Economic growth through investment

In the last few videos, we've been talking about the production possibilities frontier as a relatively static thing, something that you couldn't change but you could move along. What I want to do in this video is think about, maybe there are ways to change or expand the production possibilities frontier. And to do that let's assume that our little hunter-gatherer has decided to become a strict carnivore. So he's only focused on rabbits now. And his whole happiness in life is optimizing the number of rabbits he can catch and eat in a given day. And so let's-- on one axis let's draw, let's say the number of rabbits that he can catch in a given day. Let's say it's 1, 2, 3, 4, 5, 6, 7-- I could keep going on and on. So this right over here is rabbits that he can catch in a given day, rabbits in a day. But remember, he wants to optimize this. He wants to think about how he can increase his productivity in terms of the number of rabbits. And he knows-- we'll just assume that he knows how to build rabbit traps. So now we're going to do a production possibilities frontier, not between rabbits and berries, but between rabbits and building rabbit traps, so rabbit traps. So maybe he's able to get twigs together and he builds something. Puts the twigs together in a little thing. It's a little box that-- maybe he puts a little, I don't know some type of carrot down over there. And then if the rabbit comes then takes the carrot then the box falls on the rabbit or something like that. We don't have to go into the particulars of the actual trap. But he can also spends his time building rabbit traps. So let's say, 1 rabbit trap, 2 rabbit traps, and 3 rabbit traps. And let's say-- we're going to hold all other things equal, ceteris parabus. So we're not worrying about other things. And as we'll see, in most introductory economics class, whenever you do a production possibilities frontier you're only doing it with two dimensions. And so that's why you have a regular curve. You could have one with three dimensions, where you're doing the trade off between three things. But then you would have to have a three dimensional graph, and essentially the production possibilities frontier would be a surface. But let's just focus on this right now. Maybe I'll do a surface in the future, just for fun. So these are the rabbit traps. And let's say the production possibilities frontier between rabbit traps and rabbits look something like this. He could spend all his time making rabbit traps, but in that case he won't get any rabbits and he'll probably starve. And that wouldn't be a good scenario. Or he could spend all of this time hunting for rabbits and he would catch, on average, 5 rabbits per day. But that would leave him no time to make rabbit traps. So this is our current production possibilities-- let me just draw it. This is our current production possibilities frontier. So I'll call this p, production possibilities frontier. And I'll put a little 0 subscript there. That's our starting point. So he can he can sit anywhere over here, and he would have achieved productive efficiency anywhere on this curve. But as we saw, if he just spent all of his time doing this over here, he'll never get any rabbit traps. And so he won't be able to change the productive possibility frontier. But what happens if instead he decides that he does want to build some rabbit traps? So he decreases the number of rabbits a day to 4 and that allows him to make 1 rabbit trap per day. So he wants to hang out in this scenario. So every day that goes by, on average, he's going to make 4 rabbits. And he's going to build a rabbit trap. So what's going to happen? So as we go into, maybe into the next period, he would now have a rabbit trap after just one day that he can use to help catch rabbits. So that will actually change the production possibilities frontier. So if he makes this investment, it will actually allow him, in a given amount of time, to actually catch more rabbits. So if he does that, the production possibilities frontier-- having a rabbit trap won't make him that much, won't allow him to make more rabbit traps in a day. So the most rabbit traps he can make in a day is still going to be 3. But maybe now he can catch 6 rabbits a day. So now it might look something like that. So now he could either stop making rabbit traps, and catch 6 a day just with that 1 rabbit trap he has, or he could continue that. And now actually he can catch 5 rabbits a day and still make 1 rabbit trap a day. And maybe he decides to do that. But it could be anywhere along this production possibilities frontier. Or he could say, hey, I'm happy eating the 4 rabbits a day. I'm going to make 2 rabbit traps now every day. And now after another period he gets even more productive. And so then the production-- so let me call this one, this is after one day. Production possibilities frontier after one day, and then after two days, let's say he did this scenario right over here. Now he's produce 2 rabbit traps. And obviously, maybe I'm exaggerating how quickly his productivity would grow. But maybe now the new production possibilities frontier looks something like this. He now has 2 rabbit traps. Or he has 2 more rabbit traps, he already had 1. So now he has 3 rabbit traps after two days. And so now if he wanted to devote themselves purely to rabbit trapping he can get 8 rabbits a day. Or he could do some combination in between. And actually this curve, it shouldn't go up at all. I don't want to give you the impression that it went up and then down. It just goes kind of straight and does something like that right over here. So this right over here, I'll call that the production possibilities frontier 2. So what this hunter-gatherer is doing in this scenario right here is, he is making an investment. He is accumulating capital. This right over here, this is capital. He is choosing, instead of to consume all of his resources-- so there's two things he can do. He can either spend all of his time in pure consumption, getting as many rabbits as possible a day and then eating them all, pure consumption. Or he could reduce his consumption and then allocate some of his resources towards and investment. So this right over here, this is an investment. It makes him more productive. This right over here is consumption. There's some base level of consumption he needs to survive. But if he invests, then it increases his overall productive capacity. So if you viewed him as an economy by himself, by investing instead of consuming all of his resources, by investing some of his resources-- and in this case, his resources are his time and his expertise-- by investing some of them he's able to increase his productivity. And if you viewed him as an economy, he's experiencing economic growth. And so there's multiple types of investments. And we'll talk about these in multiple videos. In this case, he is doing capital accumulation. He is building tools that will make him more productive. Another type of investment is essentially technological change, technological improvement, which would actually make his tools even better. So we could maybe draw another production possibilities frontier between making rabbit traps and then doing R&D on inventing new types of rabbit traps. And so he could decide which of those two things he wants to decide between. But what I wanted you to just appreciate in this video is that the production possibilities frontier can change. You can become more productive if you do have investment in R&D or capital accumulation. And in this case, that just happened to be rabbit traps.