Growth

00:01 Welcome back to your online presentation of macroeconomics.

00:05 My name is James DeNicco and this presentation will be talking about growth.

00:09 When I talk about macroeconomics, there's not too many topics that are more important than growth. So let's get into it.

00:17 What are we going to be learning here? Well, what questions are we trying to answer about growth? First, what are the sources of economic growth? What policies can increase economic growth, and why are there such large differences in living standards around the world? That's what growth is about.

00:34 Growth is about evolving standards of living.

00:38 So how does a nation's growth rate evolve over time? What is the relationship between a nation standard of living, their population growth, their savings rate and technology? Those are the factors.

00:50 Those are the variables we're going to concentrate on.

00:53 So we'll poor countries catch up to rich countries or will the disparity widen over time? That's what we're going to focus on as well, something called the convergence literature.

01:05 The answer is it depends.

01:06 It depends on the country.

01:08 If their character characteristics are similar to those richer countries, they're most likely going to catch up.

01:13 If not, those disparities could widened over time.

01:17 So why do we care about growth? Well, like I said, we care because it's about evolving standards of living over time. If you take a look at these pictures here, it's very poignant.

01:28 We're trying to take children who live like this here and evolve their countries so that they can have better lives, they can be happier children like this. Nobody wants to see children starving.

01:38 Nobody wants to see children deprived.

01:40 We want to afford our children every opportunity to be able to fulfill their aspirations and their life dreams.

01:46 That sounds touchy feely, but that's what growth is about.

01:50 It's about giving people opportunity.

01:52 That's why so many people concentrate on it.

01:54 That's why so many people care about it.

01:56 It is one of the main focuses of macroeconomics trying to make people's lives better.

02:02 Trying to evolve these standards of living.

02:04 Trying to have children not look like this.

02:07 Trying to have children look happy like this, to give people a chance.

02:11 That's what growth is.

02:12 That's what growth is to me.

02:14 So you see, I get excited when I talk about it because I think it's an important topic.

02:18 So what are the different factors that it can allow us to increase countries standards of living, allow them to evolve their standards of living over time? Well, standards of living in production go hand in hand.

02:30 So how can we increase the income per person, which is our measure of standard of living. Our standard of living measures, GDP per capita.

02:38 So we take the wealth or income in an economy and we divide it by the number of people. And that's our average income per person.

02:46 That's our measure of our standard of living.

02:49 We're also it's also a measure of productivity.

02:51 How productive is an economy? The more productive an economy is the higher standard of living they're going to have.

02:57 So we're going to talk about some of these factors of growth and productivity.

03:01 The first one is physical capital.

03:04 So physical capital is a tangible asset used by firms in production. It includes a number of things our factories, our machines, our tools, our equipment, our computers, all these things we can use to make our workers more productive.

03:20 So you take a guy and you tell them you want them to go outside and break up a slab of concrete. Well, if he's using his hands, it's going to be a hard job, right? If you give him a sledge hammer, he's going to be able to do it.

03:33 It'll be more productive.

03:34 He'll be able to break up that concrete.

03:37 Now let's give him a jackhammer.

03:39 Let's give him some better physical capital.

03:41 Now that jackhammer, he's going to be much more productive in breaking up that slab of concrete.

03:47 We become better and more efficient at our jobs where we're given the proper tools and equipment or we're given physical capital to accomplish those jobs.

03:57 So that's our first factor in growth and evolving standards of living.

04:02 We also have human capital.

04:04 So human capital encompasses our education, our health and our training. So how healthy and how skilled are our workers? The more skilled a worker in he is, the more productive he is, the better he is at his job. So the more skilled worker he can earn more income, right? You can earn more overall income, which increases that GDP per capita and raises those standards of living.

04:28 We have more productive workers when they're skilled as well.

04:33 When they're healthy, the healthier worker, the better they are.

04:36 Everybody's been sick out there.

04:38 When you try to do a task, when you're sick, you find it's much harder.

04:42 So this plays into health care policy and the health of a nation. How healthy are the workers? How healthy is the workforce? In most of our developed countries, that's not as big of a deal.

04:53 But in a lot of our underdeveloped country countries where diseases like AIDS run rampant, it's hard to have a productive workforce with a high standard of living when people are worried about their health and they can't get healthy to even go to work.

