Productivity and the Per-Worker Production Function - Online Tutor, Practice Problems & Exam Prep

Productivity is defined as the goods and services produced per unit of labor, influenced by physical capital, human capital, and technology. The per worker production function illustrates the relationship between physical capital per worker and output, highlighting diminishing returns to capital. Developing countries can experience faster growth, known as the catch-up effect, due to lower initial capital levels. Technological advancements can shift the production function outward, enhancing productivity without increasing capital. Sustained economic growth relies on continuous innovation and improvements in technology.

Determining Productivity

Alright. Now let's move our discussion over to productivity and the per worker production function. It'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 when 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. Right? 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 thousand t-shirts, right? They're 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 up each person presses the button and watches the machine produce a thousand t-shirts, well, that's gonna 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 going to make them more productive. However, the oven was produced by another company that creates ovens, right? There was an 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, productivity more and more, right? So 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 twofold 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, right? 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 gonna be more productive, right? If you have 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, well 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 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, productivity, right? By putting some of our resources today into growing our human capital into making people smarter, well, they're not going to 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 gonna see is this is well technology, right? This is the processes that we use to turn the inputs into the output. So you know, maybe we have some machine that was making T-shirts a hundred years ago compared to a machine that's making T-shirts now. We would assume that technology has grown and the T-shirts can be made quicker than they were able to be made a hundred 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 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. It's 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 gotta start from scratch or something, the burning of the Library of Alexandria, something like that, 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? 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 available because we're developed country than 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 its play 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 going to show us the relationship between that physical capital and the output per hour worked. Okay? Notice 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, it leads to more output, right? And that makes sense, right? If there's more factories, there are more tools available; well, we're going to be more productive and be able to make more output per worker, right? So our per worker production function is showing us that as we have more capital available, we're able to create more output. However, notice how 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 first bullet point. The function shows us that there are diminishing returns to capital. So there are diminishing returns to capital, and 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, this is where our level of capital is in our society, and we get that much output. Well, let's do 2 tests here. Let's say, 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 going to add, let's say, one more level of capital. We're going to add one more unit of capital here and 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 1 and Red 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 add 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. Whereas in the Red economy, they had a hammer, a screwdriver, a drill. And now you threw them just like a wrench as well. And they already could've done it 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 going to get less out of a little more.

So how does this 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 going to have less capital per worker available. So there's what we call the catch-up effect. By investing in 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 country is going to 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 poorer countries will grow faster than richer countries where we say poor, right, this would be the developing countries are going to 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 the catch-up effect of the per worker production function, right? So remember, catch-up is where poor countries can grow faster than rich countries because of the diminishing returns to physical capital. Investments in a poor country are going to 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? We see that for the most part, yes, it does occur. It does for the most part occur, but obviously, there are going to be outliers, some things, there are kinks that get thrown into the mix, but we've been tracking GDP growth for a long time and we've seen that since 1960. There have been countries with slower economic growth although they still are growing at 2% to 3% which is what we would expect from a developed country. We observed this kind of growth in countries like the United States, Switzerland, and Australia. Countries that are technically considered developed. So these are countries that start out rich 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 a developed country. It's just another term, 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, 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 advancements in society that is what spawns economic growth in developed countries because, for the most part, all of their industries are grown, right? They've got big industries 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% to 3%. Whereas we notice that, in what we're saying is, higher economic growth, so countries with higher economic growth, it's only 4% to 6%. It doesn't sound like that much more, but on a grand scale, 4% to 6% growth 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. This is what we would expect more from a developing country. A developing country would have this higher economic growth of about 4 to 6% and this is growth in GDP that we're talking about. 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 in the economic sense, and this has been since 1960, so those countries have all had a lot of growth over those years and they've become big-time competitors in the worldwide economic scene, right? Another term just like we had leader countries for developed countries, well, 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 never know. So it's just good to know that there are 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 develop the Internet. Well then, in the follower countries, they can just adopt the new technology and there was actually it's actually been seen in Africa where the U.S. Has had telephones for you know over 100 years and they've 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 U.S. to be able to have these landlines in everyone's house. However, there are 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 US, right? So they're able to adopt the new technologies and sometimes forego, 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 Niger 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 are 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, the economy. Okay? So let's pause real quick and then we're going to 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 outward. So, it can push it outward. 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 the 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 here 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 something like an oven, maybe you made a more productive oven. It's still just an oven, it's more productive now, right? Per bit 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, we're able to have more output after. Right? I'll put h for high and I'll put instead of b, I'll put l for low. I'll put 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 going to 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, 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.

Here’s what students ask on this topic:

What is productivity in economics and what factors influence it?

Productivity in economics refers to the amount of goods and services produced per unit of labor. It is influenced by three main factors: physical capital, human capital, and technology. Physical capital includes tools, machinery, and structures that aid in production. Human capital encompasses the knowledge and skills of the labor force, which can be enhanced through education and training. Technology refers to the processes and innovations that improve the efficiency of converting inputs into outputs. Together, these factors determine how productive an economy can be.

What is the per worker production function and how does it relate to productivity?

The per worker production function illustrates the relationship between physical capital per worker and output per worker. It shows how increases in physical capital can lead to higher productivity. Initially, adding more capital results in significant increases in output, but over time, the gains diminish, a concept known as diminishing returns to capital. This function helps explain why developing countries can experience rapid growth when they invest in capital, as they start with lower levels of capital per worker.

What is the catch-up effect in economics?

The catch-up effect in economics refers to the phenomenon where developing countries grow faster than developed countries due to lower initial levels of capital per worker. When developing countries invest in physical capital, they experience larger increases in productivity compared to developed countries, which already have high levels of capital. This effect is driven by diminishing returns to capital, where the first units of capital added have a more significant impact on output than subsequent units.

How does technological advancement affect the per worker production function?

Technological advancement can shift the per worker production function outward, meaning that at the same level of capital, output per worker increases. This occurs because new technology makes existing capital more productive. For example, the introduction of the internet or more efficient machinery can enhance productivity without increasing the amount of capital. Continuous innovation and improvements in technology are crucial for sustaining economic growth, especially in developed countries where diminishing returns to capital are more pronounced.

What are diminishing returns to capital?

Diminishing returns to capital is an economic concept that describes how, as more capital is added, the additional output produced from each new unit of capital decreases. Initially, adding capital significantly boosts productivity, but over time, the incremental gains become smaller. This principle is illustrated by the per worker production function, which shows a steep increase in output with initial capital investments, followed by a flattening curve as more capital is added. This concept explains why developed countries with high levels of capital experience slower growth compared to developing countries.