Aggregate production function and economic growth | APⓇ Macroeconomics | Khan Academy

So we are posed with the question: all else equal, which of the following would likely cause aggregate production to go up? Pause this video and see which of these you think would do that.

All right, now let's work through this together. This first one says more people enter the labor force while the unemployment rate stays constant. Well, labor is an important factor of production, and if more people enter the labor force and the unemployment rate stays the same, that means that the absolute number of people who are working goes up. If everything else stays constant—the level of technology, the capital, the productivity per person—well then, you would expect to be able to produce more. So, aggregate production should go up in this scenario. So I'll put a check right over there.

The second one: velocity of money goes up. This one is tempting because you might associate a high velocity of money with a lot of transactions going on; you might associate that with a very positive economy. But remember, we're saying all else equal. There might be a scenario where people are transacting more—there's more, the money is circulating faster—but the total amount of output hasn't changed at all. There's the same number of people producing the same amount of goods using the same technology in the same capital, and so this does not have a direct linkage to the output going up all else equal. So I'll rule this out.

Inflation goes up. Well, this again is tempting because many times when we are producing at a high rate, when the economy is strong, that's associated with higher inflation. But there's many cases in history where you might even have hyperinflation when the economy is actually even shrinking. Remember, we're saying all else equal. So there's a situation where the price levels and the rate of the price level going up is going up, but we're producing the same amount of goods and services. And so I will rule this out.

A new method of producing more goods with the same resources is developed. Well, just imagine a very simple scenario. If the whole economy consists of me, and I produce pencils. Let's say I can produce 10 pencils a day, but I just have a new method of producing 20 pencils a day with the same resources—with just me and the same access to wood and the same tools. Well, that's going to dramatically increase my aggregate production.

So one way to think about it is this: our level of technology has gone up with this, which is an important factor of production. So I like that one. Ten new farms are constructed. Well, if the farms are constructed, and I will assume that they are used well, we're going to have more output. They're going to grow more things; our level of capital has gone up once again—another important factor of production. So I like that.

Imports go up. Well, imports are us taking advantage of or using someone else's output. It doesn't say what it's going to do to our output, so I will rule that out. And so this is quite intuitive. We've talked about factors of production like labor, capital, and technology. Economists often tie this together, taking these factors of production and showing how they lead to our aggregate output by using something known as the aggregate production function.

The aggregate production function is that our output is equal to A, which you could view as a measure of our technology—it's often known as total factor productivity, another fancy word—times a function of (that's why it's fancy, it's using the function notation) our capital. And I know capital does not start with K in the English language, but K for capital and our labor.

This is all very abstract. If we wanted to make it a little bit more tangible, especially because we just have function notation in here, we could say something like our aggregate output, our aggregate production, is equal to our total factor productivity. Then I'll make up a version of this; let's say times the square root of our capital times the square root of our labor. But in general, as you see in this example, you're going to see aggregate production functions that look something like this.

The radicals or the square roots on capital and labor might be a little bit different, but they tell the same story: that if you increase your level of technology, you're going to increase your aggregate output. If you increase your capital, you're going to increase your aggregate output. And if you increase your labor, you're going to increase your aggregate output.

The reason why you might see square roots or fractional exponents on capital or labor is this idea of diminishing marginal returns: that first farm might really add a lot to your output, but maybe that millionth farm might still add to your output, but maybe at a less level, at a lower level. Same thing; those first 10 people might add a lot of output to your labor, but after you already have 100 million people, the next 10 will still add to your output, but maybe less. At least that's what these mathematical models are saying.

So, big picture, it's pretty intuitive that if you hold everything else equal and if you increase the factors of production, well then, that would likely cause your aggregate production to go up. But economists like to describe things mathematically, and that's what's going on in something like an aggregate production function.

Now, last but not least, a related idea to an aggregate production function is this idea of productivity. Productivity—we already viewed A as total factor productivity, but it's really a measure of the technology in an economy. Typically, when people talk just about regular productivity, they're talking about output per capita, output per person.

So really, what they're doing is they're thinking about aggregate production, so Y, and then they're dividing it by labor. So then they would divide it by labor. So this would be output per person. And so you could imagine if technology improves, holding labor constant, well then your output per person is going to improve. If your capital goes up, which would improve your output holding labor constant, then once again, your productivity would improve per person. You're able to produce more in your economy.