WEBVTT 00:00:00.000 --> 00:00:00.982 align:middle line:90% [SQUEAKING] 00:00:00.982 --> 00:00:03.928 align:middle line:90% [RUSTLING] 00:00:03.928 --> 00:00:06.874 align:middle line:90% [CLICKING] 00:00:06.874 --> 00:00:16.860 align:middle line:90% 00:00:16.860 --> 00:00:19.780 align:middle line:84% ROBERT CABALLERO: OK, let's start. 00:00:19.780 --> 00:00:22.650 align:middle line:84% So today we're going to talk about technological progress 00:00:22.650 --> 00:00:24.160 align:middle line:90% and economic growth. 00:00:24.160 --> 00:00:31.410 align:middle line:84% And that's a big topic, certainly, at MIT. 00:00:31.410 --> 00:00:33.870 align:middle line:84% Perhaps this is one of the main ways we 00:00:33.870 --> 00:00:40.230 align:middle line:90% contribute to human well-being. 00:00:40.230 --> 00:00:44.310 align:middle line:84% But before I do that, let me do a brief review 00:00:44.310 --> 00:00:46.530 align:middle line:84% of the things I did in the second half 00:00:46.530 --> 00:00:49.530 align:middle line:90% of the previous lecture. 00:00:49.530 --> 00:00:51.660 align:middle line:84% For two reasons, I want to do that brief review. 00:00:51.660 --> 00:00:55.650 align:middle line:84% First, after spring break, so I assume 00:00:55.650 --> 00:00:59.430 align:middle line:84% there is some depreciation of knowledge since the last time. 00:00:59.430 --> 00:01:03.510 align:middle line:84% And the second is that while the equations I showed you 00:01:03.510 --> 00:01:05.800 align:middle line:84% at the end with population growth are correct, 00:01:05.800 --> 00:01:08.220 align:middle line:84% I think I said something which is not correct. 00:01:08.220 --> 00:01:10.092 align:middle line:90% I think I kept saying-- 00:01:10.092 --> 00:01:10.800 align:middle line:90% I don't know why. 00:01:10.800 --> 00:01:13.770 align:middle line:84% But I kept saying, look, if x is small, 00:01:13.770 --> 00:01:16.650 align:middle line:84% 1 over 1 plus x is approximately equal to minus x. 00:01:16.650 --> 00:01:21.480 align:middle line:84% No, it's approximately equal to 1 minus x not minus x. 00:01:21.480 --> 00:01:24.960 align:middle line:84% So I wanted to correct that typo. 00:01:24.960 --> 00:01:29.170 align:middle line:84% So let me remind you what we had. 00:01:29.170 --> 00:01:32.130 align:middle line:84% So we started with a production function. 00:01:32.130 --> 00:01:34.030 align:middle line:84% One important part of economic growth 00:01:34.030 --> 00:01:36.760 align:middle line:84% is we're going to have capital accumulation will be 00:01:36.760 --> 00:01:39.260 align:middle line:90% a very important variable here. 00:01:39.260 --> 00:01:41.860 align:middle line:84% And so we haven't talked about capital in the production 00:01:41.860 --> 00:01:44.980 align:middle line:84% function in the previous part of the course. 00:01:44.980 --> 00:01:46.752 align:middle line:84% But now we were explicit about it. 00:01:46.752 --> 00:01:48.460 align:middle line:84% And we started with a production function 00:01:48.460 --> 00:01:55.820 align:middle line:84% that had constant returns to scale on capital and labor. 00:01:55.820 --> 00:01:57.760 align:middle line:84% And here, remember in this part of the course, 00:01:57.760 --> 00:01:59.410 align:middle line:84% we're not talking about unemployment or anything 00:01:59.410 --> 00:01:59.910 align:middle line:90% like that. 00:01:59.910 --> 00:02:02.770 align:middle line:84% So whenever I say labor, I also mean population. 00:02:02.770 --> 00:02:05.710 align:middle line:84% I mean labor force, all of them together. 00:02:05.710 --> 00:02:08.539 align:middle line:84% You know the distinction between each of these concepts, 00:02:08.539 --> 00:02:11.740 align:middle line:84% but they're not that important for growth matters. 00:02:11.740 --> 00:02:14.230 align:middle line:84% Mostly because all of those aggregates 00:02:14.230 --> 00:02:16.750 align:middle line:84% move in tandem over the long run. 00:02:16.750 --> 00:02:22.810 align:middle line:84% It's very difficult for a population and the labor force 00:02:22.810 --> 00:02:25.630 align:middle line:84% to diverge for a very long period of time. 00:02:25.630 --> 00:02:30.970 align:middle line:84% Maybe fluctuations and so on, but then tend to move together. 00:02:30.970 --> 00:02:36.040 align:middle line:84% So but we decided that we wanted to look at things normalized 00:02:36.040 --> 00:02:38.120 align:middle line:90% by population. 00:02:38.120 --> 00:02:43.240 align:middle line:84% And so output per person is an increasing function 00:02:43.240 --> 00:02:46.570 align:middle line:84% of capital per person but also is increasing 00:02:46.570 --> 00:02:47.680 align:middle line:90% at a decreasing rate. 00:02:47.680 --> 00:02:49.660 align:middle line:84% There is decreasing returns with respect 00:02:49.660 --> 00:02:52.600 align:middle line:90% to the capital labor ratio. 00:02:52.600 --> 00:02:56.890 align:middle line:84% And so output per capita grows as the economy becomes 00:02:56.890 --> 00:02:58.450 align:middle line:84% more capital intensive, that is you 00:02:58.450 --> 00:03:00.910 align:middle line:84% have more capital per worker, but it 00:03:00.910 --> 00:03:03.380 align:middle line:90% grows at a decreasing rate. 00:03:03.380 --> 00:03:05.530 align:middle line:84% The second key equation of our model 00:03:05.530 --> 00:03:09.260 align:middle line:84% was that we're saying this part of the course, 00:03:09.260 --> 00:03:11.260 align:middle line:84% we're going to assume that the government is not 00:03:11.260 --> 00:03:13.640 align:middle line:84% running any fiscal deficit or anything like that, 00:03:13.640 --> 00:03:15.100 align:middle line:84% and the economy is closed, which is 00:03:15.100 --> 00:03:16.725 align:middle line:84% an assumption we have maintained and we 00:03:16.725 --> 00:03:20.480 align:middle line:84% will keep assuming until three lectures from now. 00:03:20.480 --> 00:03:23.050 align:middle line:84% And so in closed economy, no fiscal deficit. 00:03:23.050 --> 00:03:26.530 align:middle line:84% We have that investment is equal to saving. 00:03:26.530 --> 00:03:29.290 align:middle line:84% And we made an extra step to assume 00:03:29.290 --> 00:03:34.270 align:middle line:84% that the saving is proportional to income, so S proportional 00:03:34.270 --> 00:03:35.180 align:middle line:90% to income. 00:03:35.180 --> 00:03:37.280 align:middle line:84% So with all these things together, 00:03:37.280 --> 00:03:39.550 align:middle line:84% putting these two things together, 00:03:39.550 --> 00:03:43.670 align:middle line:84% we got to a very important equation in any growth model, 00:03:43.670 --> 00:03:45.700 align:middle line:84% which is the capital accumulation equation. 00:03:45.700 --> 00:03:49.060 align:middle line:84% And this equation says, well, the capital stock tomorrow-- 00:03:49.060 --> 00:03:52.180 align:middle line:84% tomorrow means in the next unit time, next year, 00:03:52.180 --> 00:03:57.850 align:middle line:84% or whatever --is equal to the current stock of capital 00:03:57.850 --> 00:04:00.280 align:middle line:84% minus the depreciation of that stock of capital 00:04:00.280 --> 00:04:03.430 align:middle line:84% minus the delta times kt plus investment. 00:04:03.430 --> 00:04:05.530 align:middle line:84% But investment is equal to saving, 00:04:05.530 --> 00:04:11.230 align:middle line:84% and saving is proportional to output, OK. 00:04:11.230 --> 00:04:14.500 align:middle line:84% So that was common across all the things we 00:04:14.500 --> 00:04:17.079 align:middle line:90% did in the previous lectures. 00:04:17.079 --> 00:04:19.300 align:middle line:84% Is there any question about these equations? 00:04:19.300 --> 00:04:21.220 align:middle line:90% No, no, good. 00:04:21.220 --> 00:04:23.620 align:middle line:84% OK, so the next step was to say, OK, 00:04:23.620 --> 00:04:26.530 align:middle line:84% and I did remember all the initial derivations. 00:04:26.530 --> 00:04:30.230 align:middle line:84% I assumed that n was constant, population was constant. 00:04:30.230 --> 00:04:35.360 align:middle line:84% And so the next step was I divided by a constant here. 00:04:35.360 --> 00:04:40.480 align:middle line:84% So we did everything in terms of capital output per person. 00:04:40.480 --> 00:04:43.570 align:middle line:84% But actually, since population was constant, 00:04:43.570 --> 00:04:46.300 align:middle line:84% the per person part was just trivial. 00:04:46.300 --> 00:04:48.190 align:middle line:90% We just divided by a constant. 00:04:48.190 --> 00:04:50.620 align:middle line:84% The last thing I did, though, in the previous lecture, 00:04:50.620 --> 00:04:53.420 align:middle line:84% was to say, OK, what if that's not the case? 00:04:53.420 --> 00:04:55.870 align:middle line:84% What if population is growing over time as well? 00:04:55.870 --> 00:04:58.640 align:middle line:90% How does our analysis change? 00:04:58.640 --> 00:05:01.390 align:middle line:90% And so I did this. 00:05:01.390 --> 00:05:05.950 align:middle line:84% Now, I said, well, OK, let's start by dividing everything 00:05:05.950 --> 00:05:07.330 align:middle line:90% by nt plus 1. 00:05:07.330 --> 00:05:12.130 align:middle line:84% So then we get capital per person at t plus 1. 00:05:12.130 --> 00:05:15.040 align:middle line:84% Problem is, I said is when I divide the right hand 00:05:15.040 --> 00:05:17.110 align:middle line:84% side by nt plus 1, I don't get what I want. 00:05:17.110 --> 00:05:20.860 align:middle line:84% I want capital T divided by population of t. 00:05:20.860 --> 00:05:24.040 align:middle line:84% I want output of t divided by population at t, not 00:05:24.040 --> 00:05:25.510 align:middle line:90% at t plus 1. 00:05:25.510 --> 00:05:32.180 align:middle line:84% So what I did is I multiply and divide by nt both of these. 00:05:32.180 --> 00:05:35.740 align:middle line:84% So I multiply by 1 and t over nt is 1, 00:05:35.740 --> 00:05:37.690 align:middle line:90% so I multiply by 1 everything. 