Ok, as much as I enjoy the pie metaphor, it may be getting tired. Help me understand from your perspective; how does the pie currently work, and/or how is it supposed to work?
Duly noted; I do have a strong assumption about money circulation. Is it immaterial to the health of an economy?
I'd assume all citizens would be recipients, not just low earners.
If I had to speculate on the effects on entrepreneurship, I assume it would at least have a positive, nonzero effect.
How much money depends, as it would definitely not start as a full-income replacement, but supplementary.
All else being equal, what is median wealth's correlation with the health or productivity of an economy?
Also, could each citizen be considered a potential asset?
You have good questions; let me try to deal with them each in a basic way, you can ask more questions for nuance if you want.
1. "Is [money circulation] immaterial to the health of an economy?"
The issue is whether it is a driver of economic growth. Let me answer this way: Are people fat because they eat too much, or do they eat too much because they are Fat? (See John Taube, "Why We Get Fat" for answer; not a diet book; provides basis to understand why so many think consumption drives the economy when it does not).
2. "All else being equal, what is median wealth's correlation with the health or productivity of an economy?"
First tell me what you mean by 'wealth'; based on what you have written here, I see that you conflate wealth with money, with income measured as money, probably using an AGI income tax metric so, it appears to me that you are referring to median income related to economic health or productivity. Here again, I wonder what you mean by and how you would measure 'economic health'; we have productivity measures such as they are.
I will say that you want to know how median (why not average?) income impacts the 'wealth' of an economy. Quick answer is see above.
But let me digress, can you wrap your mind around the idea that money, income, is not wealth. Rich people know this intuitively even if they don't know how to articulate it. Precisely, individual wealth, is the possessory right to a future after tax stream of income. Wealth can be measured by applying a risk adjusted discount to that cash flow to produce a present value.
In every day parlance, you are only as wealthy as what you can borrow (because what you can borrow is itself a risk adjusted discount of your future income).
The thing about money is that it is simply a unit of account for transaction and a unit of measure to articulate notions of relative value. Money is a wasting asset that is maintained because it is liquid, of itself it does not have a growing future income stream. What we use as 'money' today is an unsecured non-interest bearing demand note issued by the Federal Reserve; a debt instrument issued by our government that says right on it "Federal Reserve Note." We use debt as money.
By law we use this debt owed to us by our government to pay taxes, tender exchange, and settle debts. We pay debt with debt (a lot of that going on all over the world).
The 'money' we would hand out under UBI is an IOU issued by the Federal Government which is only as good as the Federal Government’s ability to borrow from third parties in an international government bond market. As goes the 10year bond, so goes the dollar.
So, to bring this back to the question, median income is not a measure of economic health, if you mean aggregate wealth. The fact that it is high or low is symptom of other factors; it is not a cause.
What you want for economic health is an increase in the aggregate real assets under the jurisdiction of that economy. This is the base that underwrites that economy and the government which issues paper money debt backed by longer term interest bearing debt. When the real asset base declines, so does the credit risk of the Government, and then so does the value of the money...which begs the question of whether you want adjust your notion of 'median wealth', income, to be adjusted for inflation.
3. "Also, could each citizen be considered a potential asset?"
Absolutely, the investment in capital that is required to maintain and create real assets, includes human capital, intellectual capital, innovation.
