r greater than g but less inequality

One of the core ideas of Thomas Piketty's book is if the return on capital is greater than the growth in economy, then that could drive inequality. Inequality is a natural byproduct of a market capitalist economy, and one could argue that, hey, look, some inequality is going to happen as you grow your economy and you let people be entrepreneurial. Some people get lucky, some people less lucky, some people work harder, some people work less hard, some people are able to allocate capital well, some people aren't. So it all comes into it. But in extreme forms, maybe this is bad, and in particular, maybe this is bad for democracy.

So bad for democracy, right over here, maybe too much power starts to accrue in some ways, and maybe that—and in the worst case, because that kind of starts to drive it in on itself—it actually might even hurt economic growth if you don't have enough consumers or people with enough purchasing power or discretionary income or whatever else. But what I really want to focus on here is not so much whether these causalities are actually there or how much we should worry about them.

Once again, my point isn't to give an opinion on whether I agree or disagree with some or all of the book. It's really just to give you a framework because I think the book at least raises an interesting conversation, and it gives us a lot of—I would say—fodder for interesting analysis and critical thinking. That's really what I want you to walk away with: how do you think about these things? You just need to make your own judgment.

So what I want to do here is at least show a circumstance that this might be. Returns on capital being greater than economic growth can be a reasonable proxy for rising inequality, and of course, we know this connection over here is even kind of a harder thing to necessarily draw. The connection, but even this one isn't always going to be isn't always going to be the case.

To think about that, let's just imagine an economy where the whole economy just produces apples. So let's say the whole economy, right over here, this is our whole, our entire economy. Let me copy and paste it. So copy and paste it, I'm going to paste it to show the growth in the economy.

So let's say in year one, so this is year one right over here. Year one it produced one thousand apples—one thousand apples. And let's say in year two, year two we have economic growth. So let me draw that, so g going from year one to year two. Let's say that this is equal to two percent. So two percent of a thousand would be twenty more apples. So in year two, the economy produces a thousand twenty—one thousand twenty apples right over there.

Now let's say that in year one, in year one of the thousand apples that were produced—let's say that 500 of them, I'll just split in half—let's say 500 of them go to the owners of capital, 500 to the owners of capital. Now what's the owners of capital? What do they own? Once again, it's a very simple economy that only has one industry right over here. But the owners of capital are the people who would own the orchard, who own the trees, who own the machinery, whatever they need to pick the apples. And let's say that the other 500 goes to labor—500 to labor.

And let's say that the value of the capital here—so the value of capital in apples, we're just assuming everything going on here is apples—that I guess to buy this apple orchard, the owner of it had to give, let's say, 4,000 apples—4,000 apples. So given this, what is the return on capital in year one? Well, the return on capital, I'll just write return on capital in year one is going to be, well, the return is 500 apples divided by the cost, or I guess we say the value of the capital.

So divided by 4,000 apples. So that's going to give us 5/40, which is the same thing as 5 divided by 40, which is 1/8. So that's going to be 12.5 percent. So return on capital, at least in year one, is greater than. Well, let's go to year two so we can look at the return on capital in year two and compare it—in compare it to the growth right over here.

And so let's just say that the value that over here—the value of the capital—that all of it was reinvested. So now the value of the capital—value of capital is now 4,000 plus 500 more apples. So 4,500 apples. They reinvested in the business, and they didn't necessarily use the apples as capital, but they use those extra 500 apples to go buy some more machinery or buy some more land, whatever it might be.

And let's say, though, that the laborer had a little bit of leverage this year. So in this year, because labor had leverage, only 500 still goes to the owners of capital. Now this isn't necessarily going to be the case if the owners of the capital have leverage—maybe they could negotiate the other way. But let's say in this situation still 500 goes to labor, 520 would go to labor.

So now what's the return on capital? The return on capital now is going to be still 500 apples divided by 4,500 apples, which is going to be equal to 1/9, which is the same thing as—what is that?—0.1111. Let me just—one divided by 9, you have this 0.11111. So it's going to be approximately 11 percent—or let's say 11.1 percent—approximately 11.1 percent.

Now, the whole reason why I wanted to show that—why I did this diagram—is this is a situation where r is greater than g. Our return on capital is 12.5 percent going to 11.1 percent. Both of these numbers are much larger than our growth of the entire economy. But even though that's happening, you actually don't have rising inequality over here in this situation.

Of course, I worked the numbers to make this happen—I could have worked them the other way—but in this situation, it's not necessarily the case that r being greater than g led to more inequality. Now in future videos, I'll do some spreadsheets where you see if r stays constant at a constant value higher than g that will lead to inequality.

But the whole reason why I did this one is to show you that just in a given period of time, r being greater than g doesn't necessarily mean more inequality. In this case, labor got more of a fraction of the total national income. And once again, the connection between capital and labor and income inequality is that, in general, the income that goes to labor is more indicative of the income that might go to the lower quartiles of a population, and the income that goes to capital is more indicative of the income that might go to the top percentile or decile because capital tends to be concentrated in the top few sections.