00:05:37.690 --> 00:05:42.220 align:middle line:84% And then rearrange terms, so I got expressions like this. 00:05:42.220 --> 00:05:47.470 align:middle line:84% I got what I wanted here, which is capital per person 00:05:47.470 --> 00:05:49.780 align:middle line:90% at the same point in time. 00:05:49.780 --> 00:05:53.950 align:middle line:84% But now it's multiplied by nt over nt plus 1, OK. 00:05:53.950 --> 00:05:57.370 align:middle line:90% 00:05:57.370 --> 00:06:01.890 align:middle line:84% And the same I can do for this expression here. 00:06:01.890 --> 00:06:05.970 align:middle line:84% OK so this is what I'm using the approximation here, 00:06:05.970 --> 00:06:08.940 align:middle line:90% in which x is equal to gn. 00:06:08.940 --> 00:06:12.420 align:middle line:84% This thing here, is just 1 over 1 plus gn. 00:06:12.420 --> 00:06:14.550 align:middle line:84% And I'm saying this is approximately equal. 00:06:14.550 --> 00:06:16.830 align:middle line:84% I can approximate-- if gn is a small number, 00:06:16.830 --> 00:06:19.740 align:middle line:84% this is approximately equal to 1 minus gn. 00:06:19.740 --> 00:06:21.630 align:middle line:90% So that's what we have. 00:06:21.630 --> 00:06:25.200 align:middle line:84% And this is the second approximation 00:06:25.200 --> 00:06:27.450 align:middle line:84% going from this line to this line 00:06:27.450 --> 00:06:29.010 align:middle line:90% in which we did the following. 00:06:29.010 --> 00:06:42.960 align:middle line:84% We said, OK, this is equal to 1 minus delta minus gn plus delta 00:06:42.960 --> 00:06:44.670 align:middle line:90% times gn. 00:06:44.670 --> 00:06:46.830 align:middle line:84% But the delta time gn is the multiplication 00:06:46.830 --> 00:06:48.130 align:middle line:90% of two small numbers. 00:06:48.130 --> 00:06:50.610 align:middle line:84% So I said assume that it's close to zero. 00:06:50.610 --> 00:06:52.050 align:middle line:90% And the same we have here. 00:06:52.050 --> 00:06:56.610 align:middle line:84% We have saving rate times 1 plus gn. 00:06:56.610 --> 00:07:02.670 align:middle line:84% You get you get the saving rate plus the saving rate times gn. 00:07:02.670 --> 00:07:05.760 align:middle line:84% But the saving rate times gn is also small number, 00:07:05.760 --> 00:07:07.050 align:middle line:90% so we also drop, OK. 00:07:07.050 --> 00:07:09.367 align:middle line:84% So those are the more explicit steps 00:07:09.367 --> 00:07:10.950 align:middle line:84% of what I did in the previous lecture. 00:07:10.950 --> 00:07:13.830 align:middle line:84% And I think the final equation I showed you was this, 00:07:13.830 --> 00:07:16.350 align:middle line:84% but it comes from, again, two approximations. 00:07:16.350 --> 00:07:20.010 align:middle line:84% The one down here, which I use here. 00:07:20.010 --> 00:07:24.810 align:middle line:84% And then the fact that I dropped the second order terms, OK. 00:07:24.810 --> 00:07:25.710 align:middle line:90% That's it. 00:07:25.710 --> 00:07:27.540 align:middle line:84% And then I just rearrange things. 00:07:27.540 --> 00:07:30.820 align:middle line:84% I move kt over n to the left-hand side. 00:07:30.820 --> 00:07:34.620 align:middle line:84% And so we have the change in the stock of capital per person 00:07:34.620 --> 00:07:39.240 align:middle line:84% is an increasing function of investment 00:07:39.240 --> 00:07:41.860 align:middle line:84% per person, which is this because this 00:07:41.860 --> 00:07:43.330 align:middle line:90% is saving per person. 00:07:43.330 --> 00:07:46.310 align:middle line:84% And I can replace this by the production function, 00:07:46.310 --> 00:07:48.160 align:middle line:90% which is f of k over n. 00:07:48.160 --> 00:07:50.950 align:middle line:84% And so what I have here is a difference equation 00:07:50.950 --> 00:07:55.850 align:middle line:90% in capital per person. 00:07:55.850 --> 00:07:58.930 align:middle line:90% Why is this? 00:07:58.930 --> 00:08:00.230 align:middle line:90% So this is investment. 00:08:00.230 --> 00:08:05.110 align:middle line:84% So the capital stock per person will be growing as we invest. 00:08:05.110 --> 00:08:07.870 align:middle line:84% It shrinks with the passage of time just because 00:08:07.870 --> 00:08:08.710 align:middle line:90% of depreciation. 00:08:08.710 --> 00:08:09.970 align:middle line:90% Some things break down. 00:08:09.970 --> 00:08:11.680 align:middle line:84% That reduces the stock of capital. 00:08:11.680 --> 00:08:13.660 align:middle line:84% But the new term that we introduce 00:08:13.660 --> 00:08:18.460 align:middle line:84% at the end of the last lecture, is that now this ratio also 00:08:18.460 --> 00:08:22.490 align:middle line:90% declines with population growth. 00:08:22.490 --> 00:08:25.640 align:middle line:84% And so who can explain why we get this term? 00:08:25.640 --> 00:08:31.310 align:middle line:90% 00:08:31.310 --> 00:08:37.210 align:middle line:84% I'm saying, look, suppose that we 00:08:37.210 --> 00:08:39.640 align:middle line:84% have take as given the amount of investment. 00:08:39.640 --> 00:08:41.620 align:middle line:90% We take as given depreciation. 00:08:41.620 --> 00:08:44.800 align:middle line:84% But now I say, well, if gn rises, 00:08:44.800 --> 00:08:46.610 align:middle line:84% and all the rest remains constant, 00:08:46.610 --> 00:08:51.100 align:middle line:84% then the left-hand side will start declining, 00:08:51.100 --> 00:08:53.200 align:middle line:84% or it will grow less rapidly than what's going 00:08:53.200 --> 00:08:56.390 align:middle line:90% to grow before I increase gn. 00:08:56.390 --> 00:08:59.570 align:middle line:90% Why is that the case? 00:08:59.570 --> 00:09:01.100 align:middle line:90% Sometimes it's counterintuitive. 00:09:01.100 --> 00:09:04.650 align:middle line:84% That's the reason I thought I rush in the previous lecture 00:09:04.650 --> 00:09:05.150 align:middle line:90% over that. 00:09:05.150 --> 00:09:08.480 align:middle line:84% And since it's going to be an important intermediate step 00:09:08.480 --> 00:09:11.000 align:middle line:84% into the next one, which is going to introduce 00:09:11.000 --> 00:09:13.580 align:middle line:84% technological progress, I want us 00:09:13.580 --> 00:09:16.890 align:middle line:84% to understand why that gn appears with a negative sign 00:09:16.890 --> 00:09:17.390 align:middle line:90% there. 00:09:17.390 --> 00:09:20.620 align:middle line:90% 00:09:20.620 --> 00:09:22.170 align:middle line:90% Yep. 00:09:22.170 --> 00:09:24.670 align:middle line:84% AUDIENCE: [INAUDIBLE] returns for the same amount of capital 00:09:24.670 --> 00:09:29.030 align:middle line:84% that have increased in [INAUDIBLE] 00:09:29.030 --> 00:09:35.920 align:middle line:84% ROBERT CABALLERO: That term is going to be captured here. 00:09:35.920 --> 00:09:37.570 align:middle line:90% And it's going to play a role. 00:09:37.570 --> 00:09:40.540 align:middle line:84% But this one comes from something much more mechanical 00:09:40.540 --> 00:09:41.170 align:middle line:90% than that. 00:09:41.170 --> 00:09:44.720 align:middle line:90% 00:09:44.720 --> 00:09:47.970 align:middle line:84% Hint, observe what I have on the left-hand side. 00:09:47.970 --> 00:09:51.350 align:middle line:84% I don't have on the left-hand side, the change 00:09:51.350 --> 00:09:54.460 align:middle line:90% in the stock of capital. 00:09:54.460 --> 00:09:58.290 align:middle line:84% I have the change in the stock of capital per person. 00:09:58.290 --> 00:10:00.980 align:middle line:84% So suppose I don't change the stock of capital 00:10:00.980 --> 00:10:06.170 align:middle line:84% at all from this period to the next, but population grows. 00:10:06.170 --> 00:10:09.790 align:middle line:84% What happens to this expression here? 00:10:09.790 --> 00:10:12.460 align:middle line:84% Decreases, it becomes negative because I 00:10:12.460 --> 00:10:13.960 align:middle line:84% haven't changed the capital stock, 00:10:13.960 --> 00:10:15.730 align:middle line:90% but the denominator is growing. 00:10:15.730 --> 00:10:17.080 align:middle line:90% That's the gn part. 00:10:17.080 --> 00:10:19.030 align:middle line:84% And that means this term's negative. 00:10:19.030 --> 00:10:21.400 align:middle line:84% And that's what this term is here 00:10:21.400 --> 00:10:25.060 align:middle line:84% for is to capture the fact that the denominator Now. 00:10:25.060 --> 00:10:27.910 align:middle line:84% Is also moving on the left-hand side variable. 00:10:27.910 --> 00:10:29.800 align:middle line:90% And you say, so what? 00:10:29.800 --> 00:10:32.320 align:middle line:84% At the end of the day, I care about the capital. 00:10:32.320 --> 00:10:34.750 align:middle line:84% Why do I care about capital per person? 00:10:34.750 --> 00:10:38.362 align:middle line:84% Well, my analysis, I told you it's 00:10:38.362 --> 00:10:39.820 align:middle line:84% much easier if I do it on something 00:10:39.820 --> 00:10:41.710 align:middle line:90% which has a steady state. 00:10:41.710 --> 00:10:44.410 align:middle line:84% And that's the reason I'm looking for this normalization. 00:10:44.410 --> 00:10:47.920 align:middle line:84% But once I look at the dynamic equation of accumulation 00:10:47.920 --> 00:10:51.940 align:middle line:84% of capital in this divided by population, 00:10:51.940 --> 00:10:55.420 align:middle line:84% then I need to take into account the fact that my denominator is 00:10:55.420 --> 00:10:56.680 align:middle line:90% also moving, OK. 00:10:56.680 --> 00:10:58.660 align:middle line:84% So that's the reason that gn is there. 00:10:58.660 --> 00:11:00.973 align:middle line:84% And again, the reason I wanted to pause on this 00:11:00.973 --> 00:11:03.140 align:middle line:84% is because when we introduce technological progress, 00:11:03.140 --> 00:11:04.940 align:middle line:84% we're going to have a similar effect. 00:11:04.940 --> 00:11:06.550 align:middle line:90% And so I want you to understand. 00:11:06.550 --> 00:11:08.200 align:middle line:84% It's going to be counterintuitive 00:11:08.200 --> 00:11:10.360 align:middle line:84% because it sounds like technological progress is 00:11:10.360 --> 00:11:11.200 align:middle line:90% something negative. 00:11:11.200 --> 00:11:12.820 align:middle line:90% No, it's not negative. 