Hi, in this next set of models, we're going to talk about a very specific thing, growth. We're going to talk about economic growth, even more specific, we're going to ask why is it that some countries are rich, and other countries are poor. To put a framework around that, a model around that, we're going to start out looking at an even simpler model a model of exponential growth. So here's a model where you just put money in the bank and we talk about sort of the rate at which it grows and how that accumulates over time. From that base model, we are then going to construct a model with a very primitive economy and show how economies grow. Now, one of the surprising results of that model of economic growth is going to be that there are limits, that without innovation, growth stops. So we will move from that simple model to something called a solo growth model. The solo growth model allows for there to be innovation and shows how innovation has this sort of multiplier effect on our collective well-being and why innovation is so important. And then we'll talk a little bit about some extensions, in particular we'll talk about once we've got this model how do we use it to think about why some countries. Successful in other countries are, and really what, oh, enables. Growth to continue over time. Okay so to get us started; first we just need some basic definitions. So first, what do I mean by growth, growth of what? Well you could think of growth, of overall human happiness, right? That would be a nice thing to think about, but that's harder to measure in some respects, right? So we're going to focus on the same things economists do, which is GDP. So this is Gross Domestic Product. So this is just the total market value of all the goods and services produced within an economy, okay? And there's data kept up, so if you look here's a whole bunch of countries in the world and their GDPs. So you see Luxemburg at the very top, look down a little ways and you'll see the United States, right at fifteenth and then, you know, we have a per-capita GDP of about 47,000 and further down so when you see Spain and there's very poor countries where GDP is you know measured in single digits in thousand dollars per person. Okay. We wanna know, the like, you know, what causes growth. So here's sort of an interesting graph. Right here's Botswana and Zimbabwe. Now, these countries aren't the same, right. They're both in Africa. But they, Botswana only has about 2,000,000 people, Zimbabwe has about 13,000,000 people. So Zimbabwe's much larger country. But look at GDP, right; you can see that Zimbabwe has pretty much stayed flat. Hasn't gone up from 1966 to 2005. Where in contrast right Botswana has been very successful. So understand what is it that allows one country to succeed and another country to not succeed. And we'll talk about a book by John O Simoglin James Robinson and called why nations fail. Which really focuses on this line here right, like why is it the case that Zimbabwe hasn't been successful. Now if you look at GDP. When you talk about growth it means changes in GDP. Here is the annual change in real GDP since 1930 in United State. When they said real. Notice that economist said real. When the economist said real. What they mean is taking into account inflation. So inflation got up by ten percent and the economy by fifteen percent. You gotta subtract off that ten percent just due to the price is rising. Look at GDP and see if you can notice it. During the war right there are huge increase of GDP. And let me have this nice post war fairly growth is fairly high. You noticed it stays fairly high. So you know. Averages around you know 3-4 percent throughout this whole. Range right. You see occasional dips, but basically, you see fairly you know, steady concentrates of growth. But if you look from 2006 to 2011 right, when we had this contraction, you see this period here where growth fell. We had massive decreases in growth and those are you know, people really feel that right, because they're much worse off. Now another way we look at growth, you can ask, sort of, can you sustain super high levels of growth? So if you look at China, you see these sort of unbelievable levels of growth, right? These things are all in the 8-9 percent range over the last few decades. Over the last decade and a half, 'cause what you can think is, oh my God, is China gonna become 50 times the size of the United States? When I was a kid, people said the same thing about Japan. And if you look at Japan's growth rates, what we see is, again, from 1950 to, you know the early 1980's, you see these huge growth rates. But then, if you notice since then, right, the growth rates have fallen. So. One of the things this very simple model will do is explain why that is the case. Why you can sustain really high growth rates for a long time and then have them fall off when you sort of catch up to the other countries in the world. Which is why when you look at China even though you see these high growth rates now, a lot of people expect those to fall in the future. We are going to start out by looking at exponential growth. This is where you put money in the bank and it just grows and grows and grows, up, up, up, up, up. Like this, right. When we look at economic growth it tends to not look Way. Over time growth tends to fall off. And that's because we put money into things like machinery and technologies but those depreciate over time and that prevents us from getting that upward sloping curve. And so Economic growth is often going to sort of go the other way it?s going to start out fast and then tail off sort of like it did in Japan unless we can get some innovation, and that will shift the whole curve up and I'll show you what I mean in a minute. One last thing before we get started. When you think about growth, right that's focusing on material things material wants and you can ask yourself okay, does this really matter shouldn't we be more interested in whether people are happy. And we probably should be. Right? It's probably more important that we're happy than we have a lot of stuff. We could all trade stuff for happiness. There's a question. Right? Does GDP, does higher growth make us happier? Well, that's actually a fairly complicated question. So, here's a graph that shows GDP per capita. And then here's a measure of life satisfaction. There's a survey data of life satisfaction. There's a. Notice the problem here. Gdp is what we can think of as really hard, 'cause we can measure it. Life satisfaction is sort of soft, because you're surveying people. And so, yes, in one day I can say my life is great. If you ask me another day, and I might say, oh, my life isn't that great. So you've gotta survey a lot of people. You've gotta make sure you've framed the question the right way. Still, with all those caveats, here's what you see. Does money make you happier? And I wanna focus on two different parts of this graph. If you look in this region. The answer is no. As you go from 20,000 to 60,000 people just don't get much happier. But if you look in this region. [sound] The answer's decidedly yes. Money does make you happier. Now the reason for this may be just some basic services, like health care, food, shelter. Those sorts of things. So getting from zero to 10,000, that's huge. Getting from 30,000 to 60,000 maybe that doesn't matter that much. So lifting people out of poverty clearly makes them happier. That's one reason to focus on GDP. Now, once you?re making $100,000 [laugh] a year, it may not make you any happier to make $120,000 a year. What we give. Does growth make you happy at least according to the survey data? Yes, if you?re lifting poor people up. No, if you?re making rich people richer. Okay. So that's the framework for what we're gonna do. We're going to start out by talking about exponential growth and then we're gonna move on to economic growth models and we'll do three with a simple economic growth model, we'll do something called Solow's growth model, and then I'll talk just a tiny bit about something called endogenous growth models. All right. Let's get started. Thank you.