Some points to consider......
1. Wealth and poverty can be viewed in relative terms: wealthy or poor in comparison to what? A relatively "poor person" in modern-day America enjoys a standard of living that was unthinkable even for kings of ages past. And in terms of nationality, the "poor" in a modern developed economy is much better off than the "poor" in, say, Africa. Afterall, they have television sets, radios, nike shoes, and so on. They do not technically "need" these things; they are luxuries. The average person today enjoys luxuries that simply were not available to people in the past, because the technology did not exist. One point that this brings to surface is the fact that improvements in technology increases the capacity for wealth.
2. Income is not the only measure of wealth. Indeed, it can be very misleading. You can take two people with the same income and one will be rather poor and the other rather luxurious due to their consumption habits as individuals. Someone who consumes wrecklessly is going to impoverish themselves in the long-term. On the other hand, someone with a high time-preferance is going to save more and thus have more long-term economic security. Furthermore, the purchasing power of the monetary unit is perhaps even more vital than income statistics, for it determines what standard of living any given income can afford.
3. One way to determine wealth is in terms of what quantity and/or quality of property one owns. A person who lives in a upper-middle class home in a gated community is certainly wealthy in comparison to a person who lives in a mud-brick hut or teepee. A person who owns a car is certainly wealthy in comparison to a person who uses a horse and buggy or chariot to get around. In terms of quantity, if two people are interested in baseball cards, and one has a huge collection, while the other only has a few booster packs, the former is certainly wealthy in comparison to the latter.
4. If wealth is to be defined more generally in terms of what makes one happy, "psychic wealth", it becomes utterly subjective and asthetic. What one values asthetically is within the realm of subjective value. If someone genuinely finds happiness by living the life of a hermit in the woods, there is nothing we can do to tell that person what would make them more happy. They determine that, not us. What one values in terms of consumer preferances falls within the subjective realm, as only they can determine what makes them happy. In areas such as music, movies and comic books, the wealth of happiness has no objective definition.
5. The existance of scarcity of resources implies that it is not really possible for everyone to live the lives of billionaires because the resources in terms of land, labor and capital that is necessary for such a thing to happen does not exist. Furthermore, the inherently unequal distribution of those resources across the face of the planet combined with the inequality between people's abilities as individuals means that there will never be absolute equality in economic ends. That is, there will always be multiple tiers of wealth in any given society.
6. There can be said to be two kinds of poverty. The first kind of poverty is the unfortunate result of people's own bad decisions, excessive consumption, a lack of personal initiative, and so on. The second type of poverty is created by government interventions in the economy that hamper production or stimulate excessive consumption, or simply by theft, wether governmental or not. The first kind of poverty is worsened by the latter kind. If the 2nd type of poverty were removed, poverty in general would diminish considerably, even for those who are poor as a result of their own bad decisions.