00:11:12.820 --> 00:11:17.980 align:middle line:84% But in this space, it turns out that if population 00:11:17.980 --> 00:11:20.710 align:middle line:84% grows very fast, then you need a lot of investment 00:11:20.710 --> 00:11:25.270 align:middle line:84% to keep up the capital-labor ratio constant, OK. 00:11:25.270 --> 00:11:26.830 align:middle line:90% That's the idea. 00:11:26.830 --> 00:11:30.400 align:middle line:84% If population is not growing, I don't need a lot of investment 00:11:30.400 --> 00:11:32.470 align:middle line:84% to keep the capital-labor ratio constant. 00:11:32.470 --> 00:11:34.670 align:middle line:84% But if population is growing very fast, 00:11:34.670 --> 00:11:36.670 align:middle line:84% then I need a lot of investment to really 00:11:36.670 --> 00:11:37.940 align:middle line:90% keep that ratio constant. 00:11:37.940 --> 00:11:39.820 align:middle line:84% That's what this is capturing there. 00:11:39.820 --> 00:11:46.620 align:middle line:84% So to repeat, if this guy is very large, 00:11:46.620 --> 00:11:49.150 align:middle line:84% then I need a lot of investment here 00:11:49.150 --> 00:11:50.860 align:middle line:84% to make this thing equal to zero. 00:11:50.860 --> 00:11:54.110 align:middle line:84% So the capital is stock per person is not declining. 00:11:54.110 --> 00:11:56.180 align:middle line:90% That's idea, OK. 00:11:56.180 --> 00:11:59.200 align:middle line:90% 00:11:59.200 --> 00:12:03.230 align:middle line:90% Good, OK, so and then I said-- 00:12:03.230 --> 00:12:05.350 align:middle line:90% OK, this is where we finished. 00:12:05.350 --> 00:12:09.770 align:middle line:84% Then I said, OK, so let's go back to our diagram. 00:12:09.770 --> 00:12:13.370 align:middle line:84% Once I have everything in this space, k over Ni, n, 00:12:13.370 --> 00:12:16.150 align:middle line:90% I can go back to our diagram. 00:12:16.150 --> 00:12:17.860 align:middle line:90% Assume that ga is equal to zero. 00:12:17.860 --> 00:12:19.990 align:middle line:84% You don't even know what a is for the time being. 00:12:19.990 --> 00:12:21.850 align:middle line:90% You will know in five minutes. 00:12:21.850 --> 00:12:24.850 align:middle line:84% But assume ga is equal to zero, then that's exactly 00:12:24.850 --> 00:12:26.540 align:middle line:90% the model we had before. 00:12:26.540 --> 00:12:30.533 align:middle line:84% So and remember, this is exactly the same diagram. 00:12:30.533 --> 00:12:32.450 align:middle line:84% It looked the same, at least, that we had when 00:12:32.450 --> 00:12:33.990 align:middle line:90% population was not growing. 00:12:33.990 --> 00:12:37.280 align:middle line:84% I'm saying I can use the same diagram when 00:12:37.280 --> 00:12:39.740 align:middle line:90% population is growing as well. 00:12:39.740 --> 00:12:43.150 align:middle line:84% But there is one important difference, 00:12:43.150 --> 00:12:46.390 align:middle line:84% which is this curve looks exactly the same. 00:12:46.390 --> 00:12:51.120 align:middle line:84% This is just output per worker, OK. 00:12:51.120 --> 00:12:52.800 align:middle line:90% That's the blue line. 00:12:52.800 --> 00:12:56.100 align:middle line:84% The green line looks exactly the same as in the basic model. 00:12:56.100 --> 00:12:59.260 align:middle line:84% It's just little s times the blue line. 00:12:59.260 --> 00:13:00.720 align:middle line:90% So that's exactly the same. 00:13:00.720 --> 00:13:03.640 align:middle line:90% But this line is different. 00:13:03.640 --> 00:13:08.580 align:middle line:84% What happens to this red line as gn goes up? 00:13:08.580 --> 00:13:13.290 align:middle line:84% So what happens to this line as gn goes up? 00:13:13.290 --> 00:13:14.880 align:middle line:90% Becomes steeper, no? 00:13:14.880 --> 00:13:17.195 align:middle line:90% So it rotates up, OK. 00:13:17.195 --> 00:13:19.340 align:middle line:90% It goes up. 00:13:19.340 --> 00:13:21.860 align:middle line:84% And that can sound counterintuitive sometimes 00:13:21.860 --> 00:13:24.690 align:middle line:84% because you say, look what happens here. 00:13:24.690 --> 00:13:26.820 align:middle line:90% Let's spend time on this. 00:13:26.820 --> 00:13:31.970 align:middle line:84% Suppose that we are at some steady state, say this one. 00:13:31.970 --> 00:13:34.115 align:middle line:90% And now population growth rises. 00:13:34.115 --> 00:13:36.950 align:middle line:90% 00:13:36.950 --> 00:13:44.340 align:middle line:84% OK, it sounds like Ireland in 2000s and so on. 00:13:44.340 --> 00:13:47.990 align:middle line:84% So population growth rises a lot. 00:13:47.990 --> 00:13:49.650 align:middle line:90% What happens in this diagram? 00:13:49.650 --> 00:13:54.090 align:middle line:84% So suppose we are at the steady state here. 00:13:54.090 --> 00:13:59.355 align:middle line:84% No, and that steady state investment saving, 00:13:59.355 --> 00:14:01.230 align:middle line:84% which is equal to investment, is exactly what 00:14:01.230 --> 00:14:03.060 align:middle line:84% you need to maintain the stock of capital 00:14:03.060 --> 00:14:05.700 align:middle line:90% per person constant, OK. 00:14:05.700 --> 00:14:09.400 align:middle line:84% That's what the red line tells us, that here. 00:14:09.400 --> 00:14:12.180 align:middle line:90% So the gap here is-- 00:14:12.180 --> 00:14:13.950 align:middle line:84% this is a gap between investment and what 00:14:13.950 --> 00:14:17.470 align:middle line:84% you need to maintain the stock of capital per person constant. 00:14:17.470 --> 00:14:22.560 align:middle line:84% So when the gap is zero, then this left-hand side 00:14:22.560 --> 00:14:23.820 align:middle line:90% is equal to zero. 00:14:23.820 --> 00:14:25.840 align:middle line:90% OK, that's the red line. 00:14:25.840 --> 00:14:27.990 align:middle line:90% That's the green line. 00:14:27.990 --> 00:14:31.390 align:middle line:84% When this is equal to zero, that's equal to that. 00:14:31.390 --> 00:14:33.370 align:middle line:90% That's exactly that point. 00:14:33.370 --> 00:14:36.210 align:middle line:84% OK, but I'm saying, suppose we are at that point, 00:14:36.210 --> 00:14:40.840 align:middle line:90% and now population growth rises? 00:14:40.840 --> 00:14:43.600 align:middle line:90% So what moves in that diagram? 00:14:43.600 --> 00:14:45.040 align:middle line:90% Does the blue line move? 00:14:45.040 --> 00:14:51.590 align:middle line:90% 00:14:51.590 --> 00:14:55.207 align:middle line:84% I don't see gn in the blue line, so the blue line doesn't move. 00:14:55.207 --> 00:14:57.290 align:middle line:84% If the blue line doesn't move, and the saving rate 00:14:57.290 --> 00:15:01.200 align:middle line:84% hasn't changed, then the green line doesn't move either. 00:15:01.200 --> 00:15:04.453 align:middle line:84% So for this diagram to be interesting, what moves? 00:15:04.453 --> 00:15:05.370 align:middle line:90% Something has to move. 00:15:05.370 --> 00:15:07.760 align:middle line:84% So the only thing that it has that can move here, 00:15:07.760 --> 00:15:10.100 align:middle line:90% is the red line. 00:15:10.100 --> 00:15:13.020 align:middle line:84% And the red line, we already said, if gn goes up, 00:15:13.020 --> 00:15:15.980 align:middle line:90% it's going to rotate upwards. 00:15:15.980 --> 00:15:20.290 align:middle line:84% That means, OK, so now we have that line there. 00:15:20.290 --> 00:15:25.890 align:middle line:84% So what happens at the previous stage stock of capital 00:15:25.890 --> 00:15:27.810 align:middle line:90% per worker at this level? 00:15:27.810 --> 00:15:28.860 align:middle line:90% What happened? 00:15:28.860 --> 00:15:30.195 align:middle line:90% Is that a new steady state? 00:15:30.195 --> 00:15:33.630 align:middle line:90% 00:15:33.630 --> 00:15:37.810 align:middle line:84% No, but what happens in particular? 00:15:37.810 --> 00:15:40.300 align:middle line:84% So I'm saying, suppose that you are here, 00:15:40.300 --> 00:15:43.220 align:middle line:84% and now I rotate the red line up. 00:15:43.220 --> 00:15:45.650 align:middle line:84% OK, so that means the red line that 00:15:45.650 --> 00:15:47.330 align:middle line:84% represents the amount of capital I 00:15:47.330 --> 00:15:50.670 align:middle line:84% need to maintain the stock of capital constant 00:15:50.670 --> 00:15:54.810 align:middle line:84% is greater than how much is society saving and therefore 00:15:54.810 --> 00:15:55.840 align:middle line:90% investing. 00:15:55.840 --> 00:15:59.184 align:middle line:84% So what will happen to capital per worker? 00:15:59.184 --> 00:16:02.050 align:middle line:90% AUDIENCE: Decrease. 00:16:02.050 --> 00:16:05.200 align:middle line:84% ROBERT CABALLERO: Decrease, exactly because you need 00:16:05.200 --> 00:16:07.310 align:middle line:90% more than you're investing. 00:16:07.310 --> 00:16:09.463 align:middle line:84% So the capital stock has to decline. 00:16:09.463 --> 00:16:10.630 align:middle line:90% And that's what will happen. 00:16:10.630 --> 00:16:13.690 align:middle line:84% The new steady state is going to be to the left of that point 00:16:13.690 --> 00:16:15.490 align:middle line:90% there. 00:16:15.490 --> 00:16:17.900 align:middle line:90% That sounds very weird. 00:16:17.900 --> 00:16:22.730 align:middle line:84% How can it be that-- after all, labor contributes to output. 00:16:22.730 --> 00:16:28.160 align:middle line:84% How can it be that we end up with a lower output per worker 00:16:28.160 --> 00:16:29.870 align:middle line:84% when we increase population growth? 00:16:29.870 --> 00:16:34.370 align:middle line:84% Is population growth bad in a sense for growth itself 00:16:34.370 --> 00:16:35.660 align:middle line:90% for output? 00:16:35.660 --> 00:16:42.220 align:middle line:90% 00:16:42.220 --> 00:16:44.010 align:middle line:90% Well, the answer is no. 00:16:44.010 --> 00:16:46.770 align:middle line:84% It's true that the new steady state will 00:16:46.770 --> 00:16:49.300 align:middle line:90% have lower output per person. 00:16:49.300 --> 00:16:50.643 align:middle line:90% So in that sense, it's bad. 00:16:50.643 --> 00:16:51.810 align:middle line:90% You have lots of population. 