Productivity and the Per-Worker Production Function - Video Tutorials & Practice Problems

Determining Productivity

All right now, let's move our discussion over to productivity and the per worker production function, That's a tongue twister, if I've heard one per worker production function. Alright, so let's start here with productivity. Let's go ahead and define it. So, productivity, I'm sure you've heard this word before, you're trying to be really productive studying here for class. Well, it's the goods and services produced from each unit of labor. Okay, So we're thinking about how productive an economy can be. Well, there's a few things that can determine productivity, how productive labor can be. Alright, so there's a few things backing up the labor, so to say that makes it more productive. Let's go ahead and check out a few of these. So the first one is physical capital per worker. So the amount of physical capital, Remember when we define physical capital, this is things like tools, machinery structures, right? So that's the things that help us work. So, if you imagine a factory where people are sewing t shirts by hand, or a factory with a machine where someone just has to press a button and the machine makes a thous t shirts right there going to be more productive when they have more physical capital. Right? So when there's more capital per worker, remember we're thinking this on a per worker basis. So, for each person we have working in the factory, Well, if there's enough, if there's a machine that they press each person presses the button and watches the machine produce 1000 t shirts. Well, that's going to be a lot more productive than just each person sewing one t shirt at a time. Right? So it's physical capital per worker. Now, one thing about physical capital that is unique is that physical capital can be used to create more physical capital. So you can take physical capital to make other physical capital. So, here's an example. A pizza shop uses an oven to create pizzas. Right? So the oven would be the physical capital here. Right? This is physical capital. I'm sure that the workers would have a lot harder time making a pizza if they had to, I don't know, rub two sticks together to make a fire and hold the pizza over. So, if they've got the oven, well, it's gonna make them more productive. However, the oven was produced by another company that creates ovens. Right? There was an oven manufacturing oven manufacturer that used other machinery to create the oven. Right? So they had some sort of big factory where they're creating ovens, Right? So they used other physical capital to create the oven, which is also physical capital. And you can imagine that the tool manufacturer that the tools that were used in the oven factory were made from other capital and so on. Right? So all of these are physical capital. That is making more physical capital, that's increasing productivity. Right? So that's a unique thing about physical capital, is that it can be used to create more physical capital, which in turn increases productivity more and more. Right? So by investing some of our resources into creating more physical capital, it makes other things more productive, right? So it can increase productivity to fold there. So the next one physical capital that can make things more productive. How about human capital? Do you guys remember what human capital means? Well, human capital is just knowledge and skills, right. It's how smart the labor force is. Like how well educated, how technically savvy they are at doing their job. So you can imagine the more education and training that the workforce has, well, they're going to be more productive, right? If you have uh someone in a factory who's, you know, has their master's degree in, say, oven manufacturing or whatever, compared to someone who's just they threw in there to start building ovens while they're not gonna be as productive. Right? So, human capital, although it's not the same as physical capital, you can think of this also being able to um it takes human capital to create more human capital, right? By you need teachers to educate new students to be smart at it. Right? So the teachers have to be smart to educate the students who will then educate the next class. Right? So teachers, libraries, it takes resources to to grow our human capital. Right? So to increase our productivity by increasing human capital, we must first devote resources to human capital. So increasing human capital is an investment in future productivity, right? By putting some of our resources today, into growing our human capital, into making people smarter Well, they're not gonna immediately grow productivity, right? Those smarter people need to get educated and in the future the productivity will grow, right? So there we go. Physical capital and human capital, the more we have per worker, well the more productive they're gonna be the last one here is levels of technology, so levels of technology, what we're going to see is this is, well, technology, right? This is the processes that we use uh to turn the inputs into the output. So, you know, maybe we have some machine that was making t shirts 100 years ago compared to a machine that's making t shirts Now, we would have seen assume that technology has grown and the t shirts can be made quicker than they were able to be made 100 years ago. So, one thing about technology is that it generally only increases, right? We don't kind of see us, you know, going backwards in technology, we only grow from where we have, where we've been, we create new technologies, we innovate and we have more productivity from that. So it leads to increased productivity over time, leading to increased productivity over time. Right? So we never see like a decrease in technology is generally only gonna be an increase, there would have to be some sort of, I don't know, catastrophic event where all the computers lose all the information and we got to start from scratch or something. The burning of the library of alexandria, something like that. Uh To have a decrease in technology. Right? So we're generally only gonna see increases there. So those are the three main things that determine our productivity. We're gonna see that the amount of physical capital available, the amount of human capital available and the level of technology, how much technology is available for the workers. Uh That's what's going to determine how productive workers are going to be in one economy. So you can imagine there's going to be, let's say in the U. S. They might have a lot more physical capital avail because we're a developed country then, you know, maybe the congo or something where they don't have as developed of structures to be as productive. Right? So physical capital, human capital levels of technology. Let's pause here and let's see how productivity and specifically how physical capital has has its play on on productivity in the per worker production function. Let's check that out in the next video

