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Below is the logic why r-g matters for wealth inequality and is a reasonable thing to look at. In particular this happens in so-called "random growth theories" of wealth inequality or "theories with multiplicative shocks." At the same time you're right there is nothing special that happens when r overtakes g and it's kind of irrelevant whether r>g or r<g.

This is based on a bunch of lecture notes and papers: http://www.princeton.edu/~moll/piketty_notes.pdf, http://piketty.pse.ens.fr/files/Piketty2015JEP.pdf (this one is by Piketty and also there it's about r-g rather than r>g -- see the discussion on p.75 and 76) and https://www.aeaweb.org/articles?id=10.1257/jep.29.1.29

Consider r and g in turn. It's easy to see why r matters for wealth accumulation: if you get a high return you have high capital income and so, for any given level of consumption, you will have high wealth tomorrow. In your example with a $1M endowment and assuming people consume 5% of their wealth a 10% return will mean next year's wealth is $1,050,000 and a 20% return will mean next year's wealth is $1,150,000.

Next consider g: now the idea is the economy is growing at rate g and therefore people's other income sources are growing at rate g. We therefore de-trend everything by g and end up with r-g ("Detrending" here simply means looking at things RELATIVE to the average). So it does make sense to compare r and g, simply because we're thinking about a growing economy so you want to compare EVERYTHING to g.

Also note that these "multiplicative shock" theories aren't really about rentiers vs workers. They are just about people making investments and either getting lucky or unlucky. Here is a good explanation of these theories http://nautil.us/issue/44/luck/investing-is-more-luck-than-t.... Of course, this is just one theory of wealth accumulation/inequality, and there are others with other predictions where r-g would not be so central.

> the economy is growing at rate g and therefore people's other income sources are growing at rate g

Why does a GDP growth rate of g imply that people's other income sources (wages from labor?) are also growing at rate g?

Wage growth in a country depends on confounding factors like worker productivity, relative bargaining power between workers and owners, outsourcing to other countries, automation, and the mix of manufacturing and service jobs in the economy.

It's very possible for the rate of economic growth to be, say, +3% while rate of change in the share captured by workers is flat or negative.

Yes you're 100% spot on. That other income sources and in particular labor income grow at g is just an assumption in Piketty's theory.

If labor income is growing at a different rate, the "correct" version of the theory should have r-g(labor_income). This would probably give even more extreme because it seems like in many countries the growth rate of labor income is less than the growth rate of the economy, i.e. r-g(labor_income)>r-g(GDP).

If you're interested in the dynamics of the economy and distribution if different variables grow at different rates, see here see e.g. http://www.princeton.edu/~moll/UG-slides.pdf

So g represents growth of the entire economy, not worker income or some such thing. Note that if Piketty’s hypothesis is true then the conclusion (return on capital will capture more and more of the economy) is more or less tautological.

This. A corollary of the argument is that if r > g, worker income on average grows slower than g.

Worker incomes kept pace with investment income through the 19th century where r was consistently higher than g and also in the early 20th where it didn't. If your investments are in machines that need people to work them then better machines mean that people's labor is more valuable.

It's only recently that we've seen we've seen wages as a share of total income slip from roughly 50% to roughly 40% of total income. But the delta can be almost entirely explained by large amounts of capital returns in owner occupied housing which is a far higher share of the US capital stock than it had been historically. And this form of capital doesn't require (much) labor to maintain its value.

You’re looking at it from the wrong perspective. If r>>g, Rentierism becomes an ever increasing part of the economy.

Isn't that the same fallacy as the "Joseph's Penny" - claiming because if interest, after a while a penny would be worth the weight of the whole earth in gold?

Obviously, the worth via interest can't grow forever, because there is no infinite value going around.

Also, isn't it a good thing if labor becomes less valuable, implying that less labor is REQUIRED? That is what people aim for when they invent technology to make life easier, after all.

It does seem that less labor is required. Automation has permanently removed large percentage of human workers from various industries (like mining).

The problem is that life is not easier because all that efficiency is captured by a tiny group of non-laborers.

The people whose labor was replaced are not benefiting from the end of their labor. They're now jobless and forced to compete harder for lower pay.

