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### Course: Macroeconomics > Unit 8

Lesson 2: National income and inequality- Capital by Thomas Piketty
- Difference between wealth and income
- What is capital?
- Piketty's two drivers of divergence
- Is rising inequality necessarily bad?
- Convergence on macro scale
- Education as a force of convergence
- Gilded Age versus Silicon Valley
- Inverse relationship between capital price and returns
- Connecting income to capital growth and potential inequality
- r greater than g but less inequality
- Return on capital and economic growth
- Critically looking at data on ROC and economic growth over millenia
- Simple model to understand r and g relationship

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# Return on capital and economic growth

Explore the relationship between return on capital (R) and economic growth (G). If R is greater than G, it may lead to rising income inequality. Use the example of a simple gold mine economy to show different scenarios. Created by Sal Khan.

## Want to join the conversation?

- At7:20, what determines which party has more leverage over the other? "Leverage" seems key to the distribution of income, but Sal never explains what "leverage" means.(8 votes)
- Sal just trying to show different scenarios without complicating things. examples for leverage might be that the workers started a union and are able to negotiate a better salary or someone opened a new gold mine and now the owners need to increase salaries to attract the same amount of workers(25 votes)

- Thanks!

What does income inequality mean? In the example of this video, what happens if the gold mine is owned by just 1 people, and there are 10 people who provide the labor? If I add these assumption, doesn't it show that there exist income inequality because 1 people who owns the gold mine collects 50 g.p. and 10 people who provide the labor own 50 g.p?

Hope you can get my point and I don't confuse you.(7 votes)- Yes, if there is only
`1`

owner, but`10`

workers, then owner income is`50`

per capita, and worker income is`5`

per capita. However the whole premise behind the "r > g" scenario is that even if worker income started out higher, that if`r`

is high enough it would eventually surpass worker income.(3 votes)

- So Sal is telling us the owners of capitals when they get 102 pieces there's a chance to give the 52 g.p. to the labor and not themselves?To be honest I find it naive how utopian this is because usually people are greedy and selfish by nature so they will want the 52 g.p. for themselves.From the other side usually the laborers can pressure the "owners" to share their gains by means that hurt the economy like strike etc..(6 votes)
- This seems a little bit too smooth - after all, the owners are "having" the gold mine after the first year, so the diminuishing of the income is just in a proportion to the worth of it if they had to put it up again. The laborers, however, are giving another year of work. Or am I getting this wrong?(3 votes)
- The "diminishing" return appears when the owners reinvest in capital, increasing the total value, and so the income seems a smaller percent of the total value of capital. This does not mean that they are earning less income from capital.

Yes, the laborers have to break their backs again another year.

I don't know if this answers your question but let me know!(3 votes)

- How did people in the first place determine who "owns" what? Did someone's ancestor said he owned a land and eventually everyone honored that?

We "agree" to all this when in reality we can just go caveman and kill the owner.

I am not saying we should do that, but I find it interesting that if people really feel they are not getting their fair share, they could really take a bigger share but they don't.(1 vote)- Philosophers have discussed this idea for centuries. It's the theory of the social contract.

You might enjoy reading some thinkers like Hobbes, Locke, Rousseau, and Marx.(3 votes)

- Please excuse me if you folks have addressed this question some where else, but I am wondering, what happens when g is greater than r (if that is even possible)?(3 votes)
- Yes, it is possible. g can be greater than r. In that situation, the share of profit shared among labor will increase. Per capita income of the national will increase, and labor will be a little better off.(1 vote)

- even with the possiblity no.2 where the return on capital= 4.76% , it stills much greater than the grtowh .. it's also increasing in inequality but with a smaller rate?

isn't that right?!(2 votes)- No, it's actually decreasing inequality. This is because an even larger return is going to the labor, who don't actually own the capital to start, than to the capital owners.(2 votes)

- Interesting discussion. Its unfortunate though that at no point do you mention that those who put up capital also stand too lose that capital and therefore r needs to be some factor that includes growth and compensation for risk. Inequality is capital markets arises from the greed of consumption, lack of self control in saving and lazyness to research and invest in lucrative ventures.(2 votes)
- Question! Why is it that at3:49and at6:56the percentage is multiplied by 10? Originally it was 0.495 etc. So why multiply it by 10? Is there something I'm missing?(1 vote)
- To get a percentage you have to multiply the decimal by 100, it wasn't 0.495... it was 0.0495..., which is why he got ~ 4.95, it's basic algebra.(1 vote)

- At7:26Sal makes the assumption that labour gets 52% of the national income (thus 2% more than capital owners). I understand that Sal speaks hypothetically, but isn't this a very hazardous example? Why would capital owners, who control the market (since there is only one gold mine it's a monopoly) ever give out more income to the labour rather than keeping it for themselves?(1 vote)
- Because capital owners don't control the market. If capital owners had a monosony, they would, but there is no reason to think that there would be.(1 vote)

## Video transcript

- [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.