05:07 So our human capitalists are second factor of growth.

05:11 So our next one are our natural resources.

05:13 That's another factor of growth.

05:16 So the more natural resources an economy has, the higher the standard of living can be, the higher the income per person can be.

05:24 Now, that's one a lot of countries can control the natural resources that they have, the coal in the ground or the oil in the ground or the land that they have for grazing or open waterways.

05:35 So they have access to to clean and open water.

05:39 It's hard to control whether you have these things.

05:42 You can control the policies of whether you access them or not, but you can't really control whether you have these natural resources.

05:49 But if you do, if you're a country that is lucky enough to have them, it can increase your income per person and increase the standards of living and increase your productivity. Our next factor of growth is entrepreneurship.

06:02 So the people that are willing to take the financial risk for the financial reward of profit, these are innovators.

06:09 These are people that go out there and they work and they become productive for that financial reward.

06:15 Do you have those entrepreneurs out there? Your social and legal framework, that's another factor.

06:21 So is your government and your society set up to incentivize this entrepreneurship? Does it foster entrepreneurship? Does it foster productivity? Are the rules in place to allow standards of living to increase over time? And lastly, our most important one, technology we'll see out of a star of the technology.

06:42 That's because it is the most important.

06:45 Over time, that's our best way to increase our standards of living.

06:49 It touches all of our other factors.

06:52 So when you think about physical capital, technology can make our physical capital better. You go from the sledgehammer to the jackhammer.

07:00 Our technology increases.

07:01 We become more productive.

07:03 You think about human capital, our education with the advent of the Internet and computers and all the technology that we have.

07:11 Sharing knowledge is so much easier.

07:13 We're doing this online course in the seventies.

07:17 This online course will be very difficult to do.

07:19 But now we have these capabilities so that we can share our knowledge and become more skilled. When you think about your natural resources, we have concerns about environmental degradation when we go when we access those natural resources.

07:33 But with technology, we can access them cleaner and we can access them better and we can use them more efficiently.

07:39 Used to only be able to drill one way down.

07:42 Now you drill for oil.

07:43 They can drill down over, up, around and curlicues, whatever they want.

07:47 It's amazing the technology that exists out there to access these natural resources.

07:52 Entrepreneurship, technology effects.

07:55 Entrepreneurship. You can start a business online now, so it's easier to be an entrepreneur. So technology, it just it touches all these different factors of growth.

08:05 So that's the wild card.

08:07 That's the most important one.

08:08 And that's what will give you long lasting increases in our standards of living or long lasting economic growth.

08:15 So let's get to our model.

08:17 So to model economic growth, we're going to be using what's called the solo growth model. Some people call it the neo classical model.

08:25 So this is the base model for a lot of the literature.

08:29 I'd say the large percent of literature out there right now that focuses on economic growth. It was developed by a man named Solow.

08:37 That was his last name.

08:38 So he gets credit for the model, of course, the solo growth model.

08:42 So first, we're going to define our terms.

08:44 We're going to give a functional form.

08:46 We're going to give an equation for our standard of living to see how we can increase our standards of living over time.

08:53 So here we're going to have a lowercase y equals a times or lowercase k raised to the alpha.

09:00 So let's go through these terms first.

09:03 Why that's GDP per capita.

09:06 So as GDP divided by the number of people, if you remember, GDP was our production, it was also our income, it's also our expenditures.

09:16 So GDP is overall income in economy.

09:19 Gdp per capita is the average income per person.

09:23 That's going to be our measure of our standard of living.

09:26 What does it depend on? It depends on this uppercase, A, which we call total factor productivity.

09:33 So total factor productivity, the main driver of it is technology, but it's also going to include entrepreneurship, social and legal framework, natural resources, human capital.

09:45 You can look all that into there.

09:47 It's whatever isn't captured by our lowercase K here.

09:51 Our lowercase k is going to be our capital per person or our capital to labor ratio.

09:58 Here. We're going to assume, for simplicity's sake that everybody in the economy works.

10:04 So our GDP per capita is also our labor productivity, GDP divided by the number of workers.

10:11 What's our income per person? What's our productivity per worker? It's the same thing in this model because we assume that the population equals the workforce.

10:22 Everybody's working.

10:24 So our lowercase k now is going to be our capital to labor ratio.