Per-Worker Production Function

Alright. So we've got a tongue twister here. The per worker production function. Let's see how it shows us the relationship between the physical capital per worker and the output per worker. So, it's gonna show us the relationship between that physical capital and the output per hour worked, output per hour worked. Okay. So notice what what the graph looks like. It starts rising sharply as we notice we've got capital down here on the X axis and output. So as we add more and more capital, right? The more capital there is, Well, we see increases in output. Right? So that's a conclusion we can make here. Is that the more the more capital leads to more output? Right? And that makes sense, right? If there's more factories, there's more tools available, Well, we're going to be more productive and be able to make more output per worker. Right? So, our pro worker production function is showing us that as we have more capital available, were able to create more output. However, notice how it it starts steeper, but then it kind of gets shallow, right? It's very steep at the beginning, but then it gets quite shallow over here. So, what does that mean? The function notice right below us. This this first bullet point, the function shows us that there's a diminishing there are diminishing returns to capital. So there's diminishing returns to capital. That's one of the big takeaways from this function. So what does that tell us notice if let's say we're right here on this, this is where our level of capital is in our society and we get that much output. Well, let's do two tests here. Let's say we're gonna we're right there and there's another country right here at this blue dot. Let me do it actually. Let me do it in green. And we're each gonna add, let's say one more level of capital, we're gonna add one more unit of capital here. Let's say it's that much. We'll do one square on the graph. So, notice how much more output. Red gets right, red started here. So this was output one and read only gained this much more, right? A very small gain to their output. A very small gain. It did go up right, We added capital. So it goes up. But what happens if we had that much capital to, let's say, a less developed country that has less capital per worker, if we invest in their capital and add to that? Well, look how much more they're going to get. So we'll add the same amount of capital and look how much more the output goes up. Right? And this is the diminishing returns as you already have a bunch of capital available per worker. Well, adding a little more capital isn't going to make them so much more productive, basically, the first bits of capital add a lot more productivity than adding a little bit of capital once you already have a ton of capital makes sense. So you get more out of it when you have less capital And that makes sense, right? Because there's less capital per worker. Maybe each worker only has a hammer. Right? And now you've given them a hammer and a screwdriver. Where in the red economy me, they had a hammer, a screwdriver, a drill. And now you through them, you know, just like a wrench as well. And they already could have done it with without it, but now they just have a little bit extra so they can produce a little bit extra compared to just doubling the amount of tools they have down below. Cool, Alright, So that's one of the big takeaways, is that there's diminishing returns as you already have a bunch of capital, you're gonna get less out of a little more. So how does this uh turn into a macroeconomic concept? Well, when we think about a developing country versus a developed country, well, in developing countries, there's going to be less capital per worker available. Right? In a developing country, they're gonna have less capital per worker available. So there's what we call the catch up effect by investing into these developing countries where there may be sitting, we could say that the green is a developing country where the red say is a developed country, well, there's a catch up effect, right? By adding the same amount of capital to both countries. Well, the developing countries gonna grow a lot more than the developed country, right? So smaller investments, small investments in developing countries can turn into a big effect. And that's called the catch up effect. That poor countries will grow faster than rich countries. Where we say poor, Right, This would be the developing developing countries are gonna be growing faster than developed countries. Okay, So let's take a quick pause here, now that we're familiar with the per worker production function and what it's showing us here with investments in capital and how they relate to output. Let's pause here and let's talk a little bit more about catch up on the next page.

