Not in most countries, but in America, they are usually smarter because they have more ambition. If someone inherits 30 million, but doesn't work to increase their wealth, that money will be gone in no time. I've seen it happen a lot. Usually the most financially wealthy in America aren't even known to be so. This is because they are smart enough to not squander their money, and to invest in things like land and gold. I have and aunt and uncle who both work making six digits, but they have (at least) a double morgage and have trouble paying some of their bills because of their spending habits.
Mind you wealth can offer a greater slew of resources that will indeed capitalize and increase the engagement of the brain maintaining a high IQ when it goes into it's decline after about the age of 12 or so, but beyond that there is no reason to believe that there is a marked impact created by socioeconomic status.
I suppose the one key argument that could be made is that genetically richer people do tend to go for each other which could mean that they are breeding superior-in-genes persons (since wealth and beauty tend to go together in human cultures) but even then that's a loose and probably inconclusive argument.
The wealth you have or accumulate has nothing to do with your intelligence. While wealthy people may be able to afford better schooled it will not make them more intelligent than a poor person who has the same potential and is in a so called bad school. Everyone has a brain and everyone can choose to use it responsibly rich or poor.
I'm not saying that rich people aren't intelligent, they can be spectacularly good at what they do. I'm saying that poor people aren't necessarily less intelligent.
First I want to address that there is a huge variety of human intelligence. Someone can be very good at something but at the same time its likely that he is really bad at some other things. It's a biological trade off.
Secondly, what personality we have can have a huge impact on how much money we are going to get. There are people who are more likely to be attracted by extrinsic rewards such as fame and money while others focus on relationships or their passions and interests. Due to the competitive nature of the society, some personalities are more suitable for propelling someone up the ranks while some other personalities resist or simply ignore. For example, extroverts with a gregarious outspoken personality is more likely to be recognized and praised than introverts who are softly spoken and reflective and are often misunderstood as lack of ideas and timid. Further influenced by the extrovert idea, there is a huge advantage for those who are extroverts or those who can successfully mimic them. In addition, under the influence of the extrovert ideal, introverts can think badly about themselves and that they aren't smart enough. This can become self-fulling. And this I believe is only one case out of many that shows certain personalities are undermined. And to further extrapolate this, many talents are thought to be lack of usefulness but this is just merely predicting what the world needs while the world is actually changing-creating new things and adjusting, making use of them every second.
Thirdly, we can't dismiss the fact that many poor people are to be born poor and the rich born rich. Being poor means I have less resources and opportunities that the rich does. There's a huge disadvantage in terms of environment. There are studies that show children of rich families generally have higher IQ than those of poor families. But additional studies found out that income level doesn't play any role in determining how smart in terms of IQ a kid is by studying adopted children. "The crucial finding is that children adopted by high-SES parents had IQs that averaged 12 points higher than the IQs of those adopted by low-SES parents--and this was true whether the biological mothers of the children were of low or high SES. "
My references are mainly drawn mainly from Sir Ken Robinson and Susan Cain but also in countless other articles and my personal experience.
In addition to my points, I would like to suggest an interesting conversation on what inequality does our minds and health, suggesting some grave situations facing not only the poor but also the rich. Here's the link below:
I don't care if I'm rich or not because it is not my business. Even though it is my business, I don't care really. Of course, many people wants to be rich but if they are stupid, what would happen? And we know what will happen. It is just wasting money for your life.
If you are rich, so what? Rich can't make you happy when you are stupid, because you are stupid and always wasting money. It is always useless for stupid people. Maybe it will be useful to smart people because they know how to use money and how to use it useful. You don't need to be rich so you can be trusted or something else. And there is one thing that would not change, it's of course how much you are stupid. That is the one thing.
Intelligence can help you in many ways, many things for your life and for your work. Even though your rich and stupid, it is very useless of the money if you are stupid, always wasting money. No one would like them even though they boast they are rich and they are stupid.