How has the goal for the American dream drove the people in west egg to be who they are today?

I'm not sure who you are meaning by the people of West Egg but I can speal the the American dream in relation to the book, Gatsby was never part of the establishment. He was born in rural North Dakota into a poor farming family. He hated his poverty and the limitations that went with being poor. Gatsby gets a taste for the rich through Dan Cody, a copper tycoon, and learns the ways of the filthy rich. After the war (WW!) Gatsby returns home to prohibition in the United States. Gatsby makes his fortune through an elaborate bootlegging operation. This is essentially the American dream, rags to riches. The ability to transcend one's humble lot in life and achieve a lifestyle envied by most of the population. Jay Gatsby does this and he does it in big way. Ironically Gatsby isn't recognized as worthy by the very people he aspired to be like nor is he particularly happy. You can also check this out:

http://www.gradesaver.com/the-great-gatsby/q-and-a/gatsbys-impossible-dream-as-an-analody-for-the-failure-of-the-american-dream-73291