Inverse relationship between capital price and returns | Macroeconomics | Khan Academy

So much of Piketty's book is about this idea of more, more, and more returns to capital. That the return to capital is going to grow faster than the growth of the economy. We see charts like this, where we have the value of private capital as a percentage of income. We see this dynamic played out in multiple charts. As we go through the Gilded Age, we hit kind of a peak right over here, at least a local peak. Then, as we get into the beginning of the 20th century, it drops down, and then it starts to pick back up until the present time. This is the present time right over here, this data point.

Then everything we see after that, this is Piketty's projections, really based on this idea of returns to capital being growing faster; that r is growing faster than g. But one thing to think about is why this dynamic might be happening, and then that might inform how we think about what the projections might be. So let's think about why the value of private capital could go down and why the value of private capital could go up.

One reason—let's just say we have some asset, some capital asset right over here. Let's say its current value went down to some market, and I bought it, and its current value is one hundred dollars. So this—let me just write this—this is today. Today, it has a hundred dollars, and let's say it gives an income, an annual income of ten dollars. So for this asset, my return on asset right over here is ten percent. I get ten dollars on a ten percent on a hundred dollar investment.

Now, there are several reasons why the value of this could go up. One reason is that this asset starts producing more income. So this would be in line with the idea of more income because of more capital becoming more and more valuable. It's able to capture more and more income or maybe it's utilized in a better way. So let's write this as the future.

In the future, you could have a situation where it's generating an income of, let's say, twenty dollars. Let's say that the return is the same, so the expected return is the same. People are still willing to say, "You know, I’m willing to pay as much for things, so I still get a ten percent return." So people are saying, "Okay, I’ll pay as much, so I still get a 10 percent return."

So that means that they're going to pay in the market— they’ll pay 200 for it. So this is one reason why you could have an increase in the value of something. And you could go the other way. Maybe the value is 200, but because the income goes in half and the return stays constant, the value goes in half. So this is one scenario. This is one reason why the price of an asset could go up, but it's not the only reason why the price of an asset could go up.

Another reason why the price of an asset could go up is maybe there's more and more capital, and maybe there's fewer and fewer projects to put it to, especially if the growth of the economy isn't growing. So more capital chasing fewer projects or fewer of things for it to produce, and in this world, what is going to happen?

Well, we’ll just assume that this continues to produce ten dollars of income. So the income continues to be ten dollars a year. But people, let’s say, "You know, I was able to buy this for a hundred dollars, but let’s say the next person who has a hundred dollars of capital, or to invest in capital, says, 'Well, I can't find something with ten dollars of income. I can’t get ten dollars. So hey, I’m willing to take nine percent.'"

So I’m going to bid this up. I'm willing to buy this from you for one hundred and one dollars or one hundred and two, and maybe it goes all the way where they can't get anything better than a 5 percent return on their incremental 100. So they're willing to do a 5 percent return for this asset.

So they would bid this thing up. The more and more capital you have chasing or more and more money you have chasing this asset could just bid the value of this up. So the value could go to 200, still producing the same income, and now the return is five percent.

So the reason to point this out is an increasing value of capital doesn't necessarily mean increasing returns. In fact, normally in the market, they move inversely with each other. When bonds have higher returns, then you have lower prices. When their prices are higher for bond prices, that means they have a lower return.

So when we look at something like this, when we look at something like this, this could be speaking to more and more capital accumulation chasing fewer and fewer potential projects, or whatever it might be, especially because you have slowing economic growth. But this would be a story of capital accumulation, but with r slowing down, with the actual potential return slowing down and probably starting to converge to g, to the rate of growth.

Another similar idea—this is more capital chasing fewer projects—but you also might have a reality that the reason why this is getting a 10 percent return is people find it scary. They’ve been burned on investments before; there have been wars. They don't want to put their money into some kind of factory; they want to stuff it into their mattress.

But then, over time, maybe people become a little bit less risk-averse, and they're willing to invest in the market. They're willing to invest in a project or start a business or whatever it might be. So people become more risk-tolerant.

So maybe this is a world that is very risk-averse. Risk-averse. If you want me to invest in capital, you have to give me a high return. But maybe the future is going to be more risk-tolerant. In a more risk-tolerant world, you could also go to something like this.

So this is risk in a more risk-tolerant world; you might say, "Hey, okay, well, okay, I don’t have to stuff [my money] in my mattress. I’m getting zero percent or in my bank account I’m not getting a lot, but hey, I'm willing to take my money to invest it more in capital."

So once again, they will bid up capital and they will have a lower expected return here. They needed a higher expected return because there was a lot of risk. They were scared of things. "Hey, you better give me a lot of return on my capital if you want my capital, because it's a scary world out there."

"Hey, okay, maybe now I'm less worried about wars and my wealth disappearing and whatever else." So I’m more willing to invest, and so that also is in line with this more capital. So there is a lower expected return, and so you have the value going up.

Actually, this is consistent with what we see happening right over here. This period right over here was a period of major unrest. You have the two largest wars in global history right over here. You can imagine people becoming very, very, very risk-averse. You could imagine people starting to stuff money and they're trying to sell their assets, worried what might happen.

So you're going to have less and less capital, more and more risk aversion driving that reality. But then, as we go into the post-war period, the memories of those wars go away, people become more risk-tolerant, more capital comes into the system because of the productivity. You have more and more capital accumulation.

If we go back into, you know, even pre-industrial revolution times, if we go to medieval times and all the rest, you had a limited amount of capital. It was mainly land. As you go into the industrial revolution, especially in the 20th and 21st centuries, land represents a smaller and smaller percentage of the value of total capital.

Now you have created capital; you have technology; you have intellectual property. This could be a trend. Once again, I'm not sure—it's up for you to make the judgment. This trend isn’t necessarily a return to a Gilded Age. It could be more and more capital chasing fewer and fewer projects, which actually could be a sign of lower returns, or it could be just people's risk premium is going down; they're becoming more and more risk-tolerant, and so they're willing to accept lower and lower returns.

So it's not clear what the trajectory is. But I just want to make it very clear that this isn’t necessarily saying that, hey, because this graph looks the same as here, that we’re necessarily going into a second Gilded Age. But it's up for you to decide.