53,808 --> 00:08:58,390 math is basically you could think of the growth rate, instead of thinking of this 123 00:08:58,390 --> 00:09:03,534 formula -- you know X times, one plus R to the T -- you can do something simpler. You 124 00:09:03,534 --> 00:09:08,423 can just use E to the R T, where E is this Euler's constant, this 2.71828. So what 125 00:09:08,423 --> 00:09:13,557 you can do is if you think about growth as just sort of occurring continuously, then 126 00:09:13,557 --> 00:09:18,568 this nice simple formula will give you sort of the rate at which things are gonna 127 00:09:18,568 --> 00:09:22,907 grow, and that's why it's called exponential growth. Because the rate at 128 00:09:22,907 --> 00:09:27,429 which you grow is exponential in this function, in this number e. So it's E 129 00:09:27,429 --> 00:09:31,584 raised to the exponent R T. So why is that so important? The reason it's so important is, let's 130 00:09:31,584 --> 00:09:35,382 go back, remember we talked about linear functions, in the previous set of 131 00:09:35,382 --> 00:09:40,340 lectures, right? So remember linear function looks like this. So that would 132 00:09:40,340 --> 00:09:45,774 mean that growth would sort of go ten right, eleven twelve thirteen fourteen and 133 00:09:45,774 --> 00:09:50,410 so on, right. Exponential growth goes like this, it zooms up. Even faster than 134 00:09:50,410 --> 00:09:54,610 something like X squared. So what that means that if you grow at a ten percent 135 00:09:54,610 --> 00:09:58,325 rate, right, you're not just going to go ten, eleven, twelve, thirteen, fourteen, 136 00:09:58,325 --> 00:10:02,148 fifteen, sixteen, right. In fact, if you grow at a ten percent rate, in seven years. Right. 137 00:10:02,148 --> 00:10:06,456 Remember the rule of 72. 72 divided by ten is equal to seven. In seven years, what 138 00:10:06,456 --> 00:10:10,548 you're gonna do, is you're going to double. So you'll be twice as well off as 139 00:10:10,548 --> 00:10:15,878 you were before. [sound]. What have we learned? We've learned that if we get a 140 00:10:15,878 --> 00:10:19,735 growth rate of, say, let's say three percent, four percent, five percent. 141 00:10:19,735 --> 00:10:23,591 Right, that, that can lead to significantly better, you know higher GDP 142 00:10:23,591 --> 00:10:28,174 down the road, than if the growth rate is just a little bit smaller. And the reason 143 00:10:28,174 --> 00:10:32,702 why is because we've got this exponential growth. The world is not, the outcome is 144 00:10:32,702 --> 00:10:37,285 not going to be sort of linear in these growth rates. It's going to be exponential 145 00:10:37,285 --> 00:10:41,800 over time. So what you'd like to do is sustain a higher growth rate. So what we 146 00:10:41,800 --> 00:10:47,195 want to do next is construct some models of growth where we can see how this 147 00:10:47,195 --> 00:10:52,630 economic growth depend on things like saving, depreciation and technology. Okay, 148 00:10:52,630 --> 00:10:53,270 thank you.