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The aggregate production function and growth

This video discusses how economists measure the total factor productivity, capital, and human capital for an aggregate production function.

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Video transcript

- [Instructor] In a previous video, we have introduced the idea of an aggregate production function. Which is a fancy way or a mathematical model that an economist might use to tie the factors of production in an economy to the actual aggregate output of an economy. The aggregate output is Y. And then the factors of production, we've talked about this before, it's human capital, it's technology, and it is regular capital, or non-human capital. And so A is really representing the technology factor here. And this term is often known as total factor productivity. K is referring to the non-human capital, and of course, capital starts with a C, but they use K for capital. And then L stands for the human capital. You could view it as standing for labor, but it's standing for a little bit more than that and we'll talk about that in a second. And just to make this tangible, because it's written in function notation here which might seem a little bit abstract to just saying hey, some function of K and L, you could imagine an aggregate production function that looks like this, where our aggregate output is equal to our total factor productivity, which is once again, a measure of our technology, times our capital to some power times our human capital to some other power. And in an introductory economics course, you wouldn't actually have to do this type of computation, taking things to fractional exponents, although we have many videos on Khan Academy explaining how to take fractional exponents if you are curious. But this gives you a sense that look, if any one of these inputs goes up, well then you would expect aggregate output to go up. And if, for whatever reason, these were to go down, any one of these to go down, that would have a negative impact on aggregate output. But the focus of this video is really thinking about if you were an economist, how would you actually come up with the values for A, K, and L? Pause this video and think about that. So let's start with L, which sometimes we imagine represents labor, but you really should think of it as human capital. How would you measure human capital? Well, the most obvious thing is you could measure labor. And how would you measure labor? Well, you could go and see well how many people are in the labor force? So measure, measure the labor force. And you might say, well, isn't that all that there is to human capital? But remember, not all labor is equivalent. If people are unhealthy, they're not going to be able to be output as much. If people aren't trained, they're not going to be able to output as much. So it's not just the quantity of people in the labor force, it's also measures of education that would factor into L. So the more educated a labor force, the more trained, L would go up. So higher people in labor force, L goes up. More educated labor force, L goes up. And a healthier labor force, L would go up. They are going to be able to do more. Now, what about K? What about the capital stock of a country? Well, you might be tempted to say well, maybe I could count the amount of capital or something like that. But that wouldn't really make sense because there could be some types of capital that might be some just tools, while you might have another capital that's a big building or a rail car or whatever else. And so the K is actually measured by economists as the value of the capital stock in a country. Write it this way. So the value of capital, capital, in your country. Or in the economy that we care about. Now a really interesting one is how do you measure A? There isn't an obvious index for hey, I can just observe that and say that has more technology than that other thing. And the way that economists often figure out an A for an economy, is by backing into it. They can figure out an L, and they can figure out a K. And they know what the output, they know what the GDP of that country is, the real GDP. And then if different countries have the same K and the same L, but then their GDPs are different, than that means that they have a different A. So the A you could almost view as an adjustment to fill in the gap to connect the dot between the K, L, and the Y. But it would be a measure of how technologically advanced something is. If my economy has an A of one, in order to make the numbers work, and your economy has an A of two, that means for some reason, you're getting twice the productivity given the same capital and human capital as I am, which implies that you have twice the technology.