I don't think that is strictly true. Overall life IS easier for most people, because things are also cheaper to come by. And there still seem to be jobs.

But sure, there are various ways of looking at it. As others have pointed out, with increased productivity, the value of labor could also increase.

What's cheaper nowadays?

Food, clothing, health care, TVs, computers, pretty much everything. Maybe housing is an exception, but it may also depend on where you live. At least building is probably also cheaper (more efficient methods).

Is health care really cheaper? It's obviously much better, more effective and leads to much better outcomes. However most of these medicines and procedures that gave us these better outcomes are very expensive.

I would expect the medical procedures you could get 50 years ago would be very cheap today.

But it is of course a relevant question how to measure.

I suppose you can also get a computer that is as expensive or more expensive than a computer 20 years ago. But it would also be a million times faster (or more, I am too lazy to look). You could also get a Raspberry Pie for 30$.

"Also, isn't it a good thing if labor becomes less valuable, implying that less labor is REQUIRED? "

I think you may have this backwards.

If I generate $1 of value/hr that's kind of the maximum you can justify my wages being. If you give me a machine that increases my productivity 10 fold and the machine costs $2/hr then my maximum wage tops out at $8.

Now in this situation less labour is required, but the labour isn't less valuable. Obviously now you need a new industry to come along to employ the other 9 people who aren't now needed, possibly now servicing me and my newfound wealth, or possibly building the machines that put them out of a job.

'value' is what someone is willing to pay. My employer would have been willing to pay me a maximum of $1 and $8 pre and post machine introduction, so you could say my value increased. But I'm not likely to see much of that in the short term, because all my mates are now unemployed, and would be willing to do the job for their old pay, so my leverage is very low, so worst case I keep the same pay, in which the value of the job to me hasn't changed.

With the machine, less workers would be required, so all other things remaining equal, the wages should fall because of supply and demand (assuming the machine doesn't need rare skills to operate).

Of course, as you say, it could work the other way, and working could become more valuable because one worker could generate more returns. But that requires there to be more demand for everything.

Like, say, people eat only potatoes, and all work 8 hours per day to harvest just enough potatoes for everyone. If a machine could do their work, and they couldn't think of anything else to do, there would still be the same amount of potatoes, but less work to do.

I was trying to highlight that theres your value to your employer, which is kind of divorced from your pay. And the value of the job to you, which is your pay.

Could your pay go down in the example? Theoretically yes, in practice we see the opposite. Economic development couldn't happen if it did. Although I suppose short term dislocations could lead to lower pay in the short term, before increasing long term?

Don't forget 'progress' is people increasing productivity. In a world where everyone has to work full time digging potatoes, that's all anyone has. If it only takes 1 member of the group to dig potatoes, that frees the other members to discover science, religion, chips. We are in a situation now where a fraction of the population work in food production, but we all have jobs and more wealth than potato growing us could possibly imagine.

That added productivity doesn't disappear, in our earlier example the owner of the means of production has captured all the value that I didn't get from it. He has to do something with it. Even if he puts it in the bank, that's possible seed money for a venture that ends up employing my 9 ex workmates.

Also don't forget that the one potato digger won't want to dig potatoes all day whilst everyone else sits around. If there's no reason to dig more he'll dig enough for himself and take the rest of the day off. Now you could entice him to dig for you in exchange for beans, because you know he doesn't like picking beans, and as you don't like digging potatoes. And of course I could offer to trade apples...

> implying that less labor is REQUIRED

If less labor is required for tasks A, B and C, then that frees up people to do new tasks D, E and F.

It is untrue that there is a fixed amount of work to be done, so when some of it is automated, then that necessarily creates unemployment. That's the "lump of labor fallacy".

https://en.wikipedia.org/wiki/Lump_of_labour_fallacy

It's also fallacious thinking to assume that every person must be employed working for wages.

If someday the economy as a whole can produce everything people need by employing 10% of the people to build robots, then we can organize it such that the people who like to build robots can do that, and the people who like to paint, or sculpt, or hike or sail can do that.

There is no universal law of the universe that requires the 10% of robot builders to own everything on earth, and the other 90% should live in rags, filth and sickness.

