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## Macroeconomics

### 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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# r greater than g but less inequality

The video discusses Thomas Piketty's idea that if return on capital (R) is greater than economic growth (G), it could drive inequality. The example shows that R > G doesn't always mean more inequality. The video encourages critical thinking about these concepts. Created by Sal Khan.

## Want to join the conversation?

- Until I watched this video I thought that r referred to change in return on investment over a period of time. Does that not make more sense? Given that g refers to the change in output of the economy over a period of time wouldn't it make more sense to consider the change in return on investment rather than return on investment, that is delta r instead of r?

Or does g not actually refer to delta g?

If we consider the change in r and the change in g in the scenario presented above then the change in r is less than the change in g which corresponds nicely to capital becoming a smaller share of the economy.(17 votes)- But r and g measure fundamentally different things. r represents growth in capital and g represents growth of the growth of overall capital. In calculus terms r represents the mean of the first derivative of value (of capital) over a year and g represents the second derivative of (produced) value over a year. In a sense they have different units, so they are not comparable in the first place.

Now if instead we consider the change in r we get -1% vs 2% which not only makes much more sense semantically, it is also consistent with the previous consideration that r > g <=> increase in the percentile of the overall wealth that the capital owners control.

Am I missing something?(2 votes)

- Won't this situation eventually lead to r < g? I understand that this example is meant to show that if r > g, it is not inevitable that inequality grows. However, I took from Piketty's book that macro principles of inequality have to be studied over extended periods of time; he suggests 30 years as an appropriate window of study. And if you extend this little example in perpetuity, won't the r > g principle hold?(13 votes)
- An assumption of all the growth is shared among labors is made. In theory, yes, it will lead to r<g eventually. However, in reality, it's not possible that all growth is shared among the working class.(2 votes)

- What kind of statistics suggest the rate of return on capital and labor in an economy ? Where can I found them? (sorry for my poor English : )(4 votes)
- The "return on capital" would vary from year to year dramatically. You can look at a reinvested total stock market index fund to look at the returns in recent years. See for example http://quotes.morningstar.com/fund/VTSAX/f?t=VTSAX where the return for the last 10 years is 9%. That's pretty close to the historical average, as explained in the nice book
*Stocks for the Long Run*.

The return on labor is just income. You can look up things like "median income" to see what that is.(6 votes)

- at5:31, Sal says that the reward for the capital which amounts to 500 apples will be reinvested. That's ok. But in that sense I would expect that the capital increased by 25% will also generate at least 25% more output next year and reap bigger yields in absolute terms (if not relative as well through economies of scale... etc).

Alternatively the capital owners could just pay the capital returns out to themselves as income (thus keeping the rate of return on capital constant instead of diminishing)

In both these cases it is not possible to maintain the postulate "r greater than g but less inequality" easily anymore. Or am I wrong?(2 votes)- If you want to produce more apples, you're going to need more land. However, at the moment the most fertile, easy to reach and therefore cheap land is already being used to farm apples. To get more land you maybe need to cut down some trees. Or maybe you'll just have to travel further, which requires better roads. No matter what your solution is, it's going to cost quite a lot of money for not that much more land.

To harvest those extra apples you're also going to need more labor. This will automatically increase the rewards for labor. If the owners of capital would really want to maintain their return on investment, they would have to lower wages, but maybe that's illegal because the government has minimum wages or the employees dislike it so much they go on a strike.(6 votes)

- I know it's late for asking this question, but does the "Value of Capital", in your example, present the number of apples that the capital has the POTENTIAL to produce, or, in other words, the quantity of apples that the capital is worth ?

Also, I want to know what the capital onwers should do in case the return on capital (still in your apple example) is constantly decreasing (as you can see, in Year 1 the RoC is 12.5%; in year 2 it falls to 11.1%) ? Thank You So Much ! ! !(2 votes)- "Value of capital" in this case is most reasonably the value (in apples) that you could sell the orchard for. This is the amount of apples you are giving up now, in order to have a stream of apples come in for years to come. Remember, investment is always about deferring consumption off into the future, so it's best to consider what you're giving up now.

What should the capitalist do? In this example the only thing they can do is enlarge their orchard, so they'll have to just do that. In the real world a capitalist would be looking for other new innovative industries where they could use the capital to grow somebusiness. That's how economic growth truly occurs.**other**(4 votes)

- It's probably unreasonable to assume in an economy where r > g that labor will have significant enough leverage to bargain successfully to reduce or reverse inequality. We see this is the case in America, where the leverage of capitalists has been increasing over the leverage of the workforce (labor) for the past 30 years.(3 votes)
- One of the things Piketty states early on in his book is that r>g can be a very dangerous prospect if, as you stated, the bargaining power of capital is higher than that of labor. Another thing to keep in mind is how the returns on capital were made. In Sal's simple apple economy, the ROC was made purely by the activities of labor. Unfortunately, in the modern highly financialized capitalist economy, much of the ROC are made through what is called "extractive ownership" or "rentier capitalism".(2 votes)

- What happens when instead of reinvesting those 500 apples, the owners of capital just stockpile their gains?

Also, who is to say that labor had the leverage? When is the last time that labor held leverage over capital owners in America?(2 votes)- In Sal's defense, he did state that it is possible to have capital capture more of the output. He's just trying to be as non-partisan as possible.(1 vote)

- I'm a bit confused about what happens to the 500 Apples that are paid to capital at the end of year one. It seems like it's invested in the farm, with 4500 Apples making up the investment. Are we assuming that the 20 extra apples produced come from the additional capital invested in the farm, but somehow the laborers negotiate all the gains for themselves?(2 votes)
- OK - but this is quite the departure from Piketty's r > g thesis. The point of the thesis is not, "Well if Labor negotiates well, who knows!" It's that, throughout economic history - 20+ countries and 100+ years - developed economies consistently return less to labor than to owners of Capital - the rich. So if your point is, "Well then no one in 100 years in nearly every developed country bargained hard enough for Labor, watch" - OK - but that is QUITE the extraordinary claim you're making, and you spend time really proving the least controversial thing. If your point is, "If something that has proven impossible for 100 years, Labor would be fine" well... isn't that a bit like the Doctor that tells you, if your knee hurts, don't use it so much?

What really stood out to me in the book was the contrast between Developing and Developed economies, ones that need to grow rapidly and so g > r like China for the past 30 years, vs ones that are built already like the US so r > g. In the g > r that Kuznets accidentally cherry-picked, by only looking at 3 countries destroyed in WW2, there is an implicit Wealth Tax. The economy is growing so fast it is outpacing the returns of the rich, and that is creating that pull yourself up by your bootstraps, rising Middle Class, American Dream story in those economies. In the Developed ones you don't have that implicit Wealth Tax, and in later work he proposes well - maybe you need an explicit one.

If I'm understanding your direction here, perhaps your alternative proposal is far more leverage for Labor - but how? I bet you have a policy proposal in mind? 100% Full Employment in a post-scarcity economy? Something else?(2 votes)- In this video, Sal was addressing the
*specific*claim that r being greater than g meant more inequality. Sal showed that that is not necessarily true. Whether or not his scenario happens normally is immaterial. His point is that you should not automatically assume that it must happen the way Piketty says.(1 vote)

- Isn't Delta(r)>g a more appropriate relation to look at while understanding inequality?(2 votes)

## 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.