00:16:51.810 --> 00:16:55.140 align:middle line:84% If you don't change the saving rate or something, 00:16:55.140 --> 00:16:58.260 align:middle line:84% then output per person will be lower, 00:16:58.260 --> 00:17:00.840 align:middle line:84% but output will be higher than it used 00:17:00.840 --> 00:17:02.430 align:middle line:90% to be at any point in time. 00:17:02.430 --> 00:17:05.220 align:middle line:84% It just happens that in the transition, 00:17:05.220 --> 00:17:07.230 align:middle line:90% the growth of output-- 00:17:07.230 --> 00:17:10.560 align:middle line:84% so the growth of output in this model 00:17:10.560 --> 00:17:14.230 align:middle line:84% is going to be equal to the growth of population. 00:17:14.230 --> 00:17:17.710 align:middle line:84% OK, that's if you have a steady state, where population 00:17:17.710 --> 00:17:21.200 align:middle line:84% is growing and output per worker or per person is not growing, 00:17:21.200 --> 00:17:24.740 align:middle line:84% that means output is growing at the same rate as population. 00:17:24.740 --> 00:17:28.040 align:middle line:84% So that means that if I increase the rate of population growth, 00:17:28.040 --> 00:17:31.880 align:middle line:84% the rate of growth of output will increase together 00:17:31.880 --> 00:17:33.770 align:middle line:84% with the rate of growth of population. 00:17:33.770 --> 00:17:37.550 align:middle line:84% But in the transition, as the output per capita goes lower, 00:17:37.550 --> 00:17:40.040 align:middle line:84% output will grow less than population. 00:17:40.040 --> 00:17:41.720 align:middle line:84% And that's what is happening here. 00:17:41.720 --> 00:17:42.870 align:middle line:90% But output is growing. 00:17:42.870 --> 00:17:46.220 align:middle line:84% If population starts growing, if you increase migration, 00:17:46.220 --> 00:17:48.080 align:middle line:90% you're going to see output grow. 00:17:48.080 --> 00:17:52.010 align:middle line:84% But output per person will start declining, 00:17:52.010 --> 00:17:53.730 align:middle line:84% until you get to a new steady state. 00:17:53.730 --> 00:17:54.980 align:middle line:90% And then you'll get the same-- 00:17:54.980 --> 00:17:57.530 align:middle line:90% 00:17:57.530 --> 00:17:59.060 align:middle line:84% you'll get the higher rate of growth 00:17:59.060 --> 00:18:01.040 align:middle line:84% if you continue with population growth 00:18:01.040 --> 00:18:02.660 align:middle line:84% with the higher population growth. 00:18:02.660 --> 00:18:05.960 align:middle line:84% But output per worker will be slightly lower rate, OK. 00:18:05.960 --> 00:18:09.960 align:middle line:90% 00:18:09.960 --> 00:18:13.300 align:middle line:84% Anyways, this may have been fast, the last part. 00:18:13.300 --> 00:18:15.150 align:middle line:84% But since I'm going to repeat it now, 00:18:15.150 --> 00:18:18.990 align:middle line:84% in the context of technological progress, we should be fine, OK. 00:18:18.990 --> 00:18:21.510 align:middle line:84% So if you're a little confused now, it's OK. 00:18:21.510 --> 00:18:24.640 align:middle line:84% If you're a little confused at the end of the lecture, 00:18:24.640 --> 00:18:28.560 align:middle line:84% it's not OK because I'm counting with you sort of getting it 00:18:28.560 --> 00:18:32.130 align:middle line:84% in the second pass, OK, the second try, OK. 00:18:32.130 --> 00:18:34.000 align:middle line:90% So next step is following. 00:18:34.000 --> 00:18:37.230 align:middle line:84% So here, we assume already population growth, 00:18:37.230 --> 00:18:41.220 align:middle line:84% but we assume the technology, so the production function 00:18:41.220 --> 00:18:44.400 align:middle line:84% stay put for any combination of capital and labor. 00:18:44.400 --> 00:18:49.230 align:middle line:84% The next step is to think what happens when the technology 00:18:49.230 --> 00:18:51.970 align:middle line:84% itself is getting better over time. 00:18:51.970 --> 00:18:56.220 align:middle line:84% And that's what we call technological progress, OK. 00:18:56.220 --> 00:18:58.020 align:middle line:90% This is TFP. 00:18:58.020 --> 00:18:59.760 align:middle line:84% Let me not get into the specifics. 00:18:59.760 --> 00:19:01.440 align:middle line:84% At the end, I'll say a little more. 00:19:01.440 --> 00:19:05.400 align:middle line:84% But this TFP stands for Total Factor Productivity. 00:19:05.400 --> 00:19:08.940 align:middle line:84% And this index here captures the level of TFP 00:19:08.940 --> 00:19:11.520 align:middle line:90% in the US over time. 00:19:11.520 --> 00:19:12.600 align:middle line:90% And it's clearly growing. 00:19:12.600 --> 00:19:15.450 align:middle line:84% So technology is getting better and better over time. 00:19:15.450 --> 00:19:16.350 align:middle line:90% What that means? 00:19:16.350 --> 00:19:19.580 align:middle line:84% Well, I'll say a little more, not a lot more, 00:19:19.580 --> 00:19:20.580 align:middle line:90% but it's getting better. 00:19:20.580 --> 00:19:23.250 align:middle line:90% 00:19:23.250 --> 00:19:26.190 align:middle line:84% And so the question we have here is 00:19:26.190 --> 00:19:29.393 align:middle line:84% I'm going to address next is, how does this? 00:19:29.393 --> 00:19:30.810 align:middle line:84% So now we're going to put together 00:19:30.810 --> 00:19:32.437 align:middle line:84% our entire economic growth model. 00:19:32.437 --> 00:19:34.020 align:middle line:84% We're going to have population growth. 00:19:34.020 --> 00:19:36.990 align:middle line:84% We're going to have also technology growing. 00:19:36.990 --> 00:19:43.200 align:middle line:84% Up to now, the only reason you could grow output per worker, 00:19:43.200 --> 00:19:45.360 align:middle line:84% was because you were accumulating lots of capital. 00:19:45.360 --> 00:19:47.305 align:middle line:84% You were catching up with your steady state. 00:19:47.305 --> 00:19:48.930 align:middle line:84% That's what would make you grow faster, 00:19:48.930 --> 00:19:51.930 align:middle line:90% but then there was nothing else. 00:19:51.930 --> 00:19:55.390 align:middle line:84% TFP is going to be the only growth in technology. 00:19:55.390 --> 00:19:57.030 align:middle line:84% It's going to be the only thing that 00:19:57.030 --> 00:20:00.690 align:middle line:84% will give you sustainable growth in the long run in output 00:20:00.690 --> 00:20:02.200 align:middle line:90% per person. 00:20:02.200 --> 00:20:08.110 align:middle line:84% So this is a very important component of growth. 00:20:08.110 --> 00:20:09.730 align:middle line:84% Again, it's the only thing that will 00:20:09.730 --> 00:20:15.490 align:middle line:84% make you growth in a sustainable manner in per-person terms. 00:20:15.490 --> 00:20:17.470 align:middle line:84% The previous model didn't have that. 00:20:17.470 --> 00:20:21.300 align:middle line:84% In the previous model, we had a steady state 00:20:21.300 --> 00:20:23.740 align:middle line:90% on output per worker. 00:20:23.740 --> 00:20:25.200 align:middle line:84% So in the previous model, we didn't 00:20:25.200 --> 00:20:29.500 align:middle line:84% have growth in output per worker in the steady state. 00:20:29.500 --> 00:20:33.180 align:middle line:84% We could have transitional growth when we were catching up. 00:20:33.180 --> 00:20:37.430 align:middle line:84% If you started here, then you were 00:20:37.430 --> 00:20:40.040 align:middle line:84% going to have growth, fast growth, 00:20:40.040 --> 00:20:44.460 align:middle line:84% but eventually, we'll put it out, OK, output per worker. 00:20:44.460 --> 00:20:47.820 align:middle line:84% So up to now, we don't have a reason 00:20:47.820 --> 00:20:51.830 align:middle line:84% to explain why we see that output per worker 00:20:51.830 --> 00:20:55.660 align:middle line:84% grows in most economies in the world. 00:20:55.660 --> 00:20:57.150 align:middle line:90% And the answer will be this. 00:20:57.150 --> 00:20:59.370 align:middle line:84% This is the reason really output per worker 00:20:59.370 --> 00:21:01.260 align:middle line:90% can grow in a sustained manner. 00:21:01.260 --> 00:21:04.770 align:middle line:84% Technology is getting better and better over time. 00:21:04.770 --> 00:21:07.590 align:middle line:84% So let's see, so the question is, 00:21:07.590 --> 00:21:12.080 align:middle line:84% let's now see what this does to the model we have. 00:21:12.080 --> 00:21:17.450 align:middle line:84% Now, in practice, technological progress takes many, many forms. 00:21:17.450 --> 00:21:21.410 align:middle line:90% 00:21:21.410 --> 00:21:23.990 align:middle line:84% At the most basic level, it means 00:21:23.990 --> 00:21:26.162 align:middle line:84% that you can produce larger quantities of output, 00:21:26.162 --> 00:21:27.620 align:middle line:84% and that's really the meaning we're 00:21:27.620 --> 00:21:30.230 align:middle line:84% going to have here, larger quantities of output 00:21:30.230 --> 00:21:33.780 align:middle line:84% for the same amount of capital and labor. 00:21:33.780 --> 00:21:36.210 align:middle line:84% So you have 10 machines 10 workers, 00:21:36.210 --> 00:21:38.490 align:middle line:84% technological progress means, well, you 00:21:38.490 --> 00:21:40.410 align:middle line:84% used to produce 12 units, now we're 00:21:40.410 --> 00:21:44.340 align:middle line:84% going to produce 12, 14, 15, and so on and so forth. 00:21:44.340 --> 00:21:51.330 align:middle line:84% That's one of the main ways technological progress shows up. 00:21:51.330 --> 00:21:54.390 align:middle line:84% We can do more with the same if you will. 00:21:54.390 --> 00:21:57.130 align:middle line:84% Second dimension is better product. 00:21:57.130 --> 00:21:59.010 align:middle line:84% So it's not that you produce more cars, 00:21:59.010 --> 00:22:02.825 align:middle line:84% but you produce better cars, better computers, and so on, OK. 00:22:02.825 --> 00:22:04.950 align:middle line:84% That's another dimension of technological progress. 00:22:04.950 --> 00:22:09.040 align:middle line:84% You can produce new products, things that didn't even exist, 00:22:09.040 --> 00:22:10.920 align:middle line:90% but now you have. 00:22:10.920 --> 00:22:14.160 align:middle line:84% That counts more than having one more unit of good. 00:22:14.160 --> 00:22:16.418 align:middle line:84% It counts more because you have things 00:22:16.418 --> 00:22:18.210 align:middle line:84% that you couldn't even satisfy in the past, 00:22:18.210 --> 00:22:21.540 align:middle line:84% you can satisfy now because you have this certain kind of goods. 