I would define bare minimum as the cost of living in that region. (high cost in america than india for example)
Define living.
I think that establishing a metric for the bare minimum would take too long in this thread because the opinions about what the definition of the cost of living change from person to person. I am more endorsing the idea of a bare minimum rather than trying to promote a specific metric or definition of it. If you are adamant about receiving a number from me I would define the cost of living per year as 3x the cost (tied to inflation) of food, water, healthcare based upon the environment and shelter. However I will emphasize that it is the idea of a bare minimum rather than my guess at it that is important.
As for the increasing inequality,
Imagine everyone flips a coin(representing risk) every N minutes. The gap between the highest (head-tails) and the lowest will increase with time. Given a large enough sample size and the gap will increase by 2 units every flip. (Note in a capitalist society each person also adds a constant to their total each flip due to the rising wealth)
Now the above is a drastic oversimplification of risk but the principle remains the same. Choices are risks. Inequality is the natural gap. People ought to help those that fall too low when compared with the costs of living but I see no reason to penalize those that climb high just due to their altitude. (coercion and fraud are reasons to penalize some of the rich but it would be the coercion and fraud that are the reason not the wealth.)
This is the problem with having an academic grasp on a subject and either not having or not applying street-level experience and reasoning to the same subject. Yes, your statement is correct, but it assumes an infinite timeframe. Life is not infinite -- at some point, the gap between 2 people who 'get lucky' and 'get unlucky' consistently will naturally stop spreading, because they die.
More importantly, the law of large numbers states pretty much outright that the vast bulk of people in your oversimplified coinflipping example are going to end up at 50/50, and the outliers will be exceedingly rare. It's not the outliers that have the problem in real life -- it's the people in the middle. When 72% of the wealth is concentrated in the top 5% (and that's from 2007, it's only gotten dramatically worse in the last 4 years), that's not an example of risk increasing the gap between the highest and lowest over time -- because it completely defies the law of large numbers.
First the coins get passed down from generation to generation. Hence while not infinite it is still a large enough effect over time. Yes outliers would be very rarer than in real life so it is not the best bell curve to use as a model. However it does show that even with it favoring equality due to the massive middle class, it still exhibits a spontaneous inequality.
To look at an example run of this model
Turn 41:
Wealth distribution 1-42
Total Population for even distribution: 2.19902E+12
Total Wealth: 4.7279E+13
Top 25%: 32%
2nd 25%: 24%
3rd 25%: 22%
Low 25%: 22%
Now so far we only examined two of the factors of the real world inequality. (Risk and Corruption) Neither of which is sufficient to describe the situation alone.
There are other factors that would be needed to fill out the model such as: birth rate trends (poor>rich) and the power of capital (money knows how to reproduce hence a linear progression is not as accurate as a exponential)
If we change the wealth distribution to reflect the exponential growth [(1.5)^n n:0-41]
Wealth distribution 1-16585998.48
Total Population for even distribution: 2.19902E+12
Total Wealth: 2.06795E+16
Top 25%: 75%
2nd 25%: 15%
3rd 25%: 7%
Low 25%: 3%
Another tangent:
Why does relative wealth matter after the bare minimum. Is not the objective wealth more important? After all relative wealth does not determine if I am above or below the bare minimum. Relative wealth does not tell us if everyone is starving or feasting or a mixture of both. I know it is human nature to be envious or feel pride due to gaps in relative wealth but do such gaps truly matter? or is it the objective wealth totals that matter?