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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.
• 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?
• 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?
• 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.
• 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 : )
• 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.
• at , 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?
• 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.
• 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 ! ! !
• "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 some other business. That's how economic growth truly occurs.
• 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.
• 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".
• 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?
• 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?
• 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?