Well, Drugs is a problem not just for the very poor but for the very rich too. I hear tales about how young people in villages fall prey to cheap drugs. At the same time, kids in high school at some of the most expensive schools around my place were recently busted for rave parties and abusing drugs.
Though the rich have a much better chance of coming out of addiction in one piece.

Your topic suggests that being rich and poor comes from mentality. I don't think that being poor places any sorts of restrictions on a person becoming wealthy. One of the wealthiest businessmen in Asia, the Late Dhirubhai Ambani wasn't born in wealth. There are several such examples of resourceful people coming from humble backgrounds and making it big. I think this plays out differently in the West and in the East.

The east has traditionally not been so hedonistic and materialistic. People's mentality and self-worth isn't affected by what society they are born in. Their breaking out of their classes is often a result of fearlessness, resourcefulness and just this insatiable quest to win. The poor/ middle class in the west become a part of the consumerist, debt-ridden culture. This isn't so in the east where saving and being debt free is considered important. As a young adult, you are protected from society's expectations because of your family. At the end, if you are lucky enough to have a loving, nurturing family, there is no limit to what you can achieve with hard work.