00:22:21.540 --> 00:22:22.830 align:middle line:90% That the nx is before. 00:22:22.830 --> 00:22:24.750 align:middle line:84% That's a very important dimension 00:22:24.750 --> 00:22:27.540 align:middle line:84% of technological progress, it just 00:22:27.540 --> 00:22:30.390 align:middle line:84% creates new sort of forms of inputs 00:22:30.390 --> 00:22:32.850 align:middle line:90% of production and technologies. 00:22:32.850 --> 00:22:36.930 align:middle line:84% Think of AI what that will do to technology in general 00:22:36.930 --> 00:22:41.020 align:middle line:84% and to consumption very directly. 00:22:41.020 --> 00:22:42.730 align:middle line:90% And that's what I mean. 00:22:42.730 --> 00:22:45.570 align:middle line:84% Even within a product, you can get more variety. 00:22:45.570 --> 00:22:47.850 align:middle line:84% And more variety, it improves welfare 00:22:47.850 --> 00:22:53.020 align:middle line:84% because you can align better the needs with the product 00:22:53.020 --> 00:22:53.800 align:middle line:90% and so on. 00:22:53.800 --> 00:22:55.620 align:middle line:84% But we're going to make it very simple. 00:22:55.620 --> 00:23:01.350 align:middle line:84% In this course, we're going to model technological progress 00:23:01.350 --> 00:23:04.620 align:middle line:90% as if it was workers. 00:23:04.620 --> 00:23:10.290 align:middle line:84% So we're going to capture technology 00:23:10.290 --> 00:23:14.880 align:middle line:84% with this variable a, which is going to be-- 00:23:14.880 --> 00:23:17.190 align:middle line:84% we're going to model it as labor equivalent. 00:23:17.190 --> 00:23:22.260 align:middle line:84% That is, if a grows, it's going to count for us as 00:23:22.260 --> 00:23:25.492 align:middle line:90% if we had more workers. 00:23:25.492 --> 00:23:26.950 align:middle line:84% That's just one way of modeling it. 00:23:26.950 --> 00:23:29.470 align:middle line:84% I mean I can do it in many different ways, 00:23:29.470 --> 00:23:31.330 align:middle line:84% and many of these are equivalent. 00:23:31.330 --> 00:23:34.180 align:middle line:84% But that's a very nice way of modeling, 00:23:34.180 --> 00:23:37.540 align:middle line:84% so we can use exactly the same diagrams we had and so on, OK. 00:23:37.540 --> 00:23:39.370 align:middle line:84% So you can think of technological progress. 00:23:39.370 --> 00:23:40.960 align:middle line:84% The way I'm going to model this here, 00:23:40.960 --> 00:23:43.480 align:middle line:84% is you can think of technological progress 00:23:43.480 --> 00:23:45.940 align:middle line:84% as if this economy was receiving more workers. 00:23:45.940 --> 00:23:48.680 align:middle line:90% 00:23:48.680 --> 00:23:54.230 align:middle line:84% Or a more accurate description is, with the same workers, 00:23:54.230 --> 00:23:58.160 align:middle line:84% it's as if it had more labor input, OK. 00:23:58.160 --> 00:24:02.520 align:middle line:84% That's one way of capturing technological progress. 00:24:02.520 --> 00:24:06.020 align:middle line:84% So now that means that I'm going to refer to this term 00:24:06.020 --> 00:24:10.220 align:middle line:90% a n as effective labor. 00:24:10.220 --> 00:24:13.010 align:middle line:84% So with the same number of n bodies, 00:24:13.010 --> 00:24:15.590 align:middle line:84% I may get more effective labor because each worker 00:24:15.590 --> 00:24:17.090 align:middle line:90% can produce more things. 00:24:17.090 --> 00:24:19.250 align:middle line:84% It's a better input of production, 00:24:19.250 --> 00:24:23.380 align:middle line:90% factor of production, OK. 00:24:23.380 --> 00:24:25.480 align:middle line:84% And I like to model it this way because now I 00:24:25.480 --> 00:24:27.970 align:middle line:84% can use exactly the same diagrams we had before, 00:24:27.970 --> 00:24:31.720 align:middle line:84% but rather than normalizing by population, 00:24:31.720 --> 00:24:35.660 align:middle line:84% I'm going to normalize by effective label, by a n. 00:24:35.660 --> 00:24:39.652 align:middle line:90% 00:24:39.652 --> 00:24:40.730 align:middle line:90% So, let me do that. 00:24:40.730 --> 00:24:42.910 align:middle line:84% So recall that we had our production function 00:24:42.910 --> 00:24:43.940 align:middle line:90% with constant returns. 00:24:43.940 --> 00:24:45.570 align:middle line:90% So this holds. 00:24:45.570 --> 00:24:49.080 align:middle line:84% I'm going to set this x now as 1 over a n. 00:24:49.080 --> 00:24:50.700 align:middle line:90% We used to have one over n. 00:24:50.700 --> 00:24:52.920 align:middle line:90% I'm going to have one over a n. 00:24:52.920 --> 00:24:57.480 align:middle line:84% And so I'm going to now have output per effective worker 00:24:57.480 --> 00:24:59.760 align:middle line:84% is going to be also the same little function 00:24:59.760 --> 00:25:05.310 align:middle line:84% f of capital per effective worker. 00:25:05.310 --> 00:25:07.470 align:middle line:84% And what is nice of this, is that now here 00:25:07.470 --> 00:25:11.970 align:middle line:84% rather than plotting y over n, I'm going to plot y over a n. 00:25:11.970 --> 00:25:13.860 align:middle line:84% Rather than plotting k over n here, 00:25:13.860 --> 00:25:15.900 align:middle line:90% I'm going to plot k over a n. 00:25:15.900 --> 00:25:19.560 align:middle line:84% And I have the blue line looks exactly like it used to look. 00:25:19.560 --> 00:25:21.720 align:middle line:84% It's just I'm dividing by a over n. 00:25:21.720 --> 00:25:23.940 align:middle line:84% Remember, the trick in all these models, 00:25:23.940 --> 00:25:26.100 align:middle line:84% is to find the right normalization, that 00:25:26.100 --> 00:25:29.520 align:middle line:84% is to find the right x, So I can find a steady state 00:25:29.520 --> 00:25:30.570 align:middle line:90% in my diagram. 00:25:30.570 --> 00:25:32.490 align:middle line:84% I don't want these curves to be moving around. 00:25:32.490 --> 00:25:35.790 align:middle line:84% I want to have a steady state, something, a point 00:25:35.790 --> 00:25:40.380 align:middle line:84% that we're going to converge to after enough time has passed. 00:25:40.380 --> 00:25:42.870 align:middle line:84% And I know that the thing that will do it 00:25:42.870 --> 00:25:46.170 align:middle line:84% in a model in which I have effective workers growing, 00:25:46.170 --> 00:25:51.150 align:middle line:84% is one in which I divide everything by effective workers. 00:25:51.150 --> 00:25:52.895 align:middle line:84% OK, so that's what I'm doing here. 00:25:52.895 --> 00:25:54.270 align:middle line:84% I'm going to build a diagram that 00:25:54.270 --> 00:25:56.910 align:middle line:84% looks like the other one that has a nice steady state 00:25:56.910 --> 00:25:58.560 align:middle line:90% as the previous one had, OK. 00:25:58.560 --> 00:26:00.030 align:middle line:90% So I have my blue line. 00:26:00.030 --> 00:26:01.263 align:middle line:90% Here I have my blue line. 00:26:01.263 --> 00:26:03.930 align:middle line:84% I know I have my green line, no, because the green line was just 00:26:03.930 --> 00:26:05.590 align:middle line:90% little s times the blue line. 00:26:05.590 --> 00:26:07.200 align:middle line:90% So I have that. 00:26:07.200 --> 00:26:10.380 align:middle line:84% The last thing I need, and I already showed you that, 00:26:10.380 --> 00:26:14.730 align:middle line:84% but I'm going to show it again, is the red line. 00:26:14.730 --> 00:26:18.120 align:middle line:84% But for the red line, I need to find the term-- 00:26:18.120 --> 00:26:21.030 align:middle line:84% remember, the red line represents the capital 00:26:21.030 --> 00:26:24.060 align:middle line:84% we need to maintain the current stock of capital 00:26:24.060 --> 00:26:26.530 align:middle line:90% per effective worker constant. 00:26:26.530 --> 00:26:28.470 align:middle line:84% That's what I need my red line for. 00:26:28.470 --> 00:26:29.760 align:middle line:90% So let's get there. 00:26:29.760 --> 00:26:31.463 align:middle line:84% And it always starts from this equation. 00:26:31.463 --> 00:26:33.630 align:middle line:84% So this equation is still the same as it used to be. 00:26:33.630 --> 00:26:34.890 align:middle line:90% That doesn't change. 00:26:34.890 --> 00:26:38.460 align:middle line:84% But what I'm going to do now, is rather than dividing by n, 00:26:38.460 --> 00:26:41.700 align:middle line:84% I'm going to divide by a times n. 00:26:41.700 --> 00:26:44.640 align:middle line:84% So the same as I did earlier in this lecture. 00:26:44.640 --> 00:26:47.760 align:middle line:84% I now I want to divide by a over n. 00:26:47.760 --> 00:26:51.080 align:middle line:84% So I get capital per effective worker on the left-hand side. 00:26:51.080 --> 00:26:53.050 align:middle line:84% I don't like what I get here, but you 00:26:53.050 --> 00:26:58.180 align:middle line:84% know that I can divide and multiply by a n, n over a n. 00:26:58.180 --> 00:27:00.490 align:middle line:84% So I can write the right-hand side 00:27:00.490 --> 00:27:02.365 align:middle line:84% after I do all my substitutions as this. 00:27:02.365 --> 00:27:06.660 align:middle line:90% 00:27:06.660 --> 00:27:09.450 align:middle line:84% So first step one, I divided everything 00:27:09.450 --> 00:27:12.960 align:middle line:90% by a t plus 1 times nt plus 1. 