> For example, some people give away some or all of their wealth and instead of leaving it to an heir. Inherited wealth is not automatically invested, some of it is spent.
Sure, but that's a small fraction, doesn't really move the needle. Also, much of that is given to wealthy foundations (their own or others, such as colleges) who typically invest it (to make it perpetual). It rarely "trickles down" thus reducing inequality.
> Inherited wealth can be split among many heirs, in which case returns would need to be much larger to keep inherited wealth from diminishing.
How does that math work? If I invest $1M at 5% yield I get $50K. If I break it into 5 tranches of $200K, each yielding 5%, that's $10K each or $50K total.
Sure you may get 5 people with $1B instead of one person with $5B but that doesn't reduce inequality.
>> Sure, but that's a small fraction, doesn't really move the needle
Andrew Carnegie was the richest man in the world at the beginning of the 1900's. What does "r > g" say happened to his wealth? What actually happened was that he gave it all away. Many of the richest people in the US have pledged to give away the majority of their wealth. You can't hand wave that away.
We know that "r > g" is not a good model of how the world works because 90% of the time, wealth is dissipated by the 3rd generation. If you want to know how that happens, you need to start adding more information to the model, including charitable giving, spending, taxes, and multiple inheritance.
>> Sure you may get 5 people with $1B instead of one person with $5B but that doesn't reduce inequality
Of course it reduces inequality. It's not particularly equal, but taking money from one person and giving it to multiple people reduces inequality. Take it to the extreme case, if someone with $5B gave $15 to each of the 340 some million people in the US, would that not reduce inequality? If it would, but giving it to 5 people would not, what is the number between 5 and 340,000,000 where it would start reducing inequality?
In addition, your case is only talking about one generation. If the same thing happens for 10 generations, you're talking about 10 million people. After 15 generations, it's 30 billion.
> Andrew Carnegie was the richest man in the world at the beginning of the 1900's. What does "r > g" say happened to his wealth? What actually happened was that he gave it all away. Many of the richest people in the US have pledged to give away the majority of their wealth. You can't hand wave that away.
You absolutely can hand wave it away. 1) Yes, Carnegie's actions helped reduce inequality by funding thousands of libraries, but the reason Carnegie stands out is because he was unique in both wealth and largesse. Also, he gave away 90% of his wealth _while he was living_ so not relevant to this discussion about inherence. 2) Pledging and doing are not at all the same. 3) Those who are both pledging and doing (like Gates) are doing so during their lifetimes -- again a separate issue to inheritance.
I haven't done all the math, but I'm very confident that even if you discount charitable giving, you'll find that r > g in the present era (which is the subject of Piketty's book). Look, just looking at my portfolio, it's up nearly 70% in the past 5 years -- that's miles ahead of growth. And that just standard investments, no crypto, options, derivatives, pre-IPOs, etc. The very wealthy are doing much better than that.
> We know that "r > g" is not a good model of how the world works because 90% of the time, wealth is dissipated by the 3rd generation.
I don't know where that number comes from but I would strongly dispute it. Yes, there is very new wealth being made especially in the past 50 years by people like Musk, but most wealth is generational wealth, even in the US (and much more so in Europe and elsewhere).
> If it would, but giving it to 5 people would not, what is the number between 5 and 340,000,000 where it would start reducing inequality?
Please point me to the billionaire who divided up their assets upon their death to more than a few dozen people, and we can talk about how it reduced inequality. Almost all leave it to their heirs or, if generous, to a Trust or Foundation which keeps it invested (Ford, Rockefeller, Harvard, etc.) and give away / use the proceeds over time.
Sure, but that's a small fraction, doesn't really move the needle. Also, much of that is given to wealthy foundations (their own or others, such as colleges) who typically invest it (to make it perpetual). It rarely "trickles down" thus reducing inequality.
> Inherited wealth can be split among many heirs, in which case returns would need to be much larger to keep inherited wealth from diminishing.
How does that math work? If I invest $1M at 5% yield I get $50K. If I break it into 5 tranches of $200K, each yielding 5%, that's $10K each or $50K total.
Sure you may get 5 people with $1B instead of one person with $5B but that doesn't reduce inequality.