Are rich people happier than poor people?

Is there a relation between the material wealth of a person, and the happiness which that person experiences? At first sight, it may seem that the answer may be yes. We’re culturally bounded to believe that material wealth is a synonym of welfare and happiness. Our basic needs, and even those a little bit more complex, would be satisfied, and therefore, we should be happy. Our entire economic system bases on the belief that economic growth is the answer to all the problems of the world, that we could achieve happiness if we are rich enough.
But reality is more complicated. We’re told since we were kids that having more stuff would make us happy, but our parents, and maybe other media, taught us that wealth is not everything in this world. So, whenever someone says “hey, I want to be so rich that I could poop coins when I go to the toilet”, other people answers “dude, money isn’t everything in this world, and definitely it won’t buy you happiness”. To prove the previous statement is necessary to do a little analysis.
We may notice from people’s experiences that the complexity of life problems and unhappiness is related to the amount of wealth that a random person may have. E.g. Poor people main worries and sources of unhappiness derive generally from the inability to satisfy the basic needs of their families, or beloved ones. The inability to pay debts, have enough money to survive the month, job instability, rising prices in public services, etc. Although they have also problems concerning emotional issues, the main question is about economic wealth related to happiness, so, this won’t be analyzed.
In the other hand, as richer people have their basic needs fully satisfied, the complexity, or banality of their problems increases. Therefore, e.g. we have spoiled children that burst in rage when their dad didn’t get them a white Ipod 2 for their birthday, and instead they gave them a gray one. Or adults that gets frustrated because the neighbor got a new shiny car, etc.
To conclude, happiness is not related to the wealth of a person. Unhappiness will always be present. The only relation with economic wealth is that the complexity or banality of problems will vary accordingly to the wealth of the person. Being more essential and basic as lesser the wealth of the person is, and being more banal and complex as the wealth of the person increases.