00:27:12.960 --> 00:27:18.000 align:middle line:84% Step two, I multiply each of these terms by a, t, and t. 00:27:18.000 --> 00:27:20.010 align:middle line:90% I multiply by a, t, and t. 00:27:20.010 --> 00:27:22.470 align:middle line:90% Divide by a, t, and t and. 00:27:22.470 --> 00:27:25.620 align:middle line:84% And then I regroup things, So I end up with that. 00:27:25.620 --> 00:27:27.690 align:middle line:84% Well, this, using the approximation 00:27:27.690 --> 00:27:42.850 align:middle line:84% we have here, is approximately equal to 1 minus gan and gan, 00:27:42.850 --> 00:27:49.460 align:middle line:90% is equal to ga plus gn. 00:27:49.460 --> 00:27:52.310 align:middle line:84% So I already showed you that case 00:27:52.310 --> 00:27:55.430 align:middle line:84% for the case in which ga was equal to zero. 00:27:55.430 --> 00:27:56.850 align:middle line:90% I'm doing now. 00:27:56.850 --> 00:27:59.840 align:middle line:84% The same thing but, since I renormalized things 00:27:59.840 --> 00:28:05.720 align:middle line:84% by effective workers, effective labor rather than actual labor, 00:28:05.720 --> 00:28:09.370 align:middle line:90% I need to use a n rather than n. 00:28:09.370 --> 00:28:12.230 align:middle line:84% And then by the same approximation I had before, 00:28:12.230 --> 00:28:15.970 align:middle line:84% which is that these products are close to zero, 00:28:15.970 --> 00:28:18.140 align:middle line:84% then I get to the equation I want. 00:28:18.140 --> 00:28:20.440 align:middle line:84% And if I write it in first difference, 00:28:20.440 --> 00:28:21.910 align:middle line:90% then I get my red line. 00:28:21.910 --> 00:28:25.065 align:middle line:90% This is my red line here. 00:28:25.065 --> 00:28:25.565 align:middle line:90% OK. 00:28:25.565 --> 00:28:28.230 align:middle line:90% 00:28:28.230 --> 00:28:28.740 align:middle line:90% Good. 00:28:28.740 --> 00:28:38.190 align:middle line:84% So this tells me that when the green line is 00:28:38.190 --> 00:28:42.030 align:middle line:84% equal to the red line, then I have a steady state. 00:28:42.030 --> 00:28:44.230 align:middle line:84% Capital perfected work is constant, 00:28:44.230 --> 00:28:45.630 align:middle line:90% and this is equal to zero. 00:28:45.630 --> 00:28:47.430 align:middle line:84% That's the way I find my steady state. 00:28:47.430 --> 00:28:49.740 align:middle line:84% If I ask you a question, find the steady state 00:28:49.740 --> 00:28:51.600 align:middle line:84% of this economy, what you'll do is 00:28:51.600 --> 00:28:54.570 align:middle line:84% you'll set this equal to zero and find the capital 00:28:54.570 --> 00:28:57.150 align:middle line:84% stock that gives you this equal to zero. 00:28:57.150 --> 00:29:01.490 align:middle line:90% That's the way you do it, OK. 00:29:01.490 --> 00:29:03.230 align:middle line:90% So that's that. 00:29:03.230 --> 00:29:04.670 align:middle line:90% And then we get back to-- 00:29:04.670 --> 00:29:07.730 align:middle line:90% 00:29:07.730 --> 00:29:11.660 align:middle line:84% well, this is the same as we had before. 00:29:11.660 --> 00:29:12.850 align:middle line:90% That's what I just said. 00:29:12.850 --> 00:29:16.550 align:middle line:84% That's the way you find the steady state, OK. 00:29:16.550 --> 00:29:18.410 align:middle line:84% And then we get back to the diagram 00:29:18.410 --> 00:29:20.900 align:middle line:90% I started with in this lecture. 00:29:20.900 --> 00:29:26.060 align:middle line:84% But now we have here a n, and now, in the first part, 00:29:26.060 --> 00:29:29.930 align:middle line:84% I said assume this ga equal to 0. 00:29:29.930 --> 00:29:34.820 align:middle line:84% Now the main actor is ga positive, OK, 00:29:34.820 --> 00:29:36.870 align:middle line:90% and we get this diagram. 00:29:36.870 --> 00:29:38.450 align:middle line:84% So now I can ask you the question 00:29:38.450 --> 00:29:41.810 align:middle line:84% that I asked you before with population growth, 00:29:41.810 --> 00:29:44.600 align:middle line:84% and see how much I can confuse you. 00:29:44.600 --> 00:29:46.670 align:middle line:90% Suppose that ga goes up. 00:29:46.670 --> 00:29:48.350 align:middle line:84% That sounds like a good thing, no. 00:29:48.350 --> 00:29:52.640 align:middle line:84% I mean, suppose that we are at the steady state here, 00:29:52.640 --> 00:29:55.820 align:middle line:84% and this diagram has too much stuff. 00:29:55.820 --> 00:29:56.480 align:middle line:90% Let me. 00:29:56.480 --> 00:30:19.450 align:middle line:90% 00:30:19.450 --> 00:30:20.920 align:middle line:90% OK, so we're here. 00:30:20.920 --> 00:30:23.900 align:middle line:90% 00:30:23.900 --> 00:30:38.770 align:middle line:84% That's our initial steady state zero. 00:30:38.770 --> 00:30:53.620 align:middle line:84% And this line here is delta plus ga plus gn times k over a n, OK. 00:30:53.620 --> 00:31:01.615 align:middle line:84% So well first, so suppose we are the steady state. 00:31:01.615 --> 00:31:04.750 align:middle line:90% 00:31:04.750 --> 00:31:06.100 align:middle line:90% Its output constant there. 00:31:06.100 --> 00:31:09.570 align:middle line:90% 00:31:09.570 --> 00:31:10.710 align:middle line:90% It's a steady state. 00:31:10.710 --> 00:31:13.470 align:middle line:90% Is output constant there? 00:31:13.470 --> 00:31:19.710 align:middle line:84% So suppose we are at that point here. 00:31:19.710 --> 00:31:22.290 align:middle line:84% Here, we know that investment is exactly how much we 00:31:22.290 --> 00:31:26.460 align:middle line:84% need to maintain the stock of capital per effective worker 00:31:26.460 --> 00:31:27.460 align:middle line:90% constant. 00:31:27.460 --> 00:31:29.990 align:middle line:84% That's what the steady state means. 00:31:29.990 --> 00:31:34.245 align:middle line:84% Question, is output constant there? 00:31:34.245 --> 00:31:35.395 align:middle line:90% It's steady state. 00:31:35.395 --> 00:31:49.670 align:middle line:90% 00:31:49.670 --> 00:31:52.120 align:middle line:90% No. 00:31:52.120 --> 00:31:59.980 align:middle line:84% This only says that capital per effective worker is constant. 00:31:59.980 --> 00:32:04.420 align:middle line:84% That means that if effective workers or labor is growing, 00:32:04.420 --> 00:32:07.210 align:middle line:84% then capital is growing at the same rate 00:32:07.210 --> 00:32:10.720 align:middle line:84% and therefore, output is growing at the same rate 00:32:10.720 --> 00:32:15.640 align:middle line:90% as effective workers, OK. 00:32:15.640 --> 00:32:18.060 align:middle line:84% Remember, the whole trick, so the curves would not 00:32:18.060 --> 00:32:20.730 align:middle line:84% be moving around, is I find the right normalization. 00:32:20.730 --> 00:32:24.045 align:middle line:84% So everything is growing at the same rate in that steady state. 00:32:24.045 --> 00:32:28.980 align:middle line:90% 00:32:28.980 --> 00:32:30.960 align:middle line:84% So let me actually show you that, and then 00:32:30.960 --> 00:32:34.530 align:middle line:84% I'm going to go over the experiment I want to have. 00:32:34.530 --> 00:32:38.160 align:middle line:84% So this is what is happening in that steady state. 00:32:38.160 --> 00:32:43.320 align:middle line:84% So capital per effective worker at the steady state, 00:32:43.320 --> 00:32:48.180 align:middle line:90% so at that point there, is zero. 00:32:48.180 --> 00:32:52.320 align:middle line:84% That's my definition of a steady state, OK. 00:32:52.320 --> 00:32:57.120 align:middle line:84% Output per effective worker is also growing at the rate zero. 00:32:57.120 --> 00:32:59.430 align:middle line:90% That's that one over there. 00:32:59.430 --> 00:33:02.300 align:middle line:90% Sorry. 00:33:02.300 --> 00:33:06.500 align:middle line:84% That's my steady state level of output per effective worker. 00:33:06.500 --> 00:33:12.560 align:middle line:90% 00:33:12.560 --> 00:33:14.120 align:middle line:90% So these are constant. 00:33:14.120 --> 00:33:15.530 align:middle line:90% That's a steady state. 00:33:15.530 --> 00:33:17.000 align:middle line:90% Those are constant. 00:33:17.000 --> 00:33:19.100 align:middle line:90% This ratio is constant. 00:33:19.100 --> 00:33:21.780 align:middle line:90% Each of those components is not. 00:33:21.780 --> 00:33:25.460 align:middle line:84% So that's what I'm plotting there. 00:33:25.460 --> 00:33:27.650 align:middle line:90% So those are not growing. 00:33:27.650 --> 00:33:32.650 align:middle line:84% Capital per worker, what about that? 00:33:32.650 --> 00:33:35.500 align:middle line:90% Well, you see there. 00:33:35.500 --> 00:33:41.150 align:middle line:84% So claim, capital per worker is growing at the rate ga. 00:33:41.150 --> 00:33:42.250 align:middle line:90% How do I know that? 00:33:42.250 --> 00:33:58.830 align:middle line:90% 00:33:58.830 --> 00:34:02.040 align:middle line:84% So the question I'm asking there, 00:34:02.040 --> 00:34:17.250 align:middle line:84% is what is the rate of growth of k over n given that I already 00:34:17.250 --> 00:34:26.639 align:middle line:84% know that the rate of growth of k over a n is equal to zero? 00:34:26.639 --> 00:34:33.860 align:middle line:90% 00:34:33.860 --> 00:34:37.880 align:middle line:84% Well, this, the rate of growth of k over n, 00:34:37.880 --> 00:34:43.610 align:middle line:84% is the rate of growth of k over a n 00:34:43.610 --> 00:34:50.139 align:middle line:84% plus the rate of growth of a, no. 00:34:50.139 --> 00:34:55.239 align:middle line:84% I mean, if a is growing and this ratio is constant, 00:34:55.239 --> 00:34:58.990 align:middle line:84% that means that k over n must be growing. 00:34:58.990 --> 00:35:02.050 align:middle line:84% And it has to be growing at exactly the same rate 00:35:02.050 --> 00:35:03.862 align:middle line:90% as this a is growing. 00:35:03.862 --> 00:35:06.445 align:middle line:84% Otherwise, I wouldn't be able to maintain that ratio constant. 00:35:06.445 --> 00:35:10.460 align:middle line:90% 00:35:10.460 --> 00:35:14.710 align:middle line:84% And the same logic applies to output per worker 00:35:14.710 --> 00:35:18.340 align:middle line:84% because in that steady state, output per effective worker 00:35:18.340 --> 00:35:20.110 align:middle line:90% is constant. 00:35:20.110 --> 00:35:24.010 align:middle line:84% But a is growing, so output per worker 00:35:24.010 --> 00:35:27.340 align:middle line:84% must be growing at the same rate as a i growing, 00:35:27.340 --> 00:35:32.530 align:middle line:90% and that's ga, OK, good. 00:35:32.530 --> 00:35:35.470 align:middle line:84% Labor, well, labor is exogenous which in population, is growing 00:35:35.470 --> 00:35:38.210 align:middle line:90% at the rate n that's given. 00:35:38.210 --> 00:35:42.100 align:middle line:90% What about capital and output? 