10:28 It's also going to be our capital per person.

10:31 So again, our standard of living, which is measured by our GDP per capita and GDP per worker, is going to be our total factor productivity times, our capital labor ratio or our capital per worker raise to the alpha.

10:46 We'll talk more about this Alpha in a second.

10:49 Alpha is going to be between zero and one.

10:51 It's going to give us the shape of our growth function.

10:55 It's going to allow the shape to have what we call diminishing returns.

11:00 So let's take a look.

11:02 What does this look like? Well, this is our standard graph here.

11:05 So on our vertical axis, we're going to have our our standard of living or our GDP per capita on a horizontal axis.

11:13 We're going to have our capital to labor ratio.

11:15 So obviously, physical capital per worker here, that's the main variable we're looking at. So how does the standard of living and how does GDP per capita, how does productivity increase as the capital to labor ratio increases? What you see here is this curve flattens out.

11:34 That is due to the fact that Alpha is between zero and one.

11:38 It's what we call diminishing returns.

11:42 So holding all else, constant holding our labor force constant as we increase physical capital.

11:49 How much more productive does our economy become? We assume these diminishing returns, which are empirically a valid assumption, we see that out there in the empirics, we assume these diminishing returns which drive a lot of our results.

12:06 So what do diminishing returns do? What you're going to see is as we increase the capital per worker, we're always going to have an increase in productivity.

12:16 But the size of the increases is going to get smaller and smaller and smaller.

12:22 Those are the diminishing returns.

12:25 We're going to have increases in productivity, but the size of the increases gets smaller. If you take a look here, we have this first increase in our unit of capital up to this line right here.

12:36 So if you take a look at the vertical axis, you see this large increase in productivity with that first unit.

12:45 But because that shape, that curve flattens out.

12:49 The second increase, the second unit of capital is going to increase production, but by a much lesser amount.

12:57 We see here with the with the label of second unit, this size increase is much smaller than the first increase that's due to that flattening out or those diminishing returns.

13:09 So what's the intuition behind that? So you take a farmer and he has to till his field by land.

13:16 Just one farmer.

13:17 We're going to hold that constant.

13:18 He's doing all the work by hand.

13:20 You give that farmer one tractor.

13:23 How much more productive is.

13:25 Is he now? He goes from using his hands the till of the land to do all the work he needs to do to now he has a tractor.

13:31 It takes him way less time to do.

13:33 His work is leaps and bounds.

13:35 Are the increases in productivity with that first tractor? Now remember, we're going to hold the number of workers constant here so that capital per person is increasing because we're concentrating on the capital ratio.

13:49 So now the farmer goes and gets himself a second tractor.

13:53 He's only going to use that tractor when the first one is down.

13:57 It's in the shop, or maybe it needs to refuel or something.

14:00 When he can't use the first one, he will use the second one.

14:04 So he's obviously more productive.

14:05 There's no downtime.

14:07 You always has a tractor to do his work, but most of the time that tractor, that second one is sitting there idle.

14:14 So the increase in production isn't as much as the first one.

14:17 The first one, he went from nothing to a tractor.

14:20 The product, the productivity increases were huge.

14:22 The second one, the productivity increases are much more modest because most of the time the second tractor is sitting there idle.

14:30 It's not being used.

14:31 He only uses it in times when the first one is down, when the first one is in the shop so that he is more productive.

14:38 He can always work now, but the increases in production gets smaller and smaller and smaller. That's the intuition behind diminishing returns.

14:46 So we assume these diminishing returns in our solo growth model.

14:51 So if increases in the capital labor ratio are important, we should talk about how we increase the capital to labor ratio.

15:00 Well, we increase it through investment.

15:03 So we're all in per capita terms here.

15:05 So when I say investment, we're in the lower case, it's investment per person.

15:09 So as we know from our GDP lecture, part of investment is purchasing physical capital.

15:15 So we purchase physical capital through investment.

15:19 So as we increase our investment, we increase our physical capital per worker. How does the physical capital per worker decrease over time? It's through what we call effective depreciation.

15:32 So here we're going to have our endless Delta Times K.

15:36 So that is the decrease in the capital to labor ratio through the population growth rate and and the depreciation rate delta. So why do we need both the population growth rate and the depreciation rate? Well, we're in per person terms.

