What does conflict theory tell us about income inequality? What does the functionalist perspective tell us about wealth inequality? What does the interactionist perspective tell us about the black and white income gap in the US?

The conflict theory in sociology states that income inequality arises from the ways in which the societal elite are systemically able to control and manipulate the poor. For example, the elite are able to perpetuate their wealth through tax dodges that allow them to pay a lower percentage of their income to taxes, while the poor toil at jobs which earn so little that they cannot hope to educate themselves or their children or gain the capital to ascend the economic ladder. These factors keep the working class poor.
From the functionalist perspective, parts of the society are meant to work together to contribute to the overall functioning of the society. Therefore, although an income gap exists between rich and poor, each person has their role to play, knitting society into an interdependent whole. Although the poor might earn less, there are also charities, both public and private, to help them, as all of society works together.
From the symbolic interactionist perspective, the white-black income gap persists because white people feel that they should retain the more highly paid positions in society. In this view, white peoples' interaction with black people is fraught with deeper meanings, including the idea that black people do not deserve access to power or money. Hence, these symbolic readings of race translate into racism and fewer economic opportunities for black people in society. 

First, the conflict perspective says that all aspects of our society come about through conflict between groups.  Groups compete to create the rules of our society.  When a group wins, it is able to set society up in a way that it likes (at least with regard to the issue it was competing over).  We can say that income inequality comes about because of conflict between the rich and poor/non-rich.  We could argue that the rich have won this battle.  An example of this would (arguably) be the fact that we have all sorts of free trade agreements with other countries.  We can say that the rich benefit from free trade while many poorer people lose their jobs because of it.  Therefore, if we have free trade, it is because the rich have won their conflict with the other classes.
Second, the functionalist perspective says that all aspects of our society play a part in keeping our society alive and stable, just as every part of our body plays a part in keeping us alive and healthy.  In this view, wealth inequality could come about because it gives people an incentive to better themselves.  If we all had the same amount of wealth regardless of how hard we worked to get ahead, many people would not work hard and our society would become much poorer.  Since some are rich and some are poor, everyone has the incentive to strive to achieve wealth and avoid poverty.
Finally, symbolic interactionism emphasizes the ways in which individuals perceive the world.  We assign meanings to all the things we see in our society.  The meanings that we assign affect how we interact with the aspects of our society, thus creating the society in which we live.  In this perspective, the important thing about racial income inequality is that we have, as individual members of society, chosen to believe that there is such a thing as race and that it matters. We have chosen to interpret skin color and other aspects of race as meaningful things that make us fundamentally different from one another.  In terms of economic inequality, an example of this could be the various studies that have shown that people with “white” names get more calls for interviews than people with “black” names when identical resumes are sent out with only the names changed.  Because people have defined race as something that matters, they treat these identical resumes differently on the basis of the race they associate with each.