Catch-up Effect

Alright, so let's continue our discussion here with that catch up effect of the perp worker production function. Right, So remember catch up. That's where um poor countries can grow faster than rich countries because of the diminishing returns to physical capital. So investments in a poor country are gonna end up making a lot more output than an investment in an already rich country. So does catch up actually occur, We've talked about it in theory, does it actually occur? And we see that for the most part, Yes, it does occur, it does for the most part occur, but obviously there's going to be outliers, some things uh there's kinks that get thrown into the mix, but we've been tracking GDP growth uh for a long time and we've seen that since 1960, there's been countries with slower economic growth, although they still are growing 2-3%, we would say is what we would expect from a developed country. We would expect something like 2-3% growth. And that's what we saw from the United States. Switzerland Australia countries that are technically considered developed. So these are countries that start out rich and they can and they didn't grow as much as say some of these developing countries. So another word for developed countries, sometimes we see the term leader countries and that's just the developed country. Uh It's just another term uh interchangeable leader country, developed country. And what they've noticed from these studies is that their growth is dependent on new technology. So for the most part of their growth is going to be pretty stagnant except when new technology changes the market and all sorts of new industries emerge. So with the introduction of the internet, cell phones, right? All sorts of big advance in society. That is what what spawns economic growth in developed countries. Because for the most part, all of their industries are grown right? They they've they've got big industries in all in all segments and then all of a sudden there's a new technology that changes the market, there's all sorts of new jobs available and all sorts of growth happens. So in the leader countries we see growth around averaging 2-3%. Where notice that in what we're saying is higher economic growth. So countries with higher economic growth, it's only 4-6%. It doesn't sound like that much, more. but on a grand scale 4 to 6% growth for for an economy is actually really big. And in other videos we talk about how growth rates work and how basically they compound on each other and 4 to 6% growth compounds actually pretty quickly. So this is what we would expect from, let me do it in a different color. Uh This is what we would expect more from a developing Country, a developing country would have this higher economic growth of about 4-6% and this is growth in GDP that we're talking about. Um so notice what kind of countries have experienced this growth, Taiwan Korea Hong Kong, China all countries that have become a lot more relevant and have grown a lot more uh in the economic sense And this has been since 1960. So those those countries have all had a lot of growth over those years and they've become big time competitors in the worldwide uh economic scene. Right? So another term just like we had leader countries for developed countries, we have what's called follower countries for the developing countries, this is just other terms that are used and that you should just be aware of just in case you see it on a test, they use follower country instead of developing, you know you never know. So it's just good to know that there's different terms there and what we see is that these follower countries why they're called follower countries is because let's say in the USa they developed the internet, well then in the follower countries they can just adopt the new technology and there's actually um it's actually been seen in africa where the U. S. Has had telephones for you know over 100 years and they spent tons of money on infrastructure for landlines because back in the day right everyone had a phone in their house plugged into the wall and they had all this infrastructure throughout the US to be able to have these landlines in everyone's house. However there's countries in africa that just skip that step altogether. They have cell phones now where they don't need all this infrastructure to have lines in everyone's house, everyone just has a cell phone and they don't have all that infrastructure. So you could technically say that they didn't waste their money on that landline infrastructure and they just build some cell phone towers and now they have telephone service just like we have here in the U. S. Right? So they're able to adopt the new technologies and sometimes forego um you know, middle steps that were let's say less productive, right? And it allows them to grow faster from having no phones at all to now everyone having a cell phone, right? That's a big growth factor there. Now there were some countries that didn't fit the model that actually had negative growth, negative growth here. And that was countries like *** and the Democratic Republic of Congo. They both showed an average negative growth rate over the years now, they've been a lot of countries in africa have been, you know, had constant turmoil, There's a lot of corruption in the government, there's a lot of wars, civil wars that happen and a lot of struggles that just don't help the economic factors, right? And we don't see economic growth. So when there's a lot of conflicts in government, well then there's going to be trouble stabilizing and being able to grow uh the economy. Okay, so let's pause real quick and then we're gonna talk about one more thing with the per worker production function, and then we'll move on to a new topic. Alright, let's do that in the next.

Per-Worker Production Function:Change in Technology

So what we're going to see is that new technology can push the per worker production function outwards so it can push it outwards. What does that mean? It means that at the same level of capital, right? We're at the same level of capital. However, all of that capital is now more productive, let's say with that idea of telephones where everyone had a telephone in their house, well now everyone has a telephone in their pocket. Right? So even though it's the same amount of telephones, each telephone has gotten more productive. Right? That's the idea he with technological change is that we have the same amount of capital. But all of that capital has become more productive maybe now because of the internet or because even if it's like something like an oven, maybe you made a more productive oven, it's still just an oven, it's more productive now. Right? Per per pit of capital, it's each more productive. So what does that do? It pushes us from, let's say this Blue was the original production function. Well, this is the new production function. When we have new technology notice at the same level of capital, let's say this level of capital here. X. Where before we would have only had this much output, I'll put b before Well now at that same level of capital, were able to have more output after, right? I'll put H for high and I'll put instead of be I'll put L for low output low. Right? And this is the new technology, even at the same level of capital, it pushes us outward. So what does that tell us to be able to sustain economic growth? We need improvements to technology that's going to sustain our economic growth, especially in developed countries. Because what we talked about are diminishing returns. Just adding more capital isn't gonna necessarily have big effects on our output, especially once you're a developed country. So by constantly innovating and having new technology making your capital more productive. Well, that's how we're going to have a key is it's the key to sustaining that economic growth is to constantly be innovating and improving technology. Cool. Alright. That's about it. That's the only other thing here, with the production function is that it can be pushed outward by making all of the capital more productive. So the capital per worker is also more productive. Cool. Alright. Let's pause here and let's move on to the next video.