15:54 So as the population growth rate rises, capital per person is going to be diminished.

16:00 It's going to go down.

16:03 We need the depreciation rate because we're dealing with physical capital.

16:06 That capital you can think of is wearing away over time.

16:09 The equipment is going to wear down over time as you use it.

16:13 So there's going to be a depreciation or wear down rate on that physical capital as you use it.

16:20 So we're going to have increases in physical capital with investment.

16:24 We're going to have the decreases in physical capital per person, all in per capita terms with effective depreciation.

16:32 So what is our investment? Our investment we're going to define as our savings rate times GDP per capita.

16:42 We're going to assume that investment equals savings here.

16:45 We're going to close the economy and we'll talk about this more in our later series.

16:50 But here we assume savings equals investment.

16:52 So every dollar you put in the bank, a firm or a business is going to borrow that money and they're going to buy physical capital with it.

17:00 So the savings rate times our income, a percentage of our income we're going to save and that's going to be used for investment.

17:10 So that's why we have this little s are the savings rate times our income per person. Now we can take that a step further.

17:18 We know our income per person is our total factor.

17:22 Productivity times, our capital labor ratio raise to the alpha, right? If we went back a few slides, we would see that that's what we define GDP per capita.

17:33 So these are the same equations.

17:36 I'm just elaborating on an equation one investment minus effective depreciation. In equation two, investment is just the savings rate, times the income per person.

17:47 So the amount of savings per person, that is our investment.

17:51 And now I just replace the income per person with the equation that we defined it as total factor productivity times the capital ratio raised to the alpha. This is how our capital labor ratio changes over time. We can put this on a graph.

18:09 Sometimes seeing it makes it make more sense.

18:12 So let's do that.

18:13 Let's go to the solo growth model.

18:16 So here's your basic solo growth model we already saw before our GDP per capita. It increases with those diminishing returns.

18:26 What does our investment line look like? What does our investment curve look like? It looks just like our GDP per capita curve is just smaller because it's the same curve, but it's just a percentage of that curve.

18:38 It's the savings rate, times that GDP per capita.

18:42 So it's just smaller.

18:45 Our effective depreciation rate that has a linear curve that increases linear linearly.

18:52 So the fact that we have these diminishing returns in growth and investment, but a linear increase in effective depreciation is going to drive the results of this model.

19:04 It's going to allow us to come to what we call our steady state.

19:08 Our steady state is always going to be where our effective depreciation curve intersects our investment curve.

19:16 So let's talk a little bit more about that.

19:19 First, what we see here is we're going to see y minus i equals c.

19:22 So what we're saying is there's no government spending in this model.

19:25 We're going to assume that away as well.

19:28 So all we're going to have here is investment and consumption.

19:31 So before GDP, where we had GDP equals consumption plus investment plus government spending plus net exports, we're going to assume away government spending in net exports per.

19:43 Now, you can put those back in later if you want to make it more complicated.

19:47 But for simplicity's sake, to understand the basic intuition and the model, we're going to assume those away.

19:53 So we're going to see part of our GDP per capita is our savings or our investment. The rest of it is going to be our consumption.

20:01 So again, we have our GDP per capita line here equals total factor productivity times the capital labor ratio.

20:09 That's how the standard of living evolves over time.

20:12 So how does the capital labor ratio evolve over time? It evolves with investment, which also has a diminishing return, and investment in turn depends on income per person.

20:24 So we use a bit of our income per person.

20:26 We save it. When we save it, we invest them by more physical capital.

20:30 We buy more physical capital, we become more productive.

20:33 We increase our income per person as our income per person increases.

20:37 We can save a bit of that.

20:39 We can invest more and buy more physical capital.

20:41 It's a cycle that goes on and on as you move to the right on the graph.

20:46 And it happens up until the point where effective depreciation intersects with investment per capita.

20:54 There's our steady state.

20:56 We can find our steady state at the intersection.

20:58 This is our steady state capital to labor ratio.

21:01 We draw the line up where that intersection takes place.

21:05 We go over to our horizontal axis.

21:07 That's our investment per capita steady state.

21:10 If we go up to our standard of living steady state, our GDP per capita steady state, our labor productivity, steady state, they're all the same thing.

