What motivates Paul throughout the story?

Paul is motivated to emulate the lifestyles of the rich and famous he so much admires. He wants to be somebody in life instead of the nobody he believes himself to be. He dreams of escaping his ordinary, humdrum existence and living the life of a wealthy young man about town. But there's a big problem. Paul is not prepared to take any active steps to make his dreams come true, so he remains trapped in a fantasy world of his own making.
Instead of doing something positive with his life, Paul steals from his employer and heads off to New York, where he briefly lives out his fantasies. But the harsh realities of the everyday world soon make themselves felt, and once the money runs out, the fantasy dies with it. At least while he was living the dream, Paul had something to hang on to. But now that it's gone, he has nothing left and nowhere to turn. The only way he feels that he can escape his predicament is through taking his own life.

Willa Cather's "Paul's Case: A Study is Temperament" focuses on an aspirational teenager from Pittsburgh who wants to live the "high life." In his pursuit of bigger and better things, Paul gets in trouble at school, steals a lot of money, and sets off for New York City to masquerade as a rich socialite. In the end, he throws himself in front a train rather than go back to Pittsburgh with his father, who is on the way to retrieve his errant son.
Motivation in a story can be external, internal, or a combination of both. For Paul, the external motivation is the kind of cosmopolitan lifestyle he wants for himself: money, luxury, and attention from women. At the same time, Paul is internally motivated by his desire for something more. He can’t bear the thought that he is an ordinary teenage boy, destined to become an ordinary adult like his father. Paul wants to be somebody others can admire, and for him, that person is in the world of theatre, living it up. This underscores Paul’s need for acceptance and success, and although these are external sources, his desire to achieve these is innate.
Based on Paul's suicide, one could also argue that he is motivated by an emptiness he feels within himself. Perhaps Paul wants material, worldly success because he believes it will fill the gaping hole in his psyche. This means that Paul is also motivated by the sadness and anger he feels about his past (i.e., his mother's death).