Return on capital and economic growth

- [Instructor] One of the core ideas of Capital in the Twenty-First Century is looking at the after-tax return on capital. Return, on, let me write that a little bit neater, return on capital, and comparing that to economic growth with the contention that if the return on capital, if R is greater than G, if R is greater than G, than this is associated with, this right over here would be associated with rising income equality and that more and more income is going to go towards the owners of capital versus labor. And since capital tends to be concentrated and wealth, you could view capital as wealth, and since wealth tends to be concentrated, that'll just make the concentration happen even further, even more inequalities in wealth. Now before we get into that, and whether you believe that causality or not, is let's just understand return on capital and how that might compare to economic growth and how that might create returns to income to the owners of capital or income to labor. To think this through, let's just think of a very, very simple economy. Let's say the whole economy is nothing but a gold mine. So let's say this is year one right over here and the whole value of the economy, all the wealth in the economy, so the capital in the economy, let's say that we just value it as 1,000 gold pieces. And obviously, we could go into how is that valued, etc. And that actually does come into the conversation, is are we thinking about the market value of things or are we looking at some things on a more intrinsic basis, but let's just go with this simple analogy right now just to start to get our hands around the idea, our heads around the ideas of return on capital and economic growth and how they might relate to each other. So the capital, let's say it's 1,000 gold pieces. I'll just write gp for short. 1,000 gold pieces. And let's say that in that year, the national income, so it's a gold mine, so it's just producing gold. So, let me do this in green, so national income. And the whole nation is just a big gold mine. National income, let's say we have a national income of 100 gold pieces. 100 gold pieces. And let's say that that's divided between income to labor, you needed people to work on the gold mine, to actually mine things and whatever else, and this 100 gold pieces is going to be split between the owners of the capital, the people who own the land and the tools and whatever else of the gold mine, and the people doing the work, the labor. So let's say that 50 of this, 50 gold pieces goes to labor, so that's the part that goes to labor and let's say that 50 gold pieces goes to the owners of capital. So I'll just say it goes to capital. And let's say maybe there's no taxes in this, we're not going to go into taxes and complicate things just yet. So this is the after tax. So we can now calculate the return on capital. R in year one, R is going to be equal to, well, the owners of capital got 50 gold pieces. They got 50 gold pieces. And the capital that they employed was 1,000 gold pieces, 50 divided by 1,000, this is going to be 5% right over here. Now, let's think about this in the context of economic growth. Let's say we go from year one to year two. So now let's go to year two. And we'll just say for the sake of argument that all of this capital that the owners of the capital got, that they reinvested it back into the gold mine. So now the value of the gold mine, so the capital now in year two, is going to be 1,050 gold pieces. The 1,000 that we started with, we earned another 50, we're reinvesting that back into the capital, maybe we buy some more equipment, some more land, whatever it might be, and so now it's 1,050 gold pieces. And let's say the next year, the national income grows. So, national income, once again, we're saying this is a super-simplified economy, overly simplified, arguably, that's nothing but one big gold mine. And now let's say the national income grew by, let's say it grew by 2%. So the national income is 102, 102 gold pieces. Now, there's a bunch of ways that we could split this, but let's just say for the sake of argument, well, let's just make it clear what we just said, we just said that our growth right over here is 2%. Now the question, and this is one of the central questions of the book, is just because R is greater than G in this situation, is that going to lead to more of the national income going to the owners of capital or is going to go the other way around? Or is the level of inequality going to stay neutral? I encourage you to pause this video right now and try to think about that on your own. Given all of these numbers, come up with different break downs of, say, year two's national income, breaking it down between how much goes to labor and how much goes to capital. And think about, in this situation where r is greater than g, is it always going to lead to more inequality? Well, it actually depends how you break it down this year. So you could definitely have a situation where you have, potentially, growing inequality. So, for example, you could have a situation where still labor gets 50 gold pieces, 50 gold pieces, while capital is getting 52, 52 gold pieces. Now the return on capital is going to be 52 divided by 1,050, 52 divided by 1,050. The amount of income to capital is 52, the value of the capital is 1,050 gold pieces. And so we have a return on capital of four point, almost five percent, but a little bit under five percent. 4.95%, so in this scenario, the return on capital is approximately 4.95%. And we see that, once again, R is greater than G, and inequality seems to be getting a little bit more, the owners of the capital are getting more of the income, a larger percentage. They're getting more than 50%, than they saw before. But you could have things go the other way around. You could have things go the other way around. Maybe labor had a little bit more leverage this year, and they were able to negotiate some wage increases, and so you have 52 gold pieces going to labor and 50 going to capital. Now, what's the return on capital? Well, in this situation, the return on capital is going to be 50, so they're essentially getting the same income, but over a larger investment, over a larger capital base. Over 1,050, which is equal to... So 50 divided by 1,050 gets us to 4.76%. So, approximately 4.76%. Approximately 4.76%. So just in this very, I guess you could say, simplified analysis, you could see just looking superficially at R and comparing it superficially to G from one year to the next doesn't necessarily mean that you're going to have rising income equality. Now, it could be a proxy for it, it could be kind of a very high level way of looking at things, but just in and of itself, if someone told you in a year, hey, R, the return on capital is greater than G, you can't say for sure in that year that has gone by that there has been an increase in inequality. Now, what we will do in the next few videos is dig a little bit deeper in that question and use some spreadsheets to look at some scenarios. Look at scenarios where maybe we hold R constant or R and G constant and see what happens to inequality, or maybe we hold inequality constant and see what R has to trend to. And we'll do that in the next video.