00:35:42.100 --> 00:35:45.040 align:middle line:84% Well, claim, capital and output are 00:35:45.040 --> 00:35:47.500 align:middle line:90% growing at the rate ga plus gn. 00:35:47.500 --> 00:35:50.780 align:middle line:90% 00:35:50.780 --> 00:35:52.700 align:middle line:84% And I can do the same as I was in here. 00:35:52.700 --> 00:35:56.120 align:middle line:84% I'm asking you the question, gk, what 00:35:56.120 --> 00:35:58.280 align:middle line:90% is the rate of growth of gk? 00:35:58.280 --> 00:36:02.930 align:middle line:84% Well, it's going to be equal to the rate of growth of k 00:36:02.930 --> 00:36:10.000 align:middle line:84% over n plus the rate of growth of n. 00:36:10.000 --> 00:36:12.250 align:middle line:90% This is equal to ga. 00:36:12.250 --> 00:36:15.070 align:middle line:90% 00:36:15.070 --> 00:36:17.820 align:middle line:90% So it's ga plus gn. 00:36:17.820 --> 00:36:26.610 align:middle line:84% And the same happens for output, OK. 00:36:26.610 --> 00:36:31.830 align:middle line:84% So remember, I said earlier on, that if an economy has 00:36:31.830 --> 00:36:33.600 align:middle line:84% more population growth, it will grow more. 00:36:33.600 --> 00:36:36.540 align:middle line:90% 00:36:36.540 --> 00:36:38.370 align:middle line:90% There's no doubt of that. 00:36:38.370 --> 00:36:40.950 align:middle line:84% Obviously, output per worker will not grow more 00:36:40.950 --> 00:36:44.380 align:middle line:84% because population growth grows more in the new steady state. 00:36:44.380 --> 00:36:47.780 align:middle line:90% gn doesn't show up there. 00:36:47.780 --> 00:36:52.880 align:middle line:84% But the only thing that will make output per worker grow, 00:36:52.880 --> 00:36:56.280 align:middle line:84% is technological progress, so it;s ga. 00:36:56.280 --> 00:36:58.695 align:middle line:90% And that was my claim earlier. 00:36:58.695 --> 00:37:03.980 align:middle line:90% 00:37:03.980 --> 00:37:05.750 align:middle line:90% We're going to use this later. 00:37:05.750 --> 00:37:16.940 align:middle line:90% 00:37:16.940 --> 00:37:20.360 align:middle line:84% No, I'm not going to do this to myself now. 00:37:20.360 --> 00:37:22.427 align:middle line:84% I'm going to get back to what I wanted to now. 00:37:22.427 --> 00:37:24.260 align:middle line:84% Because I need to tell you a little bit more 00:37:24.260 --> 00:37:28.740 align:middle line:84% about the production function to growth accounting, 00:37:28.740 --> 00:37:30.320 align:middle line:90% which is what I wanted to do. 00:37:30.320 --> 00:37:33.240 align:middle line:90% So but this is clear. 00:37:33.240 --> 00:37:37.100 align:middle line:90% I mean, this is important, OK. 00:37:37.100 --> 00:37:38.940 align:middle line:90% Good. 00:37:38.940 --> 00:37:42.330 align:middle line:84% So this is the reason ga is such an important variable. 00:37:42.330 --> 00:37:45.090 align:middle line:84% What you guys do here at MIT is very important. 00:37:45.090 --> 00:37:48.897 align:middle line:84% Afterwards, it's very important, OK. 00:37:48.897 --> 00:37:50.980 align:middle line:84% That's the only thing that can drive really growth 00:37:50.980 --> 00:37:53.110 align:middle line:90% in the long run, in per capita. 00:37:53.110 --> 00:37:55.680 align:middle line:90% 00:37:55.680 --> 00:37:58.140 align:middle line:90% This gn plays also a role. 00:37:58.140 --> 00:38:02.400 align:middle line:84% You look at countries, not only the growth in per capita output. 00:38:02.400 --> 00:38:05.460 align:middle line:84% You tend to look at growth at total growth. 00:38:05.460 --> 00:38:07.950 align:middle line:84% One of the big concerns in big parts of Asia 00:38:07.950 --> 00:38:11.340 align:middle line:84% now, in Europe as well, as I said earlier in the course, 00:38:11.340 --> 00:38:14.350 align:middle line:90% is that gn is turning negative. 00:38:14.350 --> 00:38:17.340 align:middle line:84% That's not going to affect output per worker growth, 00:38:17.340 --> 00:38:23.020 align:middle line:84% but it does affect output growth in general. 00:38:23.020 --> 00:38:24.830 align:middle line:90% And you can see it here. 00:38:24.830 --> 00:38:27.130 align:middle line:84% So if dn goes down, that will reduce 00:38:27.130 --> 00:38:30.020 align:middle line:90% the rate of growth of output. 00:38:30.020 --> 00:38:32.300 align:middle line:84% Doesn't reduce the rate of growth output per worker, 00:38:32.300 --> 00:38:35.660 align:middle line:84% but it does reduce the rate of growth of output, good. 00:38:35.660 --> 00:38:38.680 align:middle line:90% 00:38:38.680 --> 00:38:42.610 align:middle line:84% So what happens-- remember, we did in the basic EOQ 00:38:42.610 --> 00:38:46.570 align:middle line:84% we did an experiment in which we increased the savings rate. 00:38:46.570 --> 00:38:48.380 align:middle line:90% So we can do the same here. 00:38:48.380 --> 00:38:51.220 align:middle line:84% What happens if we get an increase in the savings rate? 00:38:51.220 --> 00:38:54.500 align:middle line:84% Do we get more growth in the long run? 00:38:54.500 --> 00:38:57.760 align:middle line:84% And the answer is, for the same reasons we had before, no. 00:38:57.760 --> 00:38:59.680 align:middle line:84% If we increase the savings rate in this, 00:38:59.680 --> 00:39:02.440 align:middle line:84% now, this full model, all that happens 00:39:02.440 --> 00:39:04.460 align:middle line:84% is that this green line moves up. 00:39:04.460 --> 00:39:06.670 align:middle line:84% It means that at the initial steady state, now 00:39:06.670 --> 00:39:07.570 align:middle line:90% we have more savings. 00:39:07.570 --> 00:39:08.980 align:middle line:84% And therefore, more investment than we 00:39:08.980 --> 00:39:11.440 align:middle line:84% need to maintain the stock of capital per effective worker 00:39:11.440 --> 00:39:13.450 align:middle line:84% constant, which means that we're going 00:39:13.450 --> 00:39:15.760 align:middle line:90% to get transitional growth. 00:39:15.760 --> 00:39:19.270 align:middle line:84% Capital per effective worker will start growing, for a while. 00:39:19.270 --> 00:39:22.420 align:middle line:84% And as that happens, output per effective worker 00:39:22.420 --> 00:39:25.500 align:middle line:90% will also start growing. 00:39:25.500 --> 00:39:28.200 align:middle line:84% But eventually, decreasing returns 00:39:28.200 --> 00:39:30.070 align:middle line:90% will kick in here, as well. 00:39:30.070 --> 00:39:33.690 align:middle line:84% And that transitional growth will stop, 00:39:33.690 --> 00:39:38.010 align:middle line:84% and we'll end up at a higher level of output 00:39:38.010 --> 00:39:40.380 align:middle line:84% per effective worker and a higher level of capital 00:39:40.380 --> 00:39:44.430 align:middle line:84% per effective worker, but the rate of growth, in the long run, 00:39:44.430 --> 00:39:46.510 align:middle line:84% will not be affected by the saving rate. 00:39:46.510 --> 00:39:48.800 align:middle line:84% We'll get more transitional growth, 00:39:48.800 --> 00:39:55.590 align:middle line:84% but we will not get faster long-term growth. 00:39:55.590 --> 00:39:59.280 align:middle line:84% A lot of the Asian miracle, the Southeast Asian miracle 00:39:59.280 --> 00:40:02.670 align:middle line:84% in particular, we saw very fast rates of growth 00:40:02.670 --> 00:40:08.020 align:middle line:84% in many economies of Asia, was a lot of that kind, 00:40:08.020 --> 00:40:10.950 align:middle line:84% meaning was a combination of what we had before. 00:40:10.950 --> 00:40:14.970 align:middle line:84% Economies that were relatively poor had low capital per worker 00:40:14.970 --> 00:40:18.430 align:middle line:84% early on in which the saving rate increased enormously. 00:40:18.430 --> 00:40:22.930 align:middle line:84% And that combination gave them enormous transitional growth. 00:40:22.930 --> 00:40:24.840 align:middle line:90% So rate of growth of 10%, 12%. 00:40:24.840 --> 00:40:28.800 align:middle line:84% That was Japan, and then it was Korea, Taiwan, and so on. 00:40:28.800 --> 00:40:31.620 align:middle line:84% All those economies had very fast rate of growth 00:40:31.620 --> 00:40:32.850 align:middle line:90% as a result of that. 00:40:32.850 --> 00:40:35.520 align:middle line:84% China, later on, and China was a big thing for the world 00:40:35.520 --> 00:40:37.990 align:middle line:84% because it was much bigger at the same time. 00:40:37.990 --> 00:40:40.990 align:middle line:84% But it was mostly a combination of those two things. 00:40:40.990 --> 00:40:45.450 align:middle line:84% It was having a lower stock of capital early on combined 00:40:45.450 --> 00:40:49.560 align:middle line:84% with, for a variety of reasons, an increase in the savings rate. 00:40:49.560 --> 00:40:53.340 align:middle line:84% And that combination gave them very fast transitional growth. 00:40:53.340 --> 00:40:55.810 align:middle line:84% But they all getting a little stuck now. 00:40:55.810 --> 00:40:57.460 align:middle line:84% And they're very concerned with that. 00:40:57.460 --> 00:41:00.630 align:middle line:84% Well, they're fighting against this model. 00:41:00.630 --> 00:41:03.480 align:middle line:84% There's lots of concerns of what is happening to China. 00:41:03.480 --> 00:41:05.760 align:middle line:84% Are we going to follow the Japan path and so on. 00:41:05.760 --> 00:41:08.040 align:middle line:84% Well, they're following this model. 00:41:08.040 --> 00:41:10.440 align:middle line:84% That's what is happening to our first order. 00:41:10.440 --> 00:41:13.640 align:middle line:90% 00:41:13.640 --> 00:41:16.770 align:middle line:84% I'll say a little bit more later on about that. 00:41:16.770 --> 00:41:22.400 align:middle line:84% So in this particular case, what I have done is, in log space, 00:41:22.400 --> 00:41:26.300 align:middle line:84% so I can have linear things when it's growing, in log space, 00:41:26.300 --> 00:41:32.360 align:middle line:84% this economy with the low saving rate was growing here. 00:41:32.360 --> 00:41:36.590 align:middle line:84% This is output, so the slope of this was ga plus gn. 00:41:36.590 --> 00:41:40.820 align:middle line:84% Remember, in the steady state, output is growing at ga plus gn. 00:41:40.820 --> 00:41:43.230 align:middle line:84% If the saving rate now increases, 00:41:43.230 --> 00:41:45.560 align:middle line:84% then output starts growing transitionally faster 00:41:45.560 --> 00:41:47.120 align:middle line:90% than ga plus gn. 00:41:47.120 --> 00:41:50.480 align:middle line:84% And that's the reason output grows faster than-- 00:41:50.480 --> 00:41:52.760 align:middle line:84% here, it's growing faster than [INAUDIBLE].. 