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.