This is a spin-off from gsprofval's post: 5 Truths You CANNOT Disagaree With
in which 'truth' #4 is:
You cannot multiply wealth by dividing it.
If you have $100 then it makes no difference whether you keep it in a single account, or if instead you divide it, so you have $50 in one account and $50 in a second account.
If we now allow time to pass, and the interest rates on the accounts varies depending on how much is in the account, (for example, if you earn 5% on balances over $80, but only 2% on balances under $80), then it will make a difference. However, as long as the interest rate is positive (and above the rate of inflation), your wealth will still be multiplying, even if you have divided it.
A better example than dividing it between different bank accounts in the same bank is moving half to a different bank, or putting half into the stock market. If you do this correctly, you can get a higher return for the same level of risk (or a similar return, but for a lower level of risk). Dividing wealth is often the sensible prudent thing to do.
On a different level, the same thing happens in families. You could give all the wealth to the person you think it best at investing, but in the long run using that strategy it only takes one mistake and the entire dynasty's wealth is squandered. A safer route is to divide the wealth among different family members, letting each increase the part of the pool they are responsible for, as best they can. Some will fail, and some will do fantastically; and if you don't have a family full of fools, when it comes to divide things out among the next generation, the total wealth of the dynasty will have increased.
We can take this reasoning a step further. It doesn't make sense, on a national level, to leave 80% of the country's wealth in the hands of only 20% of the population. You'll get a better rate of return by spreading things out sufficiently for most people to stop living hand-to-mouth, buying things that are cheap rather than things that are efficient.
A $10 pair of shoes that lasts 1 year is cheaper than a $20 pair of shoes that last 5 years, but the latter is a more efficient use of money.
I made up the 20%:80% figure, because I can't remember the correct numbers off hand.