00:41:52.760 --> 00:41:54.782 align:middle line:90% Here, it's very fast, OK. 00:41:54.782 --> 00:41:56.990 align:middle line:84% This is what we saw in [INAUDIBLE] the rate of growth 00:41:56.990 --> 00:41:59.040 align:middle line:90% of 12% and stuff like that. 00:41:59.040 --> 00:42:01.680 align:middle line:90% We were there moving there. 00:42:01.680 --> 00:42:04.540 align:middle line:84% And but eventually, it sort of peters out. 00:42:04.540 --> 00:42:09.160 align:middle line:84% You end up with a higher level of output per capita per worker, 00:42:09.160 --> 00:42:13.710 align:middle line:84% a higher sort of path, an entire path. 00:42:13.710 --> 00:42:18.750 align:middle line:84% The rate of growth goes back to ga plus gn, 00:42:18.750 --> 00:42:23.260 align:middle line:84% but you get this transitional growth, which is very strong. 00:42:23.260 --> 00:42:26.180 align:middle line:84% And once you're here, once you run out 00:42:26.180 --> 00:42:28.490 align:middle line:84% of the high saving and the catching up growth 00:42:28.490 --> 00:42:32.350 align:middle line:84% and so on, the only way you're going to really change 00:42:32.350 --> 00:42:35.470 align:middle line:84% your rate of growth in a sustained manner is doing what? 00:42:35.470 --> 00:42:39.900 align:middle line:90% 00:42:39.900 --> 00:42:44.220 align:middle line:84% Once you have used the tool of catching up 00:42:44.220 --> 00:42:48.060 align:middle line:84% with the world, of increasing your saving rate sometimes 00:42:48.060 --> 00:42:51.570 align:middle line:84% to levels that incredibly high, you still 00:42:51.570 --> 00:42:53.490 align:middle line:90% want to keep growing very fast. 00:42:53.490 --> 00:42:56.370 align:middle line:84% What is the only option you have according to this model? 00:42:56.370 --> 00:43:06.520 align:middle line:90% 00:43:06.520 --> 00:43:12.340 align:middle line:84% Particularly, let me bring even more realism to the story. 00:43:12.340 --> 00:43:14.890 align:middle line:84% Particularly, if gn is dropping, and you still 00:43:14.890 --> 00:43:16.540 align:middle line:90% want to keep your growth high. 00:43:16.540 --> 00:43:20.110 align:middle line:84% And your gn now, you used the catching up growth. 00:43:20.110 --> 00:43:22.807 align:middle line:84% You used the higher saving rate, which gives you 00:43:22.807 --> 00:43:24.640 align:middle line:84% transitional growth, but it doesn't give you 00:43:24.640 --> 00:43:26.230 align:middle line:84% permanently higher rate of growth. 00:43:26.230 --> 00:43:28.330 align:middle line:84% And on top of that. for reasons you don't control, 00:43:28.330 --> 00:43:30.010 align:middle line:84% population growth is declining, even 00:43:30.010 --> 00:43:33.340 align:middle line:90% turning negative in some cases. 00:43:33.340 --> 00:43:35.560 align:middle line:84% But suppose you still want to keep the rate of growth 00:43:35.560 --> 00:43:36.290 align:middle line:90% very high. 00:43:36.290 --> 00:43:40.145 align:middle line:84% What is the only option you have. 00:43:40.145 --> 00:43:42.110 align:middle line:90% AUDIENCE: Increase ga. 00:43:42.110 --> 00:43:42.887 align:middle line:90% Increase ga. 00:43:42.887 --> 00:43:44.970 align:middle line:84% ROBERT CABALLERO: Exactly, technological progress, 00:43:44.970 --> 00:43:46.303 align:middle line:90% that's the only option you have. 00:43:46.303 --> 00:43:47.330 align:middle line:90% So it makes sense. 00:43:47.330 --> 00:43:49.070 align:middle line:84% You see, that in the case of China. 00:43:49.070 --> 00:43:51.570 align:middle line:84% They're obsessed about technology and so on. 00:43:51.570 --> 00:43:53.690 align:middle line:90% They understand the Solow model. 00:43:53.690 --> 00:43:56.960 align:middle line:84% If you want to maintain growth at a high pace, 00:43:56.960 --> 00:44:00.317 align:middle line:84% you're going to need to work on that side a lot. 00:44:00.317 --> 00:44:02.150 align:middle line:84% Now, it doesn't have to be you, necessarily. 00:44:02.150 --> 00:44:05.072 align:middle line:84% It's the world as a whole because technology moves 00:44:05.072 --> 00:44:05.780 align:middle line:90% around the world. 00:44:05.780 --> 00:44:10.880 align:middle line:84% But ga is at the end what puts the limits of what we can do. 00:44:10.880 --> 00:44:14.070 align:middle line:90% 00:44:14.070 --> 00:44:15.960 align:middle line:84% What I was going to do is, that's 00:44:15.960 --> 00:44:18.550 align:middle line:84% what I was drawing this diagram for, is say, 00:44:18.550 --> 00:44:20.790 align:middle line:84% well, suppose that in this situation, 00:44:20.790 --> 00:44:22.260 align:middle line:90% we are in a steady state. 00:44:22.260 --> 00:44:25.860 align:middle line:90% And we do increase ga. 00:44:25.860 --> 00:44:27.360 align:middle line:90% What happens if we increase ga? 00:44:27.360 --> 00:44:32.590 align:middle line:90% Well, this curve rotates up, no. 00:44:32.590 --> 00:44:37.300 align:middle line:84% And at that point, it's clear that if ga grows, 00:44:37.300 --> 00:44:39.660 align:middle line:84% you're going to start growing at the faster rate. 00:44:39.660 --> 00:44:41.430 align:middle line:84% But transitionally, actually, you're 00:44:41.430 --> 00:44:44.245 align:middle line:84% going to grow less than in your long-term rate of growth. 00:44:44.245 --> 00:44:45.120 align:middle line:90% Why is that the case? 00:44:45.120 --> 00:44:48.380 align:middle line:90% 00:44:48.380 --> 00:44:52.630 align:middle line:84% So my claim is, suppose we manage to increase ga. 00:44:52.630 --> 00:45:00.580 align:middle line:84% So now we know that this line here now is a bit steeper. 00:45:00.580 --> 00:45:01.480 align:middle line:90% Or say this. 00:45:01.480 --> 00:45:04.910 align:middle line:84% We were in this line, whatever, we were in this line, 00:45:04.910 --> 00:45:06.380 align:middle line:90% and now we make it steeper. 00:45:06.380 --> 00:45:08.770 align:middle line:84% So we want to start growing faster, eventually, 00:45:08.770 --> 00:45:10.130 align:middle line:90% in the new steady state. 00:45:10.130 --> 00:45:13.090 align:middle line:84% And my claim now, is that in the transition, 00:45:13.090 --> 00:45:15.940 align:middle line:84% growth is less than the new rate of growth-- 00:45:15.940 --> 00:45:19.240 align:middle line:84% in the new steady state rate of growth. 00:45:19.240 --> 00:45:21.640 align:middle line:84% It's higher than the rate of growth 00:45:21.640 --> 00:45:24.040 align:middle line:84% of the previous steady state, but it's 00:45:24.040 --> 00:45:25.400 align:middle line:90% lower than the long run. 00:45:25.400 --> 00:45:27.460 align:middle line:90% How do I see that? 00:45:27.460 --> 00:45:29.110 align:middle line:90% I need another diagram, I think. 00:45:29.110 --> 00:45:37.520 align:middle line:90% 00:45:37.520 --> 00:45:43.160 align:middle line:84% So let me just put the sy curve here. 00:45:43.160 --> 00:45:46.050 align:middle line:90% 00:45:46.050 --> 00:45:51.470 align:middle line:84% So we're here at this steady state. 00:45:51.470 --> 00:45:54.740 align:middle line:84% If I increase ga, the only thing that 00:45:54.740 --> 00:45:57.200 align:middle line:84% will move here, and remember the output equation is there 00:45:57.200 --> 00:45:59.750 align:middle line:84% but I don't want to put it, the only thing I do, 00:45:59.750 --> 00:46:03.560 align:middle line:90% is I rotate this curve up. 00:46:03.560 --> 00:46:05.480 align:middle line:90% OK, so this moves up. 00:46:05.480 --> 00:46:08.030 align:middle line:90% 00:46:08.030 --> 00:46:09.590 align:middle line:90% Do you see? 00:46:09.590 --> 00:46:10.220 align:middle line:90% Yes. 00:46:10.220 --> 00:46:14.670 align:middle line:84% So this curves moves up when ga goes up. 00:46:14.670 --> 00:46:17.540 align:middle line:84% So at the old steady state, what I have now 00:46:17.540 --> 00:46:21.110 align:middle line:84% is a gap between the savings, this economy in investment, 00:46:21.110 --> 00:46:24.740 align:middle line:84% and how much I need in order to maintain capital 00:46:24.740 --> 00:46:27.740 align:middle line:84% per effective worker constant, which 00:46:27.740 --> 00:46:31.640 align:middle line:84% means that I'm going to start moving in this direction, 00:46:31.640 --> 00:46:35.510 align:middle line:84% until I reach the new steady state. 00:46:35.510 --> 00:46:39.870 align:middle line:84% OK, during this transition, I'm growing at a lower pace 00:46:39.870 --> 00:46:41.490 align:middle line:90% than in the new steady state. 00:46:41.490 --> 00:46:47.255 align:middle line:84% In this new steady state, I'll be growing at a much 00:46:47.255 --> 00:46:48.630 align:middle line:84% faster than in this steady state. 00:46:48.630 --> 00:46:49.420 align:middle line:90% How much faster? 00:46:49.420 --> 00:46:51.840 align:middle line:90% Well, equal to delta ga. 00:46:51.840 --> 00:46:54.240 align:middle line:84% But in the transition, I will grow faster than that 00:46:54.240 --> 00:46:56.640 align:middle line:84% but not as fast as in the new steady state. 00:46:56.640 --> 00:46:57.930 align:middle line:90% That's the claim I was making. 00:46:57.930 --> 00:47:08.540 align:middle line:90% 00:47:08.540 --> 00:47:09.560 align:middle line:90% OK, good. 00:47:09.560 --> 00:47:16.900 align:middle line:90% 00:47:16.900 --> 00:47:19.457 align:middle line:84% You know, I'd rather discuss this with more time. 00:47:19.457 --> 00:47:21.415 align:middle line:84% So questions about what we have done up to now? 00:47:21.415 --> 00:47:31.170 align:middle line:90% 00:47:31.170 --> 00:47:34.380 align:middle line:84% Is it clear, or is it very unclear? 00:47:34.380 --> 00:47:35.295 align:middle line:90% Probably both. 00:47:35.295 --> 00:47:39.070 align:middle line:90% 00:47:39.070 --> 00:47:43.690 align:middle line:84% So let me keep this for the next lecture 00:47:43.690 --> 00:47:47.880 align:middle line:84% because might take a little time to explain, OK. 00:47:47.880 --> 00:48:00.000 align:middle line:90%