21:19 We've made it so so that they're all the same.

21:22 We go over to the vertical axis.

21:24 That's our standard of living per capita.

21:27 That's where we get stuck.

21:28 We get stuck at this point.

21:30 What's going on at this steady state? Well, let's take a look to the left of the steady state.

21:35 So remember, our change in capital is our investment per person, minus our effective depreciation.

21:43 So when investment per person is greater than effective depreciation, we're going to be growing.

21:49 We're going to be moving to the right here when this investment curve is greater than effective depreciation, we're going to be growing and moving to the right now if we're to the right of the steady state.

22:02 And again, the change in the capital ratio equals investment minus effective depreciation.

22:09 If this effective depreciation curve is greater than investment, we're going to be moving back to the left.

22:16 So intuitively, what's going on here? Well, let's start over here where we're the capital labor ratio is lower than the steady state. So we have a certain income per person.

22:26 We use a percentage of that income per person for investment.

22:30 We buy more physical capital, we add more physical capital.

22:34 We become more productive.

22:36 We're more productive.

22:37 We have more income per person.

22:39 We have more income.

22:40 We can invest more.

22:41 We can buy more physical capital.

22:43 We have more physical capital become more productive.

22:46 We have more income.

22:47 We can invest more, we can buy more physical capital.

22:49 It goes in a cycle.

22:51 So we keep moving to the right towards that steady state.

22:56 However, because of diminishing returns, the increases in productivity, the increases in income per person, the increases in investment per person are getting smaller and smaller and smaller, so that by the time we hit our steady state, the increase in capital which increases income per person, is just enough to buy capital to replace what's depreciated away.

23:23 We have just enough money.

23:25 We're making just enough money to replace our worn down or used our equipment, our factories, our machines and our tools.

23:34 We have just enough money to keep up with what we have at that steady state. We can't break that steady state unless there's a change in one of the variables that dictate our GDP per capita.

23:48 Where our investment per capita.

23:50 Things like total factor productivity or the savings rate.

23:54 That's how we can break that steady state and move further to the right.

23:59 You'll notice it's steady state.

24:01 If you look back at the equation, what we're saying there is the capital to labor ratio is zero for the changes in the capital labor ratio or zero because investment equals effective depreciation.

24:14 Again, the change in the capital labor ratio equals investment minus effective depreciation.

24:20 You look at these this graph right here, that's where these two curves intersect.

24:25 That means investment and effective depreciation are the same.

24:29 So the change in the capital labor ratio is zero.

24:32 We get stuck at this steady state.

24:35 So that's what the steady state is all about.

24:38 Now there's this convergence literature that evolves from the solo growth model.

24:46 So what is the convergence literature? Will poor countries catch up to rich countries? Well, there's two general theories on this.

24:52 One is unconditional convergence.

24:55 So you can read the words, you can read the definition.

24:57 But basically it says poor countries are going to catch up to rich countries no matter what. So if you look in the graph, what does that mean? You'll see a country here, K rich and K poor.

25:09 They're both away from the steady state.

25:11 K poor is further away from the steady state.

25:15 The further away you are from the steady state, the faster you're going to grow towards that steady state.

25:22 You'll see. I drew lines in here that are tangent to the slope of our income per person.

25:29 So if you like calculus, if you take a derivative of that line, that's the growth rate, the slope at that point.

25:36 So I'm drawing in the slope at that point, you'll see for the poor country, the slope is steeper than the slope for the rich country.

25:45 That steeper slope indicates faster growth.

25:48 So the poor country is going to catch up to rich country, to the rich country when they hit their steady state.

25:55 That unconditional convergence says that that is definitely going to happen.

26:00 But what that assumes is that the two countries have the same steady state.

26:04 Unconditional convergence has been shown to be quite false.

26:08 Now, conditional convergence, on the other hand, says that poor countries will catch up the rich countries, if they share similar characteristics, that one bears out much better.

26:20 So if you take a look at all the countries out there and plot GDP per capita versus growth rates, you're not going to see that smaller levels of GDP per capita correlate to higher growth rates because that's what the solo growth model says.

26:37 It says the lower your GDP per capita, the higher your growth rate.

26:42 Now, if you take similar countries or say you take the states within the United States and you plot that on a graph, you will see that.

