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r greater than g but less inequality

Created by Sal Khan.

Video transcript

- [Instructor] 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. That could drive inequality. Inequality. And 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, and 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 in on itself. It actually might even hurt economic growth if you don't have enough consumers or people with enough purchasing power, discretionary income. Or whatever else. But what I really wanna 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. And that's really what I want you to walk away with. How do you think about these things? And you just need to make your own judgment. So what I wanna 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, you 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 the case. And to think about that, let's just imagine an economy where the whole economy just produces. It just produces apples. So let's say the whole economy right over here, this is our whole, our entire economy. And let me copy and paste it. So copy and paste it. I'm gonna 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 1000 apples. 1000 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 2%. So 2% of 1000 would be 20 more apples. So in year two the economy produces 1020. 1020 apples, right over there. Now let's say that in year one. In year one, of the 1000 apples that were produced. Let's say that 500 of them, I'll just split it 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 and what's 'cause 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. I guess to buy this apple orchard, the owner of it had to give, let's say 4000 apples. 4000 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. Capital in year one is going to be. well, the return is 500 apples. 500 apples. Divided by the cost, or I guess we could say the value of the capital. So divided by 4000. 4000 apples. So that's going to give us five. Five divided by, assuming it's five divided by 40. Which is one-eighth. So that's going to 12.5%. 12.5%. So the 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. And compare it to the growth right over here. And so let's just say that the value of the capital. That all of it was reinvested. So now the value of the capital. Value of capital. Is now 4000 plus 500 more apples. So 4500 apples, they reinvested it 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 the laborer 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 can negotiate the other way. But let's say in this situation, still 500 goes to labor. Sorry, 500 goes to capital. Capital. And here, 520. 520 would go to labor. 520 to labor. So now what's the return on capital? The return on capital now is going to be. Still 500 apples. 500 apples. Divided by 4500. 4500 apples. Which is going to be equal to one-ninth. Which is the same thing as, what is that? 0.99. So let's see, oh actually 0.1111. Let me just, one divided by nine. Yep, it's 0.11111. So it's going to be approximately 11%. Or let's say 11.1%. Approximately 11.1%. Now the whole reason why I wanted to show that. Why I did this diagram. Is that this is a situation where R is greater than G. Our return on capital, is 12.5% going to 11.1%. 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 in equality 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 lead 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 being 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.