In Act I of Romeo and Juliet, why does Lord Capulet throw a party/feast?
In Romeo and Juliet, Old Capulet throws a masquerade party because it is tradition (it's "an old accustom'd feast") and, well, because he can. He is perhaps the richest man in Verona and he wants to not only show off his wealth but to socialize with his friends, family, and fellow citizens. He says:
His servant unwittingly invites some of the Montague boys:
Lady Montague also wants Juliet to meet Paris so that they may wed. Although Juliet's father thinks she is too young to marry, her mother uses the feast for match-making:
Shakespeare uses the masque as a metaphorical and symbolic place for his two lovers to meet. Masques are formal games in which the guests try to figure out who's who. In this way, it's a great place to meet a lover, maybe even a husband, but also your great enemy.
The play itself doesn't have Lord Capulet giving any reason except that he tells Paris "tonight I hold an old accustomed feast." It seems like a party just for party's sake.
The event does serve several purposes though. Capulet further explains to Paris who is wanting to marry Juliet that this would give Paris an opportunity to woo her or flirt with her as well as compare her to Verona's other beauties making sure that he indeed likes Juliet above others.
During the party, it also serves the purpose of letting Romeo and Juliet meet and building Tybalt's rage over Romeo's presence. These are very specific inciting incidents that much action later on in the story hinges on.