What was the author's purpose in writing The Great Gatsby?

As with most writers, Fitzgerald's goal is to delight, to entertain, and to inform, but more specifically, his purpose is to advocate for going after our dreams. Dreams may be doomed to failure, but it is nevertheless important to dream big.

Nick admires Gatsby, despite their class differences, because Gatsby had the audacity and sincerity of heart to dream big dreams and go after them. Nick likens Gatsby's personal dream to the American dream: both are attempts to right wrongs of the past and to start afresh as if the past never happened. (This never works, but that doesn't matter.)

Nick both looks down on Gatsby's ostentation (as expressed in his oversized mansion, pink suits, and big yellow car) and yet deeply admires him for coming so close incarnating his dream of reconnecting with Daisy and starting all over again with her as if the intervening five years never happened.

It is actually the power of the past that destroys the dream. The past haunts Gatsby in the form of Tom Buchanan, who represents the arrogance and narrow-mindedness of inherited wealth and privilege, which he uses to crush and kill people like George Wilson and Gatsby.

Nevertheless, the novel says, we must dare to dream, because it is the journey that matters, not the reward:

So we beat on, boats against the current . . .

One of the book's major themes is that the American Dream is, essentially, a fiction, and so it seems that this was part of Fitzgerald's purpose in writing it. Theoretically, any person who works hard enough ought to be able to achieve personal success, financial stability (or, better yet, wealth), and happiness. This is the dream. However, George Wilson, for example, works incredibly hard and can never seem to get ahead; he's an ashen, sad-sack ghost of a man whose smoldering but horrible wife cheats on him. Despite his hard work, it seems that Wilson simply cannot achieve the dream.

Gatsby, on the other hand, seems to have done so. At least, until we realize that he is a bootlegging criminal. His "success" can hardly be called the American Dream, because he made his fortune by breaking the law. If working hard and being honest, like Wilson, cannot help one to achieve the American Dream, and the only way to achieve financial wealth, like Gatsby, is through criminal activity, then it seems that the dream is really more like a fantasy.

This novel can be seen as an exploration of class aspirations in America, of a materialistic distortion of the American Dream of self-determination and self-improvement, and a satire on contemporary values in the Jazz Age. 

Beyond it's value as a work of art (which may be its principal value as the work is a considerable achievement of form, craft, character, and language), Fitzgerald's novel is open to claims that it is intended to affect the reader's thoughts in any of these thematic areas.

The novel is written in the form of a satire. This gives credence to the notion that the book is meant to highlight the moral failings of a society mesmerized by the trappings of wealth, by the bright lights of glamour, and the false beauty of accumulating material goods instead of living a "good life".

These comments are all drawn from the novel's depiction of the upper class in America during the Jazz Age. 

The Great Gatsby is the tale of the irresponsible rich. Originally, the title of the book was “Trimalchio,” based on an ancient satire of a man called Trimalchio who dresses up to be rich.

Going back to the question at hand, we might say that Fitzgerald wrote the novel to suggest that the aspiration to become wealthy in America was, in reality, not as great as people imagined it to be. In this way, it is a novel of disillusionment. 

Yet, there is a great hope at the center of the novel. Though Gatsby, like Trimalchio, is only dressed up to be rich and is therefore essentially false in his self-presentation, there remains something true about his character. 

[Gatsby had] an extraordinary gift for hope, a romantic readiness such as I have never found in any other person and which it is not likely I shall ever find again.

Keeping Nick in mind (as a man who learns to look past the surfaces of people), we can say this is a novel intending to find the heart of virtue in an age where it has become obscured; lost in the bright lights and the nihilism of shallow ambitions. 

The classic novel The Great Gatsbywas brilliantly written by F. Scott Fitzgerald from the narrating standpoint of Nick Carraway. Nick's telling of this particular tale is undeniable honest. The author's intention is to write about the great American dream and in doing so he illuminates the forces that have tainted and possibly even destroyed this notion. Fitzgerald uses Nick, an intelligent and critical thinker who constantly analyzes his surroundings and tells the reader about them with his particular touch of animation. Fitzgerald frequently uses hyperbole as he tells this story in order to emphasize the romantic notions of the American dream and therefore Gatsby himself. He compares Gatsby to "one of those intricate machines that register earthquakes ten thousand miles away". He further explains that Gatsby contained "an extraordinary gift for hope, a romantic readiness such as I have never found in any other person adn which it is not likely I shall ever find again". This shows the romantic view of the character that we later see in exaggerated forms when describing the 1920's and the death of the American dream.

What was the author's purpose in writing "The Great Gatsby", and what symbol best represents it?

Building on the motif of color, Daisy's name suggests both white and gold with the center.  So, while Daisy's white clothing suggests purity, she is corrupt at her core, falsely gilded like her gold center, her voice that "sounded like money." Representative of the novel, then, is the name of Daisy, symbolic of the illusion of beauty, purity, and idealism that is the American Dream in the Jazz Age of F. Scott Fitzgerald. 

In regards to the most appropriate symbol, I would most definitely choose the green light at the end of Daisy's dock.  For Gatsby, that green light represents Daisy herself, ... for us, we think about Gatsby's warped American Dream of obtaining her.  This is Gatsby's entire purpose as well as the ironic twist around the title of The Great Gatsby.  Of course, there are numerous other symbols in the book (my mind wanders, of course, to The Valley of the Ashes and Dr. Eckleburg), but it's the green light that nicely encapsulates Fitzgerald's vision.