But the question still remains of how "rich people invest in the economy". Do they really? Or is it entirely indirect? Not one of them is giving small farmers money to buy tractors. Maybe they're building hotels which eventually employ housekeepers, sure. That's what I think of as the general economy. There's probably a more specific technical term for this. But I think using a billion dollars to give small farmers loans would be the worst possible use for it. You'd probably speculate in oil futures or whatever. While it's technically all the economy, sure, I'd argue that the super-wealthy generally don't add much to the economy, they extract value from the economy using their existing wealth as leverage.
What I'm getting at is that money spent on stuff/food/buildings/etc is different than money used as a tool/leverage/instrument just to make more money. I get the sense that it's an entirely different game (again, mostly an intuition from reading a lot of commentary about economic issues).
Sure, we all earn money and pay rent in dollars. Those dollars and that activity are only tangentially related to what a hedge fund uses dollars for.
Why do you believe lending to farmers is a bad use for resources?
Investing in oil futures is transmitting information to the markets. It encourages current users to avoid unnecessary use of oil and produces to produce more. That's a valuable service.
What exactly do you think a hedge fund does?
In contrast, money spent on consumption does not grow at the rate r. Picketty even speculates (providing no real evidence however) that only the rich can achieve growth rate r - investments by others will only achieve r' < r.
Did you even read Picketty? (The math parts, not the mood affiliation.)