26:49 You will see that countries with lower GDP per capita have higher growth rates.

26:55 The states with lower GDP per capita are catching up to the states with higher GDP per capita.

27:02 So again, unconditional convergence.

27:05 Poor countries will catch up to rich countries.

27:07 Conditional convergence, poor countries will catch up the rich countries if they share similar characteristics, those similar characteristics being total factor productivity, the savings rate, the population growth rate and the depreciation rate, all those things that decide where the steady state is. So that's our convergence literature.

27:30 So what effects will we have with an increase in the savings rate? Let's now focus on these different factors that decide our steady state.

27:40 Let's focus on these different factors that decide our standard of living.

27:44 We'll focus on the savings rate first here we want to know a few questions about it.

27:49 So what are the short and long run effects on the growth rate with an increase in the savings rate? And then lastly, what are the effects on consumption? Because that's important, because we all want to consume, whether it's for survival or for utility, to make ourselves happy, we like to consume.

28:07 So here we're going to assume that the savings rate goes up.

28:10 We're going to have an S two greater than an S one, a savings rate to greater than savings rate one.

28:18 So what's that going to look like on the graph? Let me show you. An increase in the savings rate is going to shift up. The only line with an S in it is the savings rate goes up.

28:31 You're going to see a higher level of investment per capita at every point along that graph.

28:38 So the savings rate goes up, it shifts that steady state to the right.

28:43 We have more investment per person.

28:45 We have more physical capital.

28:47 So that increases our productivity again.

28:49 So now we have more income again.

28:51 So now we can buy more physical capital and we can continue that cycle for a longer period of time until again, our effective depreciation overwhelms our investment and we get stuck at a new steady state.

29:06 That higher savings rate allows for a higher standard of living.

29:10 So what are the short and long run effects on growth? In the short run, as that steady state moves to the right, you're going to have positive but diminishing growth.

29:21 So again, we're moving along this curve here.

29:23 You jump from here up to here and grow to the right.

29:26 As you grow to the right, you have positive but diminishing growth.

29:30 Again, that's the short run.

29:33 In the long run, you hit your new steady state and the growth rate goes back to zero.

29:40 The effects on consumption with an increase in the savings rate are ambiguous.

29:45 We don't know.

29:46 We know now that our GDP per capita or income per person has gone up because we increase the savings rate so we have more money to buy stuff.

29:56 But at the same time, we're saving a larger percentage of our income.

30:01 So it depends on which one of those factors overwhelm.

30:04 If the increase in income is enough to overwhelm the increase in the savings rate, than consumption will go up.

30:11 If the increase in income isn't enough to overwhelm the fact that you're saving a larger percent of your money, well, then consumption is actually going to go down. So if you have $100 in, it increases the $200.

30:26 Obviously, you can buy more stuff if your savings rates stay the same.

30:30 If your savings rate goes up too much, well, then you're not going to be able to consume as much as you were before.

30:37 So it depends on which one of those factors overwhelm.

30:40 So again, the short and long run effects, with an increase in the savings rate, we're able to buy more physical capital and become more productive.

30:49 Now we can break our steady state and steady state moves to the right.

30:53 We'll grow in the short run with positive but diminishing returns until we hit our new steady state.

30:59 And the long run, we are at a pretty steady state.

31:02 The fact is depreciation has overwhelmed investment per person.

31:07 So now we're stuck at that new steady state.

31:09 The growth rate goes back to zero.

31:12 Consumption is ambiguous.

31:14 It depends on whether the increase in income overwhelms the increase in the savings rate or the increase in the savings rate over well overwhelms the increase in income per person. So that's our savings rate.

31:26 So we see that we can increase our standards of living with an increase in our savings rate. However, it's bounded, you can't save more than 100% of your money.

31:36 So in the long run, increasing the savings rate is probably not the way to go if you want these long run increases in your standard of living.

31:45 It's bounded.

31:46 And on top of that, who wants to save 100% of their money? What's the point of making money if you're going to save all of it? You want to consume some of your money, so you're going to have an unhappy population out there if you're saving 100% of every dollar you make.

32:00 So that brings us to our next factor, total factor productivity.

32:05 Now, let's take a look at this.

32:06 What happens if total factor productivity goes up? We're going to go from a one to a two here with a two being higher than a one. So what's that going to look like on our graph? Well, every line when total factor productivity in it is going to shift up, say it's an increase in technology.

