We're learning about "decision-making under uncertainty" in microeconomics at the moment. It's sort of interesting, although like with most economics it's just common sense. I was thinking about wealth maximisation versus utilitity maximisation, as you do. Risk theorists folk say that people don't look at expected profit from a gamble, but expected utility. For a very poor person a 50:50 bet for all the money they have isn't really "fair". Because if they lose their life will be ruined, but if they win their life will only be marginally better. So economists assume that the value of a dollar diminishes as you get more dollars, which makes sense.
But what it also means is that any investment is going to be cheaper for a rich person than a poor person. A rich person will say yes to a 51:49 bet in their favour, while a very poor person might say no to a 60:40 bet in their favour. The "worse" risk ratio is actually cheaper to the rich person, than the "better" risk ratio is to the poor person. In a fluid market any investment made by any poor person can be trumped by someone with a little more money. Which means that all the best investments will be snaffled by the rich. So incomes won't necessarily ever converge. That is, unless the poor are able to systematically collect better information than the rich. Which seems unlikely.
This is only a version of "it takes money to make money". I guess I'm saying that "it takes having more money than everyone else to make money".
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