When is a person monetarily wealthy?
The question is inherently relative. A person living in a housing project or in the poor hills of Appalachia is wealthy compared to the average person in many parts of Africa. A person considered rich in my small town of Sturgis, Michigan would probably be middle class in my wife's home town of Grosse Pointe, Michigan (home of the Fords and thousands of other wealthy families).
Now, if wealth is relative, then it boils down to a question of comparison: Compared to X, Y is wealthy. Compared to Z, Y is not wealthy. In other words, in order to determine whether a person is wealthy, you need first to determine who or what you're comparing/contrasting them with.
If we're looking to outside variables, they're seemingly endless: Grosse Pointe or Beverly Hills? Sturgis, Michigan or Bedford Falls, New York? Africa or the Projects? You could try averaging the factors, but the result would be too amorphous to give any meaningful guidance.
Perhaps we could compare our wealth to our own situation. What did we start with? What did our parents have? That would be a decent barometer, but it still presents problems (if my sibling is wealthy by Beverly Hills standards and I earn a mere $90,000 a year in Sturgis, am I poor?).
Nonetheless, I think a certain type of personal barometer might work. If we compare our monetary wealth to what we want, we have a readily-discernible measure. It's a good measure, too, because material wealth is, after all, merely the ability to buy material things.
Now, if the best barometer is oneself, we run into a paradox: The poor are the richest. If a person has no desire for material things or keeps his desires very simple, but he has a moderate amount of money, isn't he wealthy compared to the person with elaborate material lusts and a hefty salary who accumulates debt to satisfy his desires?
The paradox is most true in day-to-day lives, but it also often holds true, in a wholly material sense, in the long run: The "poor" man with a modest salary sometimes accumulates a million dollars while the "rich" spender ends up in bankruptcy