If you are talking about the effect of privilege within a school, I've taught in just such an environment. It was very hard to return from spring break with some kids talking about trips to the Galapagos Islands while other kids barely had enough money for their families to afford their apartments. I did not see blatant teasing (although I'm sure it happened) but I did see kids making choices on friendships based on money...with the more "popular" kids tending to be those with money. Interestingly enough, however, I watched many very wealthy kids flounder because of lack of time with parents. While I suppose it was also true of the poorer students, it's the wealthier ones that really seemed to struggle for lack of parental supervision. But that may just have been that particular school.
This question might be better served if on a discussion board and if further specified.
There are schools with privilege and there are privileges within schools.
As a public educator, I send two of my children to a private prepatory school. Some feel this makes me a hypocrite, others think its brilliant.
I realize what we can't do in public education because we work for the masses and are limited by every legal right students are given these days. Thus I put my children in a school where they can be challenged because teachers are encouraged to challenge instead of coddle, and students who drain teachers' ability to work are kept out. They are in privilege... but I pay for it... I pay a lot.
On the other hand, privilege in our public schools regularly occurs when schools in places where property values are high receive direct financial benefit from property taxes.
It would be much easier to answer this question if you told us more about what you want to know.
Are you talking about the effect of privilege within one school, or are you talking about the comparison between a rich school and a poor one? And in what country?
In the United States, richer schools tend to have much better results than poor ones. They have better facilities, often have better teachers, and have parents who are more involved in their children's education.
Within a school, economic differences can make for jealousy. Poorer people often feel the richer kids are treated differently.
I believe you might be talking about the inequality it brings about when a few have many resources and others do not have any. It creates friction, tension, jealousy, and could lead to violence or other behavior. It also produces an inequality in the education itself.