> There is no universal law of the universe that requires the 10% of robot builders to own everything on earth

In your universe the universal law is that the robot builders have (collectively) nigh absolute leverage over the rest of society. Without the angel assumption they would slowly (or quickly) use that leverage to amass power.

People wouldn't live in rags or whatever but all secondary economies point to providing value to the robot builders.

That's assuming the robot builders have some kind of a monopoly. If anybody can build robots but it only takes 10% of people to do it before we have all the robots we need to do everything then the wages for robot builders will be as low as the wages for anything else, otherwise more people would become robot builders and drive down their wages.

But wages are always relative to prices. If everything is being made by robots that nobody has a monopoly on then everything should be very inexpensive. Having to work for the same nominal wages as you had in 2003 is not that much of a problem if nominal prices are now 5% of what they were then.

The problem comes when you have some kind of corruption or distortion or regulatory compliance costs keeping some prices high (see: housing, education, medicine) even as general wages are flat or decline, or just grow less than those costs.

We will have to pass regulations to keep those evil tech companies under control, and those regulations will conveniently create huge barriers to entry in the robot construction business.

The economy already produces "everything people need" using 10% of the labor force in nations with industrialized economies. It's just that the standard of living would be at about 1970's levels.

I know this sounds hard to believe for some. But today, agriculture takes up about 2% of labor, and manufacturing about 10%. And we consume about 2x what we did per person compared to the late 1970's. So, cut back manufacturing to about 4% of the labor force and use another 3% of the labor force for distribution. Voila, 10% of the labor force is used to sustain a 1970's level standard of living. Everyone else can improve their themselves, create arts, study nature or contemplate the nature of existence (that's sarcasm there).

Doesn't your robot example say exactly what I meant?

"Also, isn't it a good thing if labor becomes less valuable, implying that less labor is REQUIRED? That is what people aim for when they invent technology to make life easier, after all."

I used to think this.

I came to the conclusion that families and familial lines, like individual people, are living organisms.

Some of those living organisms (familial lines) are relatively young and inexperienced - and they will not gain that experience within one family members' lifetime. It will take multiple generations of growth and nurturing to "grow up" to produce individuals, like you, who can operate in a more complicated society and transact more abstracted work products for more abstracted rewards.

In the meantime, as in all of history, members of juvenile family lines need meaningful, satisfying labor that they can transact for reasonable currency to thrive as a living organism.

Asking why we need any labor to be done is like asking why all those infants can't just get with the program and eat solid foods already.

Your assumption of a 100% savings rate is not quite reality though. More realistically, suppose both people save 50%. Then in 20 years, the rentier is about 2x richer than the worker. https://www.wolframalpha.com/input/?i=sum+i+from+0+to+20+(50... vs https://www.wolframalpha.com/input/?i=sum+i+from+0+to+20+(50...

Your numbers are off. If both people save $50k each from their investment/wage income, then both of them will earn 10% returns on that $50k of savings. Hence why they cancel each other out. You've only given the worker 3% returns on his savings, not 10%

Despite the parent, it's never been an argument that owning is better than working, or anything at all to do with individual people at the micro scale.

The argument is when returns are greater than growth, societal inequality increases because the "haves" continue to hold on to their wealth, essentially creating a kind of permanent upper-class, that isn't based on merit the way it should be under capitalism, and that this (arguably) feels fundamentally unfair.

Capitalism had never been about merit. The word “Capitalism” is even a word coined by socialists in the 19th century which means « some people (the capitalists) are owning the means of production and keep all the wealth »

During each generation of rich people about 20% go bankrupt. Maybe they are alcoholics or they are fools who fall for scams. Your example would come close — a person who is not especially wealthy and who doesn’t work and who consumes 100% of their income. That would put them at a heightened risk of dropping out of the category of the wealthy.

A better example would be 2 people who work and who both make $100,000 and who consume 100% of their labor income. But one of these individuals has a $1 million endowment and reinvests every penny earned from interest. You can see how that would accelerate the concentration of wealth.

When wealth increases, less and less of the investment income is consumed. It's not fixed income anymore, it's added to the capital creating compound interest.

Rentier with a real investment income of $100,000 may have just few million in wealth