32:26 Right. Where all of a sudden more productive.

32:28 We're more productive.

32:30 So we can increase our income per person as their income per person goes up. We can invest more and buy more physical capital.

32:38 Again, we can break that steady state as we have more income, more capital.

32:42 More capital makes us more productive.

32:45 More productive. We have more income, more income.

32:48 We can buy more physical capital.

32:49 You get back in that cycle of those diminishing returns for a longer period of time. Now you break that steady state and you move to the right.

32:59 So again, in the short run, it's going to be the same effect as the increase in the savings rate. It's going to be positive, but diminishing returns.

33:08 As we move to the right, though, we will hit our steady state at some point further down the road. Now, when we hit that steady state where our effective depreciation overwhelms our investment per capita, we'll get stuck again.

33:21 So our long run, our growth rate will go back to zero.

33:26 So in the short run, positive, but diminishing returns.

33:30 In the long run, our growth rate goes back to zero.

33:34 What are the effects on consumption? Well, they're unambiguously positive.

33:38 We know what's going to happen.

33:40 Consumption per person is going to go up.

33:43 We have more income per person and we're saving the same percentage amount of money.

33:48 So if we have $100 now and we're saving 50%, that means we're consuming $50.

33:55 If it goes up to $200 and we continue to save 50% of our money, now we're consuming $100.

34:02 We went from 50 to 100.

34:04 We know there's going to be an increase in consumption per person with an increase in total factor productivity.

34:11 So if you think back to our factors of growth, we were talking about it, put a little star there on technology.

34:17 Technology is the main driver of total factor productivity.

34:21 Total factor. Productivity is unbounded.

34:24 It's constrained only by the human imagination.

34:27 The human imagination is unbounded.

34:29 It's unconstrained.

34:30 So we could always increase our total factory productivity.

34:34 We can always increase that.

34:36 So we can continually move to the right and drive up our standard of living.

34:41 Total factor productivity and technology are the key to unbounded long term economic growth.

34:50 So we've covered the savings rate.

34:52 We've covered total factor productivity.

34:55 Now let's cover the population growth rate so this can apply to both the population growth rate and the depreciation rate.

35:02 So here we're going to have the population growth rate and to greater than our population growth three and one.

35:09 So what happens is the population growth rate goes up in the solar growth model.

35:14 Well, we're going to see that line bend up from the origin.

35:19 That straight linear line is going to move up to the left.

35:23 What that means is our steady state is going to move to the left as well.

35:28 So we're going to have negative growth to our new steady state until we hit that steady state, that lower steady state, and our growth rate goes back to zero. That's because the capital labor ratio has to go down its capital per person.

35:44 So as the population growth rate goes up, capital per person will come down. Just like if the depreciation rate went up.

35:52 If Delta went up, then you're going to have a decrease in the capital per person and a lower steady state.

35:58 So you'll have negative growth back to the left until you hit your new lower steady state, at which point the growth rate goes back to zero.

36:07 So this might be a flaw in the Slow growth model.

36:10 There's not a definite correlation between population growth rates and growth.

36:14 Sometimes you see it countries that are poorer have higher population growth rates.

36:18 But at the same time, higher population growth rates mean more people, which mean more brains.

36:24 As we know more brains, we can have more innovation and increases in total factor productivity. So that is one question about the Solow growth model.

36:33 All these models aren't perfect, but if they were perfect else, economists would be out of job. So thank goodness they're not perfect so we can continue to develop them.

36:43 So that brings us to the end of this presentation.

36:46 What we've talked about here, we know the sources of economic growth, why it's important to develop and evolve these standards of living for countries over time.

36:56 We know how to construct and graph that solo growth model.

36:59 The Solow growth model is the model we're using here for growth.

37:04 We've learned about diminishing returns and how poor countries can catch up to rich countries. And we learn that total factor productivity is the key to sustained long term economic growth.

37:15 Again, it's unbounded because it's only constrained by the human imagination.

37:19 And the human imagination is unbounded itself.

37:23 Things we're doing today, technologies today, even 20, 30 years ago were unthought of, except by a few brave and innovative entrepreneurs that make things happen. So that's your growth presentation.

37:36 Thank you.